{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "3NwHunx5EjGp" }, "source": [ "# 5장 - 차원 축소를 사용한 데이터 압축" ] }, { "cell_type": "markdown", "metadata": { "id": "1_84RVKeEjGl" }, "source": [ "# 머신 러닝 교과서 3판" ] }, { "cell_type": "markdown", "metadata": { "id": "vUWZwyuKEjGp" }, "source": [ "**아래 링크를 통해 이 노트북을 주피터 노트북 뷰어(nbviewer.jupyter.org)로 보거나 구글 코랩(colab.research.google.com)에서 실행할 수 있습니다.**\n", "\n", "\n", " \n", " \n", "
\n", " 주피터 노트북 뷰어로 보기\n", " \n", " 구글 코랩(Colab)에서 실행하기\n", "
" ] }, { "cell_type": "markdown", "metadata": { "id": "BKL9EjK2EjGq" }, "source": [ "### 목차" ] }, { "cell_type": "markdown", "metadata": { "id": "zgkdYleMEjGq" }, "source": [ "- 주성분 분석을 통한 비지도 차원 축소\n", " - 주성분 분석의 주요 단계\n", " - 주성분 추출 단계\n", " - 총분산과 설명된 분산\n", " - 특성 변환\n", " - 사이킷런의 주성분 분석\n", "- 선형 판별 분석을 통한 지도 방식의 데이터 압축\n", " - 주성분 분석 vs 선형 판별 분석\n", " - 선형 판별 분석의 내부 동작 방식\n", " - 산포 행렬 계산\n", " - 새로운 특성 부분 공간을 위해 선형 판별 벡터 선택\n", " - 새로운 특성 공간으로 샘플 투영\n", " - 사이킷런의 LDA\n", "- 커널 PCA를 사용하여 비선형 매핑\n", " - 커널 함수와 커널 트릭\n", " - 파이썬으로 커널 PCA 구현\n", " - 예제 1 - 반달 모양 구분하기\n", " - 예제 2 - 동심원 분리하기\n", " - 새로운 데이터 포인트 투영\n", " - 사이킷런의 커널 PCA\n", "- 요약" ] }, { "cell_type": "markdown", "metadata": { "id": "zdfxyBijEjGq" }, "source": [ "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:28.820829Z", "iopub.status.busy": "2021-10-23T05:55:28.819949Z", "iopub.status.idle": "2021-10-23T05:55:28.823060Z", "shell.execute_reply": "2021-10-23T05:55:28.822150Z" }, "id": "nSf82FR-EjGr" }, "outputs": [], "source": [ "from IPython.display import Image" ] }, { "cell_type": "markdown", "metadata": { "id": "8_p4a2DdEjGr" }, "source": [ "# 5.1 주성분 분석을 통한 비지도 차원 축소" ] }, { "cell_type": "markdown", "metadata": { "id": "aMwZJrGQEjGr" }, "source": [ "## 5.1.1 주성분 분석의 주요 단계" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 387 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:28.835839Z", "iopub.status.busy": "2021-10-23T05:55:28.834819Z", "iopub.status.idle": "2021-10-23T05:55:28.839717Z", "shell.execute_reply": "2021-10-23T05:55:28.838955Z" }, "id": "MiqBHvISEjGr", "outputId": "564e94dc-dfe8-4bdd-8a4d-54c5da84d5bb" }, "outputs": [ { "output_type": "execute_result", "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "execution_count": 2 } ], "source": [ "Image(url='https://git.io/JtsvW', width=400)" ] }, { "cell_type": "markdown", "metadata": { "id": "QNt8vZP229rW" }, "source": [ "$\\boldsymbol{x}\\boldsymbol{W}=\\boldsymbol{z}$" ] }, { "cell_type": "markdown", "metadata": { "id": "ZT7XQlR5EjGs" }, "source": [ "## 5.1.2 주성분 추출 단계" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 271 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:28.847062Z", "iopub.status.busy": "2021-10-23T05:55:28.846167Z", "iopub.status.idle": "2021-10-23T05:55:29.762319Z", "shell.execute_reply": "2021-10-23T05:55:29.761696Z" }, "id": "Fod9IR5ZEjGs", "outputId": "7f21c063-91e5-46bf-a1f5-2c68752b2909" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " Class label Alcohol Malic acid Ash Alcalinity of ash Magnesium \\\n", "0 1 14.23 1.71 2.43 15.6 127 \n", "1 1 13.20 1.78 2.14 11.2 100 \n", "2 1 13.16 2.36 2.67 18.6 101 \n", "3 1 14.37 1.95 2.50 16.8 113 \n", "4 1 13.24 2.59 2.87 21.0 118 \n", "\n", " Total phenols Flavanoids Nonflavanoid phenols Proanthocyanins \\\n", "0 2.80 3.06 0.28 2.29 \n", "1 2.65 2.76 0.26 1.28 \n", "2 2.80 3.24 0.30 2.81 \n", "3 3.85 3.49 0.24 2.18 \n", "4 2.80 2.69 0.39 1.82 \n", "\n", " Color intensity Hue OD280/OD315 of diluted wines Proline \n", "0 5.64 1.04 3.92 1065 \n", "1 4.38 1.05 3.40 1050 \n", "2 5.68 1.03 3.17 1185 \n", "3 7.80 0.86 3.45 1480 \n", "4 4.32 1.04 2.93 735 " ], "text/html": [ "\n", "
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Class labelAlcoholMalic acidAshAlcalinity of ashMagnesiumTotal phenolsFlavanoidsNonflavanoid phenolsProanthocyaninsColor intensityHueOD280/OD315 of diluted winesProline
0114.231.712.4315.61272.803.060.282.295.641.043.921065
1113.201.782.1411.21002.652.760.261.284.381.053.401050
2113.162.362.6718.61012.803.240.302.815.681.033.171185
3114.371.952.5016.81133.853.490.242.187.800.863.451480
4113.242.592.8721.01182.802.690.391.824.321.042.93735
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\n" ], "application/vnd.google.colaboratory.intrinsic+json": { "type": "dataframe", "variable_name": "df_wine", "summary": "{\n \"name\": \"df_wine\",\n \"rows\": 178,\n \"fields\": [\n {\n \"column\": \"Class label\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0,\n \"min\": 1,\n \"max\": 3,\n \"num_unique_values\": 3,\n \"samples\": [\n 1,\n 2,\n 3\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Alcohol\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0.8118265380058577,\n \"min\": 11.03,\n \"max\": 14.83,\n \"num_unique_values\": 126,\n \"samples\": [\n 11.62,\n 13.64,\n 13.69\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Malic acid\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 1.1171460976144627,\n \"min\": 0.74,\n \"max\": 5.8,\n \"num_unique_values\": 133,\n \"samples\": [\n 1.21,\n 2.83,\n 1.8\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Ash\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0.2743440090608148,\n \"min\": 1.36,\n \"max\": 3.23,\n \"num_unique_values\": 79,\n \"samples\": [\n 2.31,\n 2.43,\n 2.52\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Alcalinity of ash\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 3.3395637671735052,\n \"min\": 10.6,\n \"max\": 30.0,\n \"num_unique_values\": 63,\n \"samples\": [\n 25.5,\n 28.5,\n 15.6\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Magnesium\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 14,\n \"min\": 70,\n \"max\": 162,\n \"num_unique_values\": 53,\n \"samples\": [\n 126,\n 85,\n 162\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Total phenols\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0.6258510488339891,\n \"min\": 0.98,\n \"max\": 3.88,\n \"num_unique_values\": 97,\n \"samples\": [\n 1.68,\n 2.11,\n 1.35\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Flavanoids\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0.9988586850169465,\n \"min\": 0.34,\n \"max\": 5.08,\n \"num_unique_values\": 132,\n \"samples\": [\n 3.18,\n 2.5,\n 3.17\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Nonflavanoid phenols\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0.12445334029667939,\n \"min\": 0.13,\n \"max\": 0.66,\n \"num_unique_values\": 39,\n \"samples\": [\n 0.58,\n 0.41,\n 0.39\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Proanthocyanins\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0.5723588626747611,\n \"min\": 0.41,\n \"max\": 3.58,\n \"num_unique_values\": 101,\n \"samples\": [\n 0.75,\n 1.77,\n 1.42\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Color intensity\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 2.318285871822413,\n \"min\": 1.28,\n \"max\": 13.0,\n \"num_unique_values\": 132,\n \"samples\": [\n 2.95,\n 3.3,\n 5.1\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Hue\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0.22857156582982338,\n \"min\": 0.48,\n \"max\": 1.71,\n \"num_unique_values\": 78,\n \"samples\": [\n 1.22,\n 1.04,\n 1.45\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"OD280/OD315 of diluted wines\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 0.7099904287650505,\n \"min\": 1.27,\n \"max\": 4.0,\n \"num_unique_values\": 122,\n \"samples\": [\n 4.0,\n 1.82,\n 1.59\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Proline\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": 314,\n \"min\": 278,\n \"max\": 1680,\n \"num_unique_values\": 121,\n \"samples\": [\n 1375,\n 1270,\n 735\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n }\n ]\n}" } }, "metadata": {}, "execution_count": 3 } ], "source": [ "import pandas as pd\n", "\n", "df_wine = pd.read_csv('https://archive.ics.uci.edu/ml/'\n", " 'machine-learning-databases/wine/wine.data',\n", " header=None)\n", "\n", "# UCI 머신 러닝 저장소에서 Wine 데이터셋을 다운로드할 수 없을 때\n", "# 다음 주석을 해제하고 로컬 경로에서 데이터셋을 적재하세요:\n", "\n", "# df_wine = pd.read_csv('wine.data', header=None)\n", "\n", "df_wine.columns = ['Class label', 'Alcohol', 'Malic acid', 'Ash',\n", " 'Alcalinity of ash', 'Magnesium', 'Total phenols',\n", " 'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins',\n", " 'Color intensity', 'Hue',\n", " 'OD280/OD315 of diluted wines', 'Proline']\n", "\n", "df_wine.head()" ] }, { "cell_type": "markdown", "metadata": { "id": "d1bnkLDTEjGt" }, "source": [ "70%는 훈련 세트로 30%는 테스트 세트로 나눕니다." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:29.770202Z", "iopub.status.busy": "2021-10-23T05:55:29.769434Z", "iopub.status.idle": "2021-10-23T05:55:30.169388Z", "shell.execute_reply": "2021-10-23T05:55:30.168720Z" }, "id": "EA5J2XWMEjGt" }, "outputs": [], "source": [ "from sklearn.model_selection import train_test_split\n", "\n", "X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values\n", "\n", "X_train, X_test, y_train, y_test = \\\n", " train_test_split(X, y, test_size=0.3,\n", " stratify=y,\n", " random_state=0)" ] }, { "cell_type": "markdown", "metadata": { "id": "hMMoofvmEjGt" }, "source": [ "데이터를 표준화합니다." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:30.175564Z", "iopub.status.busy": "2021-10-23T05:55:30.174871Z", "iopub.status.idle": "2021-10-23T05:55:30.178647Z", "shell.execute_reply": "2021-10-23T05:55:30.177919Z" }, "id": "AqQpTbYaEjGt" }, "outputs": [], "source": [ "from sklearn.preprocessing import StandardScaler\n", "\n", "sc = StandardScaler()\n", "X_train_std = sc.fit_transform(X_train)\n", "X_test_std = sc.transform(X_test)" ] }, { "cell_type": "markdown", "metadata": { "id": "edcNE-glEjGt" }, "source": [ "---\n", "\n", "**노트**\n", "\n", "`X_test_std = sc.fit_transform(X_test)` 대신에 `X_test_std = sc.transform(X_test)`를 사용했습니다. 이 경우에 테스트 데이터셋의 평균과 표준편차가 훈련 데이터셋과 매우 비슷하기 때문에 큰 차이가 없습니다. 하지만 3장에서 보았듯이 데이터를 변환할 때 훈련 데이터셋에서 학습한 파라미터를 재사용하는 것이 올바른 방법입니다. 테스트 데이터셋은 \"새로운 본 적 없는\" 데이터를 의미하기 때문입니다.\n", "\n", "초기에 `fit_transform(X_test)`를 사용했는데 이것은 모델 훈련에서 얻은 파라미터를 재사용하여 새로운 데이터를 표준화하지 않는 일반적인 실수입니다. 왜 이것이 문제가 되는지 간단한 예를 살펴 보겠습니다.\n", "\n", "훈련 데이터셋에 1개의 특성(\"길이\")을 가진 샘플 3개가 들어 있다고 가정해 보죠:\n", "\n", "- train_1: 10 cm -> class_2\n", "- train_2: 20 cm -> class_2\n", "- train_3: 30 cm -> class_1\n", "\n", "mean: 20, std.: 8.2\n", "\n", "표준화를 한 후에 변환된 특성 값은 다음과 같습니다:\n", "\n", "- train_std_1: -1.22 -> class_2\n", "- train_std_2: 0 -> class_2\n", "- train_std_3: 1.22 -> class_1\n", "\n", "그다음 표준화된 길이가 0.6보다 작은 샘플을 class_2로 분류한다고 가정해 보죠(그 외에는 class_1). 지금까지는 좋습니다. 이제 레이블이 없는 3개의 포인트를 분류한다고 가정해 보죠:\n", "\n", "- new_4: 5 cm -> class ?\n", "- new_5: 6 cm -> class ?\n", "- new_6: 7 cm -> class ?\n", "\n", "훈련 데이터셋에 있는 표준화되기 전의 \"길이\" 값과 비교해 보면 직관적으로 이 샘플들은 class_2로 보입니다. 하지만 훈련 데이터셋에서 했던 것처럼 평균과 표준편차를 다시 계산하여 표준화하면 아마도 분류기가 샘플 4번과 5번만 class_2로 분류할 것입니다.\n", "\n", "- new_std_4: -1.22 -> class 2\n", "- new_std_5: 0 -> class 2\n", "- new_std_6: 1.22 -> class 1\n", "\n", "하지만 훈련 데이터셋의 표준화에 사용했던 파라미터를 사용하면 다음과 같은 값을 얻습니다:\n", "\n", "- example5: -1.84 -> class 2\n", "- example6: -1.71 -> class 2\n", "- example7: -1.59 -> class 2\n", "\n", "5 cm, 6 cm, 7 cm는 훈련 데이터셋에 있는 어떤 것보다도 작습니다. 따라서 훈련 데이터셋을 표준화한 값보다도 훨씬 작은 값으로 표준화되어야 합니다.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": { "id": "cKUsKeCWEjGu" }, "source": [ "공분산 행렬의 고윳값 분해" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:30.184644Z", "iopub.status.busy": "2021-10-23T05:55:30.183924Z", "iopub.status.idle": "2021-10-23T05:55:30.189344Z", "shell.execute_reply": "2021-10-23T05:55:30.188641Z" }, "id": "C1p8pEbVEjGu", "outputId": "039660a7-55f2-4961-a19f-4e57af238413" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "\n", "고윳값 \n", "[4.84274532 2.41602459 1.54845825 0.96120438 0.84166161 0.6620634\n", " 0.51828472 0.34650377 0.3131368 0.10754642 0.21357215 0.15362835\n", " 0.1808613 ]\n" ] } ], "source": [ "import numpy as np\n", "cov_mat = np.cov(X_train_std.T)\n", "eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)\n", "\n", "print('\\n고윳값 \\n%s' % eigen_vals)" ] }, { "cell_type": "markdown", "metadata": { "id": "sWQdxyAFEjGu" }, "source": [ "**노트**:\n", "\n", "위에서 [`numpy.linalg.eig`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html) 함수를 사용해 대칭 공분산 행렬을 고윳값과 고유벡터로 분해했습니다.\n", "\n", "
>>> eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)
\n", "\n", "이것이 잘못된 것은 아니지만 최적은 아닙니다. [에르미트(Hermetian) 행렬](https://en.wikipedia.org/wiki/Hermitian_matrix)를 위해서 설계된 [`numpy.linalg.eigh`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eigh.html)를 사용하는 것이 더 좋습니다. 이 함수는 항상 실수 고윳값을 반환합니다. 수치적으로 약간 덜 안정적인 `np.linalg.eig`는 비대칭 정방행렬을 분해할 수 있지만 어떤 경우에 복소수 고윳값을 반환할 수 있습니다." ] }, { "cell_type": "markdown", "metadata": { "id": "v5uHAyy7EjGu" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "6Ziezfe6EjGu" }, "source": [ "## 5.1.3 총분산과 설명된 분산" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:30.195398Z", "iopub.status.busy": "2021-10-23T05:55:30.194539Z", "iopub.status.idle": "2021-10-23T05:55:30.197315Z", "shell.execute_reply": "2021-10-23T05:55:30.196587Z" }, "id": "VrKFIi3ZEjGu" }, "outputs": [], "source": [ "tot = sum(eigen_vals)\n", "var_exp = [(i / tot) for i in sorted(eigen_vals, reverse=True)]\n", "cum_var_exp = np.cumsum(var_exp)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:30.204262Z", "iopub.status.busy": "2021-10-23T05:55:30.203303Z", "iopub.status.idle": "2021-10-23T05:55:30.611363Z", "shell.execute_reply": "2021-10-23T05:55:30.611911Z" }, "id": "iQmRwT46EjGu", "outputId": "e34ab7cd-5f7c-4d5d-ec1a-31d4cc6ac3c8" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "\n", "plt.bar(range(1, 14), var_exp, alpha=0.5, align='center',\n", " label='Individual explained variance')\n", "plt.step(range(1, 14), cum_var_exp, where='mid',\n", " label='Cumulative explained variance')\n", "plt.ylabel('Explained variance ratio')\n", "plt.xlabel('Principal component index')\n", "plt.legend(loc='best')\n", "plt.tight_layout()\n", "# plt.savefig('images/05_02.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "-03gKjrPEjGv" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "KWhLM7GoEjGv" }, "source": [ "## 5.1.4 특성 변환" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:30.619803Z", "iopub.status.busy": "2021-10-23T05:55:30.618811Z", "iopub.status.idle": "2021-10-23T05:55:30.622004Z", "shell.execute_reply": "2021-10-23T05:55:30.620902Z" }, "id": "1F3O3rx-EjGv" }, "outputs": [], "source": [ "# (고윳값, 고유벡터) 튜플의 리스트를 만듭니다\n", "eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:, i])\n", " for i in range(len(eigen_vals))]\n", "\n", "# 높은 값에서 낮은 값으로 (고윳값, 고유벡터) 튜플을 정렬합니다\n", "eigen_pairs.sort(key=lambda k: k[0], reverse=True)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:30.628402Z", "iopub.status.busy": "2021-10-23T05:55:30.627677Z", "iopub.status.idle": "2021-10-23T05:55:30.631055Z", "shell.execute_reply": "2021-10-23T05:55:30.630384Z" }, "id": "bvcxCj6REjGv", "outputId": "d37ba7d7-def6-4ee1-eecc-0f6850fd1550" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "투영 행렬 W:\n", " [[-0.13724218 0.50303478]\n", " [ 0.24724326 0.16487119]\n", " [-0.02545159 0.24456476]\n", " [ 0.20694508 -0.11352904]\n", " [-0.15436582 0.28974518]\n", " [-0.39376952 0.05080104]\n", " [-0.41735106 -0.02287338]\n", " [ 0.30572896 0.09048885]\n", " [-0.30668347 0.00835233]\n", " [ 0.07554066 0.54977581]\n", " [-0.32613263 -0.20716433]\n", " [-0.36861022 -0.24902536]\n", " [-0.29669651 0.38022942]]\n" ] } ], "source": [ "w = np.hstack((eigen_pairs[0][1][:, np.newaxis],\n", " eigen_pairs[1][1][:, np.newaxis]))\n", "print('투영 행렬 W:\\n', w)" ] }, { "cell_type": "markdown", "metadata": { "id": "tuaO_K8cEjGv" }, "source": [ "**노트:**\n", "\n", "사용하는 Numpy와 LAPACK 버전에 따라 행렬 W의 부호가 바뀔 수 있습니다. 이는 문제가 아닙니다. $v$가 행렬 $\\Sigma$의 고유벡터라면 다음을 얻을 수 있습니다.\n", "\n", "$$\\Sigma v = \\lambda v,$$\n", "\n", "여기에서 $\\lambda$는 고윳값입니다.\n", "\n", "$$\\Sigma \\cdot (-v) = -\\Sigma v = -\\lambda v = \\lambda \\cdot (-v).$$이기 때문에 $-v$도 동일한 고윳값을 가진 고유벡터입니다." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:30.636732Z", "iopub.status.busy": "2021-10-23T05:55:30.636062Z", "iopub.status.idle": "2021-10-23T05:55:30.640470Z", "shell.execute_reply": "2021-10-23T05:55:30.639549Z" }, "id": "BvUbmNzoEjGv", "outputId": "e98dd581-a5cd-46cd-d63a-0ee656852384" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([2.38299011, 0.45458499])" ] }, "metadata": {}, "execution_count": 11 } ], "source": [ "X_train_std[0].dot(w)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:30.728896Z", "iopub.status.busy": "2021-10-23T05:55:30.728171Z", "iopub.status.idle": "2021-10-23T05:55:30.873997Z", "shell.execute_reply": "2021-10-23T05:55:30.874920Z" }, "id": "KxFGjRojEjGw", "outputId": "67fabe11-4092-4a8e-8d6e-ccc8aa3b99dd" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ], "source": [ "X_train_pca = X_train_std.dot(w)\n", "colors = ['r', 'b', 'g']\n", "markers = ['s', 'x', 'o']\n", "\n", "for l, c, m in zip(np.unique(y_train), colors, markers):\n", " plt.scatter(X_train_pca[y_train == l, 0],\n", " X_train_pca[y_train == l, 1],\n", " c=c, label=l, marker=m)\n", "\n", "plt.xlabel('PC 1')\n", "plt.ylabel('PC 2')\n", "plt.legend(loc='lower left')\n", "plt.tight_layout()\n", "# plt.savefig('images/05_03.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "5GFN87VuEjGw" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "M_KY060EEjGw" }, "source": [ "## 5.1.5 사이킷런의 주성분 분석" ] }, { "cell_type": "markdown", "metadata": { "id": "f5vqSfXIEjGw" }, "source": [ "**노트**\n", "\n", "이어지는 네 개의 셀은 책에 없는 내용입니다. 사이킷런에서 앞의 PCA 구현 결과를 재현하기 위해 추가했습니다:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:30.883098Z", "iopub.status.busy": "2021-10-23T05:55:30.881755Z", "iopub.status.idle": "2021-10-23T05:55:30.908844Z", "shell.execute_reply": "2021-10-23T05:55:30.908035Z" }, "id": "SrIDFuzvEjGw", "outputId": "22066e5e-7163-4815-ee65-5aa1105cb637" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([0.36951469, 0.18434927, 0.11815159, 0.07334252, 0.06422108,\n", " 0.05051724, 0.03954654, 0.02643918, 0.02389319, 0.01629614,\n", " 0.01380021, 0.01172226, 0.00820609])" ] }, "metadata": {}, "execution_count": 13 } ], "source": [ "from sklearn.decomposition import PCA\n", "\n", "pca = PCA()\n", "X_train_pca = pca.fit_transform(X_train_std)\n", "pca.explained_variance_ratio_" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 449 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:30.946201Z", "iopub.status.busy": "2021-10-23T05:55:30.941740Z", "iopub.status.idle": "2021-10-23T05:55:31.092214Z", "shell.execute_reply": "2021-10-23T05:55:31.091400Z" }, "id": "Bdlq_npKEjGw", "outputId": "5cbe1079-c919-4a17-a1b1-01c3704d2ca0" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "plt.bar(range(1, 14), pca.explained_variance_ratio_, alpha=0.5, align='center')\n", "plt.step(range(1, 14), np.cumsum(pca.explained_variance_ratio_), where='mid')\n", "plt.ylabel('Explained variance ratio')\n", "plt.xlabel('Principal components')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:31.100672Z", "iopub.status.busy": "2021-10-23T05:55:31.099825Z", "iopub.status.idle": "2021-10-23T05:55:31.104806Z", "shell.execute_reply": "2021-10-23T05:55:31.103857Z" }, "id": "siTpt9sXEjGx" }, "outputs": [], "source": [ "pca = PCA(n_components=2)\n", "X_train_pca = pca.fit_transform(X_train_std)\n", "X_test_pca = pca.transform(X_test_std)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 449 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.164901Z", "iopub.status.busy": "2021-10-23T05:55:31.154877Z", "iopub.status.idle": "2021-10-23T05:55:31.264136Z", "shell.execute_reply": "2021-10-23T05:55:31.263310Z" }, "id": "xc8dWtb5EjGx", "outputId": "74978a0d-81d9-4ee4-e472-94f21a0c0c62" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "plt.scatter(X_train_pca[:, 0], X_train_pca[:, 1])\n", "plt.xlabel('PC 1')\n", "plt.ylabel('PC 2')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:31.276907Z", "iopub.status.busy": "2021-10-23T05:55:31.276038Z", "iopub.status.idle": "2021-10-23T05:55:31.280568Z", "shell.execute_reply": "2021-10-23T05:55:31.279061Z" }, "id": "audMeNXmEjGx" }, "outputs": [], "source": [ "from matplotlib.colors import ListedColormap\n", "\n", "def plot_decision_regions(X, y, classifier, resolution=0.02):\n", "\n", " # 마커와 컬러맵을 준비합니다\n", " markers = ('s', 'x', 'o', '^', 'v')\n", " colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')\n", " cmap = ListedColormap(colors[:len(np.unique(y))])\n", "\n", " # 결정 경계를 그립니다\n", " x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n", " x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n", " xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),\n", " np.arange(x2_min, x2_max, resolution))\n", " Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)\n", " Z = Z.reshape(xx1.shape)\n", " plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)\n", " plt.xlim(xx1.min(), xx1.max())\n", " plt.ylim(xx2.min(), xx2.max())\n", "\n", " # 클래스별로 샘플을 그립니다\n", " for idx, cl in enumerate(np.unique(y)):\n", " plt.scatter(x=X[y == cl, 0],\n", " y=X[y == cl, 1],\n", " alpha=0.6,\n", " color=cmap(idx),\n", " edgecolor=None if idx==1 else 'black',\n", " marker=markers[idx],\n", " label=cl)" ] }, { "cell_type": "markdown", "metadata": { "id": "7beQNiiFEjGx" }, "source": [ "처음 두 개의 주성분을 사용하여 로지스틱 회귀 분류기를 훈련합니다." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:31.289418Z", "iopub.status.busy": "2021-10-23T05:55:31.287927Z", "iopub.status.idle": "2021-10-23T05:55:31.306778Z", "shell.execute_reply": "2021-10-23T05:55:31.305830Z" }, "id": "3E1HW9RlEjGy" }, "outputs": [], "source": [ "from sklearn.linear_model import LogisticRegression\n", "\n", "pca = PCA(n_components=2)\n", "X_train_pca = pca.fit_transform(X_train_std)\n", "X_test_pca = pca.transform(X_test_std)\n", "\n", "lr = LogisticRegression(random_state=1)\n", "lr = lr.fit(X_train_pca, y_train)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.314386Z", "iopub.status.busy": "2021-10-23T05:55:31.313626Z", "iopub.status.idle": "2021-10-23T05:55:31.637730Z", "shell.execute_reply": "2021-10-23T05:55:31.638352Z" }, "id": "KljC04RyEjGy", "outputId": "6104ff9f-10d0-4898-da45-1db036f09097", "scrolled": true }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ], "source": [ "plot_decision_regions(X_train_pca, y_train, classifier=lr)\n", "plt.xlabel('PC 1')\n", "plt.ylabel('PC 2')\n", "plt.legend(loc='lower left')\n", "plt.tight_layout()\n", "# plt.savefig('images/05_04.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.645785Z", "iopub.status.busy": "2021-10-23T05:55:31.644587Z", "iopub.status.idle": "2021-10-23T05:55:31.915219Z", "shell.execute_reply": "2021-10-23T05:55:31.916134Z" }, "id": "Q190-SbDEjGy", "outputId": "d1c1858c-0f0e-4ddd-e2cb-2fd227a17ce6" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "plot_decision_regions(X_test_pca, y_test, classifier=lr)\n", "plt.xlabel('PC 1')\n", "plt.ylabel('PC 2')\n", "plt.legend(loc='lower left')\n", "plt.tight_layout()\n", "# plt.savefig('images/05_05.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.924332Z", "iopub.status.busy": "2021-10-23T05:55:31.923574Z", "iopub.status.idle": "2021-10-23T05:55:31.928195Z", "shell.execute_reply": "2021-10-23T05:55:31.927426Z" }, "id": "nYN0rAe2EjGy", "outputId": "4abbc717-caec-4e04-b0f7-c88125c68edf" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([0.36951469, 0.18434927, 0.11815159, 0.07334252, 0.06422108,\n", " 0.05051724, 0.03954654, 0.02643918, 0.02389319, 0.01629614,\n", " 0.01380021, 0.01172226, 0.00820609])" ] }, "metadata": {}, "execution_count": 21 } ], "source": [ "pca = PCA(n_components=None)\n", "X_train_pca = pca.fit_transform(X_train_std)\n", "pca.explained_variance_ratio_" ] }, { "cell_type": "markdown", "metadata": { "id": "bwBzhFTHEjGy" }, "source": [ "`n_components`에 (0, 1) 사이 실수를 입력하면 설명된 분산의 비율을 나타냅니다. 이 비율을 달성하기 위해 필요한 주성분 개수를 선택합니다." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.934787Z", "iopub.status.busy": "2021-10-23T05:55:31.934096Z", "iopub.status.idle": "2021-10-23T05:55:31.937151Z", "shell.execute_reply": "2021-10-23T05:55:31.937632Z" }, "id": "hAudlTvIEjGz", "outputId": "5840cbd0-9504-476d-ffc3-724da7b9f1d7" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "주성분 개수: 10\n", "설명된 분산 비율: 0.966271440655874\n" ] } ], "source": [ "pca = PCA(n_components=0.95)\n", "pca.fit(X_train_std)\n", "print('주성분 개수:', pca.n_components_)\n", "print('설명된 분산 비율:', np.sum(pca.explained_variance_ratio_))" ] }, { "cell_type": "markdown", "metadata": { "id": "vVqwwK7TEjGz" }, "source": [ "`n_components='mle'`로 지정하면 토마스 민카(Thomas Minka)가 제안한 차원 선택 방식을 사용합니다(Minka, T. P. “Automatic choice of dimensionality for PCA”. In NIPS, pp. 598-604)." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.945593Z", "iopub.status.busy": "2021-10-23T05:55:31.944785Z", "iopub.status.idle": "2021-10-23T05:55:31.948514Z", "shell.execute_reply": "2021-10-23T05:55:31.947694Z" }, "id": "aq0ejdBgEjGz", "outputId": "5255d1b4-2921-4eea-8fe8-68cdbecc20bf" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "주성분 개수: 9\n", "설명된 분산 비율: 0.949975302918623\n" ] } ], "source": [ "pca = PCA(n_components='mle')\n", "pca.fit(X_train_std)\n", "print('주성분 개수:', pca.n_components_)\n", "print('설명된 분산 비율:', np.sum(pca.explained_variance_ratio_))" ] }, { "cell_type": "markdown", "metadata": { "id": "6AKyi0DfEjGz" }, "source": [ "`PCA`의 가장 큰 제약 사항 중 하나는 배치로만 실행되기 때문에 대용량 데이터셋을 처리하려면 많은 메모리가 필요합니다. `IncrementalPCA`를 사용하면 데이터셋의 일부를 사용하여 반복적으로 훈련할 수 있습니다.\n", "\n", "`partial_fit()` 메서드는 네트워크나 로컬 파일 시스템으로부터 조금씩 데이터를 받아와 훈련할 수 있습니다. `fit()` 메서드는 `numpy.memmap`을 사용하여 로컬 파일로부터 데이터를 조금씩 읽어 올 수 있습니다. 한 번에 읽어 올 데이터 크기는 `IncrementalPCA` 클래스의 `batch_size`로 지정합니다. 기본값은 특성 개수의 5배입니다.\n", "\n", "`IncrementalPCA`의 `n_components` 매개변수는 정수 값만 입력할 수 있습니다. 다음은 `partial_fit()` 메서드를 사용하여 앞의 `PCA`로 찾은 주성분의 결과와 비교하는 간단한 예입니다." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.959001Z", "iopub.status.busy": "2021-10-23T05:55:31.958249Z", "iopub.status.idle": "2021-10-23T05:55:31.962449Z", "shell.execute_reply": "2021-10-23T05:55:31.961845Z" }, "id": "1DcUF_ySEjGz", "outputId": "c688aa2b-8ddd-4bf8-b1b8-bdeeaa69a2ee" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "주성분 개수: 9\n", "설명된 분산 비율: 0.9478392700446645\n" ] } ], "source": [ "from sklearn.decomposition import IncrementalPCA\n", "\n", "ipca = IncrementalPCA(n_components=9)\n", "for batch in range(len(X_train_std)//25+1):\n", " X_batch = X_train_std[batch*25:(batch+1)*25]\n", " ipca.partial_fit(X_batch)\n", "\n", "print('주성분 개수:', ipca.n_components_)\n", "print('설명된 분산 비율:', np.sum(ipca.explained_variance_ratio_))" ] }, { "cell_type": "markdown", "metadata": { "id": "A75qiYlzEjGz" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "vrV-l0OtEjG0" }, "source": [ "# 5.2 선형 판별 분석을 통한 지도방식의 데이터 압축" ] }, { "cell_type": "markdown", "metadata": { "id": "rZ1yv2kdEjG0" }, "source": [ "## 5.2.1 주성분 분석 vs 선형 판별 분석" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 367 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.969437Z", "iopub.status.busy": "2021-10-23T05:55:31.968722Z", "iopub.status.idle": "2021-10-23T05:55:31.972530Z", "shell.execute_reply": "2021-10-23T05:55:31.971797Z" }, "id": "BwDzcypZEjG0", "outputId": "e0e038c3-936a-4d07-fdc8-c1c007cc1026", "scrolled": true }, "outputs": [ { "output_type": "execute_result", "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "execution_count": 25 } ], "source": [ "Image(url='https://git.io/Jtsv8', width=400)" ] }, { "cell_type": "markdown", "metadata": { "id": "dqNYW_1JEjG0" }, "source": [ "## 5.2.2 선형 판별 분석의 내부 동작 방식" ] }, { "cell_type": "markdown", "metadata": { "id": "vf61UaXf29rd" }, "source": [ "1. 표준화 전처리\n", "2. 클래스별 평균 벡터\n", "3. 클래스 간 산포 행렬 $\\boldsymbol S_B$, 클래스 내 산포 행렬 $\\boldsymbol S_W$\n", "4. $\\boldsymbol S_W^{-1}\\boldsymbol S_B$ 행렬의 고윳값\n", "5. 고윳값을 내림차순 정렬\n", "6. 고윳값이 가장 큰 k개의 고유 벡터 선택\n", "7. 고유 벡터로 만든 변환 행렬로 데이터셋 투영" ] }, { "cell_type": "markdown", "metadata": { "id": "73eS4jTgEjG0" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "swEC9tzxEjG0" }, "source": [ "## 5.2.3 산포 행렬 계산" ] }, { "cell_type": "markdown", "metadata": { "id": "v_bJB6JaEjG0" }, "source": [ "각 클래스에 대한 평균 벡터를 계산합니다:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.980804Z", "iopub.status.busy": "2021-10-23T05:55:31.980127Z", "iopub.status.idle": "2021-10-23T05:55:31.984121Z", "shell.execute_reply": "2021-10-23T05:55:31.984579Z" }, "id": "3LeJnkK_EjG0", "outputId": "5992452a-fff7-4ce1-f11d-865a6d0ff7bb" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "MV 1: [ 0.9066 -0.3497 0.3201 -0.7189 0.5056 0.8807 0.9589 -0.5516 0.5416\n", " 0.2338 0.5897 0.6563 1.2075]\n", "\n", "MV 2: [-0.8749 -0.2848 -0.3735 0.3157 -0.3848 -0.0433 0.0635 -0.0946 0.0703\n", " -0.8286 0.3144 0.3608 -0.7253]\n", "\n", "MV 3: [ 0.1992 0.866 0.1682 0.4148 -0.0451 -1.0286 -1.2876 0.8287 -0.7795\n", " 0.9649 -1.209 -1.3622 -0.4013]\n", "\n" ] } ], "source": [ "np.set_printoptions(precision=4)\n", "\n", "mean_vecs = []\n", "for label in range(1, 4):\n", " mean_vecs.append(np.mean(X_train_std[y_train == label], axis=0))\n", " print('MV %s: %s\\n' % (label, mean_vecs[label - 1]))" ] }, { "cell_type": "markdown", "metadata": { "id": "c-nwJBF5EjG1" }, "source": [ "클래스 내 산포 행렬을 계산합니다:\n", "\n", "$\\boldsymbol S_W=\\sum_{i=1}^c \\boldsymbol S_i$\n", "\n", "$\\boldsymbol S_i=\\sum_{x\\in D_i}(\\boldsymbol x-\\boldsymbol m_i)^T(\\boldsymbol x-\\boldsymbol m_i)$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:31.992949Z", "iopub.status.busy": "2021-10-23T05:55:31.992029Z", "iopub.status.idle": "2021-10-23T05:55:31.997162Z", "shell.execute_reply": "2021-10-23T05:55:31.996380Z" }, "id": "TRb957tiEjG1", "outputId": "83e19c5b-ddd4-40e0-a54f-7d3010832d1b", "scrolled": true }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "클래스 내의 산포 행렬: 13x13\n" ] } ], "source": [ "d = 13 # 특성의 수\n", "S_W = np.zeros((d, d))\n", "for label, mv in zip(range(1, 4), mean_vecs):\n", " class_scatter = np.zeros((d, d)) # 각 클래스에 대한 산포 행렬\n", " for row in X_train_std[y_train == label]:\n", " row, mv = row.reshape(d, 1), mv.reshape(d, 1) # 열 벡터를 만듭니다\n", " class_scatter += (row - mv).dot((row - mv).T)\n", " S_W += class_scatter # 클래스 산포 행렬을 더합니다\n", "\n", "print('클래스 내의 산포 행렬: %sx%s' % (S_W.shape[0], S_W.shape[1]))" ] }, { "cell_type": "markdown", "metadata": { "id": "Dalrtl0AEjG1" }, "source": [ "클래스가 균일하게 분포되어 있지 않기 때문에 공분산 행렬을 사용하는 것이 더 낫습니다:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:32.002902Z", "iopub.status.busy": "2021-10-23T05:55:32.002108Z", "iopub.status.idle": "2021-10-23T05:55:32.005311Z", "shell.execute_reply": "2021-10-23T05:55:32.005845Z" }, "id": "2xb6G0WKEjG1", "outputId": "9d0c87cf-2466-4f80-9d43-0ff5867c7440", "scrolled": true }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "클래스 레이블 분포: [41 50 33]\n" ] } ], "source": [ "print('클래스 레이블 분포: %s'\n", " % np.bincount(y_train)[1:])" ] }, { "cell_type": "markdown", "metadata": { "id": "hkbEqkWl29re" }, "source": [ "$\\sum_i=\\dfrac{1}{n_i}\\boldsymbol S_i=\\dfrac{1}{n_i}\\sum_{x\\in D_i}(\\boldsymbol x-\\boldsymbol m_i)^T(\\boldsymbol x-\\boldsymbol m_i)$" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:32.013843Z", "iopub.status.busy": "2021-10-23T05:55:32.012713Z", "iopub.status.idle": "2021-10-23T05:55:32.017636Z", "shell.execute_reply": "2021-10-23T05:55:32.016860Z" }, "id": "XWzi_qzwEjG1", "outputId": "15825e92-7dd2-4879-e5fc-b83a4bbbef79" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "스케일 조정된 클래스 내의 산포 행렬: 13x13\n" ] } ], "source": [ "d = 13 # 특성의 수\n", "S_W = np.zeros((d, d))\n", "for label, mv in zip(range(1, 4), mean_vecs):\n", " class_scatter = np.cov(X_train_std[y_train == label].T)\n", " S_W += class_scatter\n", "print('스케일 조정된 클래스 내의 산포 행렬: %sx%s' %\n", " (S_W.shape[0], S_W.shape[1]))" ] }, { "cell_type": "markdown", "metadata": { "id": "7dBT2KJKEjG1" }, "source": [ "클래스 간 산포 행렬을 계산합니다:\n", "\n", "$\\boldsymbol S_B=\\sum_{i=1}^c n_i(\\boldsymbol m_i-\\boldsymbol m)^T(\\boldsymbol m_i-\\boldsymbol m)$" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:32.026837Z", "iopub.status.busy": "2021-10-23T05:55:32.025588Z", "iopub.status.idle": "2021-10-23T05:55:32.029158Z", "shell.execute_reply": "2021-10-23T05:55:32.029777Z" }, "id": "xdPoDmAZEjG1", "outputId": "a1effde7-af1e-44ec-ee4b-e9450d1a06fd" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "클래스 간의 산포 행렬: 13x13\n" ] } ], "source": [ "mean_overall = np.mean(X_train_std, axis=0)\n", "mean_overall = mean_overall.reshape(d, 1) # 열 벡터로 만들기\n", "d = 13 # 특성 개수\n", "S_B = np.zeros((d, d))\n", "for i, mean_vec in enumerate(mean_vecs):\n", " n = X_train_std[y_train == i + 1, :].shape[0]\n", " mean_vec = mean_vec.reshape(d, 1) # 열 벡터로 만들기\n", " S_B += n * (mean_vec - mean_overall).dot((mean_vec - mean_overall).T)\n", "\n", "print('클래스 간의 산포 행렬: %sx%s' % (S_B.shape[0], S_B.shape[1]))" ] }, { "cell_type": "markdown", "metadata": { "id": "cCw6Yv1sEjG1" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "M_7csaMHEjG2" }, "source": [ "## 5.2.4 새로운 특성 부분 공간을 위해 선형 판별 벡터 선택하기" ] }, { "cell_type": "markdown", "metadata": { "id": "CDTcT3twEjG2" }, "source": [ "행렬 $\\boldsymbol S_W^{-1}\\boldsymbol S_B$의 일반적인 고윳값 분해 문제를 풉니다:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:32.046564Z", "iopub.status.busy": "2021-10-23T05:55:32.045183Z", "iopub.status.idle": "2021-10-23T05:55:32.051551Z", "shell.execute_reply": "2021-10-23T05:55:32.052568Z" }, "id": "jdm4jT5EEjG2" }, "outputs": [], "source": [ "eigen_vals, eigen_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))" ] }, { "cell_type": "markdown", "metadata": { "id": "2lJf-i8oEjG2" }, "source": [ "고윳값의 역순으로 고유 벡터를 정렬합니다(판별 벡터의 개수 = 클래스 개수 - 1):" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:32.064918Z", "iopub.status.busy": "2021-10-23T05:55:32.063321Z", "iopub.status.idle": "2021-10-23T05:55:32.074143Z", "shell.execute_reply": "2021-10-23T05:55:32.075028Z" }, "id": "cFCra1wjEjG2", "outputId": "d6317f18-4281-40dd-9837-78edf42b716e" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "내림차순의 고윳값:\n", "\n", "349.61780890599397\n", "172.7615221897938\n", "3.277875948160424e-14\n", "2.842170943040401e-14\n", "2.6347620763320822e-14\n", "2.6347620763320822e-14\n", "1.7169492680170306e-14\n", "1.7169492680170306e-14\n", "1.674335053365992e-14\n", "1.2740060380615543e-14\n", "7.458378098449665e-15\n", "4.737048557054326e-15\n", "3.688843187314971e-15\n" ] } ], "source": [ "# (고윳값, 고유벡터) 튜플의 리스트를 만듭니다.\n", "eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:, i])\n", " for i in range(len(eigen_vals))]\n", "\n", "# (고윳값, 고유벡터) 튜플을 큰 값에서 작은 값 순서대로 정렬합니다.\n", "eigen_pairs = sorted(eigen_pairs, key=lambda k: k[0], reverse=True)\n", "\n", "# 고윳값의 역순으로 올바르게 정렬되었는지 확인합니다.\n", "print('내림차순의 고윳값:\\n')\n", "for eigen_val in eigen_pairs:\n", " print(eigen_val[0])" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:32.087753Z", "iopub.status.busy": "2021-10-23T05:55:32.086021Z", "iopub.status.idle": "2021-10-23T05:55:32.318933Z", "shell.execute_reply": "2021-10-23T05:55:32.319404Z" }, "id": "QTBSkyVPEjG2", "outputId": "3320adaf-f5e9-46c3-f79d-8a4029135147" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "tot = sum(eigen_vals.real)\n", "discr = [(i / tot) for i in sorted(eigen_vals.real, reverse=True)]\n", "cum_discr = np.cumsum(discr)\n", "\n", "plt.bar(range(1, 14), discr, alpha=0.5, align='center',\n", " label='Individual \"discriminability\"')\n", "plt.step(range(1, 14), cum_discr, where='mid',\n", " label='Cumulative \"discriminability\"')\n", "plt.ylabel('\"Discriminability\" ratio')\n", "plt.xlabel('Linear discriminants')\n", "plt.ylim([-0.1, 1.1])\n", "plt.legend(loc='best')\n", "plt.tight_layout()\n", "# plt.savefig('images/05_07.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "Yh8la8xQ29rf" }, "source": [ "변환 행렬 $\\boldsymbol W$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:32.326617Z", "iopub.status.busy": "2021-10-23T05:55:32.325907Z", "iopub.status.idle": "2021-10-23T05:55:32.332190Z", "shell.execute_reply": "2021-10-23T05:55:32.331505Z" }, "id": "KDxlXzVBEjG2", "outputId": "fb9d56f8-38f8-4013-debe-baae79618e20" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "행렬 W:\n", " [[-0.1481 -0.4092]\n", " [ 0.0908 -0.1577]\n", " [-0.0168 -0.3537]\n", " [ 0.1484 0.3223]\n", " [-0.0163 -0.0817]\n", " [ 0.1913 0.0842]\n", " [-0.7338 0.2823]\n", " [-0.075 -0.0102]\n", " [ 0.0018 0.0907]\n", " [ 0.294 -0.2152]\n", " [-0.0328 0.2747]\n", " [-0.3547 -0.0124]\n", " [-0.3915 -0.5958]]\n" ] } ], "source": [ "w = np.hstack((eigen_pairs[0][1][:, np.newaxis].real,\n", " eigen_pairs[1][1][:, np.newaxis].real))\n", "print('행렬 W:\\n', w)" ] }, { "cell_type": "markdown", "metadata": { "id": "tu490rQsEjG3" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "D21vo1QlEjG3" }, "source": [ "## 5.2.5 새로운 특성 공간으로 샘플 투영하기\n", "\n", "$\\boldsymbol X'=\\boldsymbol X \\boldsymbol W$" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:32.370486Z", "iopub.status.busy": "2021-10-23T05:55:32.366663Z", "iopub.status.idle": "2021-10-23T05:55:32.497666Z", "shell.execute_reply": "2021-10-23T05:55:32.498474Z" }, "id": "8rtNnz74EjG3", "outputId": "ccdb8c16-a330-4a1e-f51d-bc9594eea361", "scrolled": true }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ], "source": [ "X_train_lda = X_train_std.dot(w)\n", "colors = ['r', 'b', 'g']\n", "markers = ['s', 'x', 'o']\n", "\n", "for l, c, m in zip(np.unique(y_train), colors, markers):\n", " plt.scatter(X_train_lda[y_train == l, 0],\n", " X_train_lda[y_train == l, 1] * (-1),\n", " c=c, label=l, marker=m)\n", "\n", "plt.xlabel('LD 1')\n", "plt.ylabel('LD 2')\n", "plt.legend(loc='lower right')\n", "plt.tight_layout()\n", "# plt.savefig('images/05_08.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "15asQXTuEjG3" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "2CbXbBQ7EjG3" }, "source": [ "## 5.2.6 사이킷런의 LDA" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:32.503861Z", "iopub.status.busy": "2021-10-23T05:55:32.502708Z", "iopub.status.idle": "2021-10-23T05:55:32.510923Z", "shell.execute_reply": "2021-10-23T05:55:32.512007Z" }, "id": "gHB0KzvjEjG3" }, "outputs": [], "source": [ "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n", "\n", "lda = LDA(n_components=2)\n", "X_train_lda = lda.fit_transform(X_train_std, y_train)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:32.517407Z", "iopub.status.busy": "2021-10-23T05:55:32.516163Z", "iopub.status.idle": "2021-10-23T05:55:32.833697Z", "shell.execute_reply": "2021-10-23T05:55:32.833075Z" }, "id": "ykehu9ocEjG3", "outputId": "aeda79c5-f620-4526-93dc-482d5a4e4f4d" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "from sklearn.linear_model import LogisticRegression\n", "\n", "lr = LogisticRegression(random_state=1)\n", "lr = lr.fit(X_train_lda, y_train)\n", "\n", "plot_decision_regions(X_train_lda, y_train, classifier=lr)\n", "plt.xlabel('LD 1')\n", "plt.ylabel('LD 2')\n", "plt.legend(loc='lower left')\n", "plt.tight_layout()\n", "# plt.savefig('images/05_09.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:32.838491Z", "iopub.status.busy": "2021-10-23T05:55:32.837753Z", "iopub.status.idle": "2021-10-23T05:55:33.139738Z", "shell.execute_reply": "2021-10-23T05:55:33.138881Z" }, "id": "2vpC6hmuEjG3", "outputId": "a8248397-7048-40cd-820f-4b11a66ccb29" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "X_test_lda = lda.transform(X_test_std)\n", "\n", "plot_decision_regions(X_test_lda, y_test, classifier=lr)\n", "plt.xlabel('LD 1')\n", "plt.ylabel('LD 2')\n", "plt.legend(loc='lower left')\n", "plt.tight_layout()\n", "# plt.savefig('images/05_10.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "Y27NfOE6EjG4" }, "source": [ "사이킷런의 LDA 구현 방식" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.147353Z", "iopub.status.busy": "2021-10-23T05:55:33.146563Z", "iopub.status.idle": "2021-10-23T05:55:33.151217Z", "shell.execute_reply": "2021-10-23T05:55:33.150381Z" }, "id": "LqX58-YBEjG4", "outputId": "80111b20-df11-4796-96df-784e9c80036a" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([0.3306, 0.4032, 0.2661])" ] }, "metadata": {}, "execution_count": 39 } ], "source": [ "y_uniq, y_count = np.unique(y_train, return_counts=True)\n", "priors = y_count / X_train_std.shape[0]\n", "priors" ] }, { "cell_type": "markdown", "metadata": { "id": "Au9anyYvEjG4" }, "source": [ "$m = \\sum_{i=1}^c \\frac{n_i}{n} m_i$\n", "\n", "$S_W = \\sum_{i=1}^c \\frac{n_i}{n} S_i = \\sum_{i=1}^c \\frac{n_i}{n} \\Sigma_i$" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:33.158180Z", "iopub.status.busy": "2021-10-23T05:55:33.157401Z", "iopub.status.idle": "2021-10-23T05:55:33.160279Z", "shell.execute_reply": "2021-10-23T05:55:33.160734Z" }, "id": "3fmRyzDIEjG4" }, "outputs": [], "source": [ "s_w = np.zeros((X_train_std.shape[1], X_train_std.shape[1]))\n", "for i, label in enumerate(y_uniq):\n", " # 1/(n-1)이 아니라 1/n로 나눈 공분산 행렬을 얻기 위해 bias=True로 지정합니다.\n", " s_w += priors[i] * np.cov(X_train_std[y_train == label].T, bias=True)" ] }, { "cell_type": "markdown", "metadata": { "id": "NXQShs0DEjG4" }, "source": [ "$ S_B = \\sum_{i=1}^{c}\\frac{n_i}{n}(m_i-m)(m_i-m)^T $" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:33.168192Z", "iopub.status.busy": "2021-10-23T05:55:33.163967Z", "iopub.status.idle": "2021-10-23T05:55:33.171374Z", "shell.execute_reply": "2021-10-23T05:55:33.172019Z" }, "id": "PBu3Ajq5EjG4" }, "outputs": [], "source": [ "s_b = np.zeros((X_train_std.shape[1], X_train_std.shape[1]))\n", "for i, mean_vec in enumerate(mean_vecs):\n", " n = X_train_std[y_train == i + 1].shape[0]\n", " mean_vec = mean_vec.reshape(-1, 1)\n", " s_b += priors[i] * (mean_vec - mean_overall).dot((mean_vec - mean_overall).T)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:33.179070Z", "iopub.status.busy": "2021-10-23T05:55:33.178259Z", "iopub.status.idle": "2021-10-23T05:55:33.180927Z", "shell.execute_reply": "2021-10-23T05:55:33.181409Z" }, "id": "De00twRIEjG4" }, "outputs": [], "source": [ "import scipy\n", "ei_val, ei_vec = scipy.linalg.eigh(s_b, s_w)\n", "ei_vec = ei_vec[:, np.argsort(ei_val)[::-1]]" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 83 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.189989Z", "iopub.status.busy": "2021-10-23T05:55:33.189015Z", "iopub.status.idle": "2021-10-23T05:55:33.201490Z", "shell.execute_reply": "2021-10-23T05:55:33.202322Z" }, "id": "515DAp_oEjG4", "outputId": "e2a4a122-6a7f-4dbb-ceb3-840a06546f16" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "LinearDiscriminantAnalysis(solver='eigen')" ], "text/html": [ "
LinearDiscriminantAnalysis(solver='eigen')
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" ] }, "metadata": {}, "execution_count": 43 } ], "source": [ "lda_eigen = LDA(solver='eigen')\n", "lda_eigen.fit(X_train_std, y_train)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.211608Z", "iopub.status.busy": "2021-10-23T05:55:33.210706Z", "iopub.status.idle": "2021-10-23T05:55:33.216924Z", "shell.execute_reply": "2021-10-23T05:55:33.215634Z" }, "id": "Wdo7kBhhEjG5", "outputId": "2f5fbf7e-1e84-461f-b044-8d1c30f5c035" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "True" ] }, "metadata": {}, "execution_count": 44 } ], "source": [ "# 클래스 내의 산포 행렬은 covariance_ 속성에 저장되어 있습니다.\n", "np.allclose(s_w, lda_eigen.covariance_)" ] }, { "cell_type": "markdown", "metadata": { "id": "xXMXbCfA29rh" }, "source": [ "클래스 간 산포 행렬은 총 산포 행렬에서 클래스 내 산포 행렬을 빼서 구할 수 있다.\n", "\n", "$\\boldsymbol S_B = \\boldsymbol S_T - \\boldsymbol S_W$" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.227409Z", "iopub.status.busy": "2021-10-23T05:55:33.226396Z", "iopub.status.idle": "2021-10-23T05:55:33.232252Z", "shell.execute_reply": "2021-10-23T05:55:33.230693Z" }, "id": "PFBAWEaQEjG5", "outputId": "7dae41f6-0e8b-48b8-adcb-95c081ad4e79" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "True" ] }, "metadata": {}, "execution_count": 45 } ], "source": [ "Sb = np.cov(X_train_std.T, bias=True) - lda_eigen.covariance_\n", "np.allclose(Sb, s_b)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.241162Z", "iopub.status.busy": "2021-10-23T05:55:33.239636Z", "iopub.status.idle": "2021-10-23T05:55:33.245396Z", "shell.execute_reply": "2021-10-23T05:55:33.246246Z" }, "id": "Kjks6O2NEjG5", "outputId": "2337ea8b-f6e2-4047-98a0-9bb2113b1c18" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "True" ] }, "metadata": {}, "execution_count": 46 } ], "source": [ "# 고유 벡터는 scalings_ 속성에 저장되어 있습니다.\n", "np.allclose(lda_eigen.scalings_[:, :2], ei_vec[:, :2])" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.255043Z", "iopub.status.busy": "2021-10-23T05:55:33.253662Z", "iopub.status.idle": "2021-10-23T05:55:33.260071Z", "shell.execute_reply": "2021-10-23T05:55:33.261507Z" }, "id": "YQ_v9IPfEjG5", "outputId": "1fc8c2c0-8648-48d7-fc8d-d497924276f2" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "True" ] }, "metadata": {}, "execution_count": 47 } ], "source": [ "np.allclose(lda_eigen.transform(X_test_std), np.dot(X_test_std, ei_vec[:, :2]))" ] }, { "cell_type": "markdown", "metadata": { "id": "F12wsUaYEjG5" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "QmdF0zmSEjG5" }, "source": [ "# 5.3 커널 PCA를 사용하여 비선형 매핑하기" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 230 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.270238Z", "iopub.status.busy": "2021-10-23T05:55:33.269483Z", "iopub.status.idle": "2021-10-23T05:55:33.278501Z", "shell.execute_reply": "2021-10-23T05:55:33.277726Z" }, "id": "LeKVh3F0EjG5", "outputId": "55e5bc4b-1147-4a59-f90c-6fe8d1d29ceb" }, "outputs": [ { "output_type": "execute_result", "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "execution_count": 48 } ], "source": [ "Image(url='https://git.io/JtsvB', width=500)" ] }, { "cell_type": "markdown", "metadata": { "id": "bZKSwJLtEjG6" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "Z8OlvQunEjG6" }, "source": [ "## 5.3.2 파이썬으로 커널 PCA 구현하기" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:33.291648Z", "iopub.status.busy": "2021-10-23T05:55:33.288546Z", "iopub.status.idle": "2021-10-23T05:55:33.294640Z", "shell.execute_reply": "2021-10-23T05:55:33.295264Z" }, "id": "AWwSJwROEjG6", "outputId": "2a276be7-1f30-4406-f33b-a3a1a4d531d7", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stderr", "text": [ "/tmp/ipython-input-858286342.py:9: DeprecationWarning: distutils Version classes are deprecated. Use packaging.version instead.\n", " if scipy_version >= Version('1.4.1'):\n" ] } ], "source": [ "from scipy.spatial.distance import pdist, squareform\n", "from scipy.linalg import eigh\n", "import numpy as np\n", "\n", "from distutils.version import LooseVersion as Version\n", "from scipy import __version__ as scipy_version\n", "\n", "# scipy 2.0.0에서 삭제될 예정이므로 대신 numpy.exp를 사용합니다.\n", "if scipy_version >= Version('1.4.1'):\n", " from numpy import exp\n", "else:\n", " from scipy import exp\n", "\n", "\n", "def rbf_kernel_pca(X, gamma, n_components):\n", " \"\"\"\n", " RBF 커널 PCA 구현\n", "\n", " 매개변수\n", " ------------\n", " X: {넘파이 ndarray}, shape = [n_samples, n_features]\n", "\n", " gamma: float\n", " RBF 커널 튜닝 매개변수\n", "\n", " n_components: int\n", " 반환할 주성분 개수\n", "\n", " 반환값\n", " ------------\n", " X_pc: {넘파이 ndarray}, shape = [n_samples, k_features]\n", " 투영된 데이터셋\n", "\n", " \"\"\"\n", " # MxN 차원의 데이터셋에서 샘플 간의 유클리디안 거리의 제곱을 계산합니다.\n", " sq_dists = pdist(X, 'sqeuclidean')\n", "\n", " # 샘플 간의 거리를 정방 대칭 행렬로 변환합니다.\n", " mat_sq_dists = squareform(sq_dists)\n", "\n", " # 커널 행렬을 계산합니다.\n", " K = exp(-gamma * mat_sq_dists)\n", "\n", " # 커널 행렬을 중앙에 맞춥니다.\n", " N = K.shape[0]\n", " one_n = np.ones((N, N)) / N\n", " K = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n)\n", "\n", " # 중앙에 맞춰진 커널 행렬의 고윳값과 고유벡터를 구합니다.\n", " # scipy.linalg.eigh 함수는 오름차순으로 반환합니다.\n", " eigvals, eigvecs = eigh(K)\n", " eigvals, eigvecs = eigvals[::-1], eigvecs[:, ::-1]\n", "\n", " # 최상위 k 개의 고유벡터를 선택합니다(결과값은 투영된 샘플입니다).\n", " X_pc = np.column_stack([eigvecs[:, i]\n", " for i in range(n_components)])\n", "\n", " return X_pc" ] }, { "cell_type": "markdown", "metadata": { "id": "q5LH1FhQEjG6" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "-7CDFufCEjG6" }, "source": [ "### 예제 1: 반달 모양 구분하기" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.305697Z", "iopub.status.busy": "2021-10-23T05:55:33.304207Z", "iopub.status.idle": "2021-10-23T05:55:33.579140Z", "shell.execute_reply": "2021-10-23T05:55:33.578488Z" }, "id": "eK5WLaYkEjG6", "outputId": "925d5105-d86d-4865-c405-37b2e3ef306a" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "import matplotlib.pyplot as plt\n", "from sklearn.datasets import make_moons\n", "\n", "X, y = make_moons(n_samples=100, random_state=123)\n", "\n", "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='red', marker='^', alpha=0.5)\n", "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='blue', marker='o', alpha=0.5)\n", "\n", "plt.tight_layout()\n", "# plt.savefig('images/05_12.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 307 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.618864Z", "iopub.status.busy": "2021-10-23T05:55:33.604036Z", "iopub.status.idle": "2021-10-23T05:55:33.825153Z", "shell.execute_reply": "2021-10-23T05:55:33.824401Z" }, "id": "3XUrxsG1EjG6", "outputId": "cb8f0a68-1401-43f1-9eff-29d756b5daa5" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "from sklearn.decomposition import PCA\n", "\n", "scikit_pca = PCA(n_components=2)\n", "X_spca = scikit_pca.fit_transform(X)\n", "\n", "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))\n", "\n", "ax[0].scatter(X_spca[y == 0, 0], X_spca[y == 0, 1],\n", " color='red', marker='^', alpha=0.5)\n", "ax[0].scatter(X_spca[y == 1, 0], X_spca[y == 1, 1],\n", " color='blue', marker='o', alpha=0.5)\n", "\n", "ax[1].scatter(X_spca[y == 0, 0], np.zeros((50, 1)) + 0.02,\n", " color='red', marker='^', alpha=0.5)\n", "ax[1].scatter(X_spca[y == 1, 0], np.zeros((50, 1)) - 0.02,\n", " color='blue', marker='o', alpha=0.5)\n", "\n", "ax[0].set_xlabel('PC1')\n", "ax[0].set_ylabel('PC2')\n", "ax[1].set_ylim([-1, 1])\n", "ax[1].set_yticks([])\n", "ax[1].set_xlabel('PC1')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('images/05_13.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 307 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:33.846342Z", "iopub.status.busy": "2021-10-23T05:55:33.845036Z", "iopub.status.idle": "2021-10-23T05:55:34.170272Z", "shell.execute_reply": "2021-10-23T05:55:34.169538Z" }, "id": "CKQnqpCuEjG6", "outputId": "b9981f1a-d9c4-400d-e02e-3bc7fb004392" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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ZMJgXmIjIGKYJgJOTkxEVFYXq6mqH5dXV1UhPTw/qMePi4tyOKfarAwckAJ40CaiqkuA30gM7X9OkUcC5qoIWzmnOfGG1SsC7cSPQ1ibD191NEmReYCKi4DHN6TY2NhZTp07Ftm3bupbZbDZs27YNubm5IXNMv9Hf5uckLztf0qRpmtTYdZ6JRL1is0lRwgMH5LvN5vqWf7imOfOVL5MEiYgoOEzTAwwAS5YswZ133olp06Zh+vTpWLNmDZqbmzF//nwAwNy5czF48GCsWrUKgExyKy4u7vq5oqICe/fuxYABA3DppZd6dUzDeJrkFcm9wL6kSWORDL/zVOxCf8s/nNOc+cqbSYIVFZEzSZCIKBSYKgC+7bbbcPr0aTz22GOoqqrCZZddhs2bN3dNYisrK4NV92l78uRJTJ48uevxs88+i2effRYzZsxAQUGBV8c0RCTl/fWVSpN2Ic5FMiL5d+YnqthFTY1cj7kbx8rqZo6YF5iIKPRYNI33h3uroaEBiYmJqK+vR4KrTzhf7dsHPP00kJHh+KnY2AhUVko1AfZoeqZ+hwMGyLR7/s56xWaTjAXuJroVF8twh4cf5nWGs2D+7npzLvL7eYyIqIeCcT7iR1WocTXJi3l/fcPx037Hcaw95ykvcHFxZE8SJCIyiqmGQEQENckLAL76Su6NOkccapIX7zW7xvHTfsdxrL2jJgmq8dMnTsgw9qFDgX/5Fxk7TUREwcMAONSoSV7FxcD770vX0OjRjttEWt5fX3D8dEBwHGvvqUmCn34KfPCBBMEnTwJvvAHs2mWfSEhERIHHSCDUREfLp+Dx4zLe99gxCdomTrR/jRsn21F33hTJIJ+pYhfl5d2zyqliF9nZkVfswlelpcB//Zf8aw8fLr/T5GR5a65dy6pwRETBwgA4FKkg7pJLGLT5guOnA4bjWHvPZpMhEDU1MhkuIUFu5qiCGDU1UhCDb08iosBjN2KocZ7AVVzMW/feci6S4YoaP33xxXL/OTOz+xhrgs3WPZ+v8zjWigoZ9jBligS/vH3vmS8TCTm8n4gosBgAhxpO4Oo5FsnwCxa7CAxOJCQiCh0MgEMJJ3D1Dotk9BqLXQQOJxISEYUOfuqHEk7gCg6OsXaJY1QDixMJiYhCBwPgUMEJXMHBIhlusdhFYHEiIRFR6OAQiFDhywQu3n/uOY6xdotjVAOPEwmJiEIDA+BQMWQIcO+9kiA0NdV1ZgIWwOgdjrH2iGNUg8N5IqG64GhulvTfnFRIRBR4DIBDRXS0ZC/4+GNmJggUb8ZYR/DvXY1RLSqSMb/6azA1RnXKFI5R9QerVW7klJQA77zjPuMGEREFBvsZQoVzZgKOSfUvjrG+II5RDS6VcaOoSH63WVmsCkdEFCzsAQ4VrjITRHBvpN9xjLVXOEY1OJwzbqjedpVxo7hYMm5kZfGCg4goEBgAhwJWfws8X4pkAHLPP4wrxbmq9Kbeaix2EXisCkdEZCwGwKGAmQkCz9siGUoYV4q7UKU3wD5GlQKDGTeIiIzFPh2juctMwPy0xgnj8dgcdxoa9Bk3XGHGDSKiwGIAbDRWfws9YVopjpXeQgerwhERGYsBsJGYmSD0hHGlOFZ6Cx3MuEFEZCyOATYSMxOEnjAej81xp6GFGTeIiIzDANhIKjNBRwdw6pTrCnCs/hY8YV4pjpXeQo8+40Z9vT3rRt++8nY08duNiCikMQA2kspMsG8fK8CFgjCvFMdKb6HJagXOnQM++ogV4YiIgoX9C0YL44wDphIB47E57jQ0MTMHEVHwsQfYaKwAFxoiZDw2x52GFlaEIyIyBgNgI7ECXOgIs0pxrPRmDqwIR0RkDAbARgrjjAOmE0aV4ljpzTyYmYOIyBim6/N56aWXMHz4cPTp0wc5OTnYtWuXx+3fffddjBkzBn369MGECRPw8ccfO6yfN28eLBaLw1d+fn4gX4JgBTjzCuFx2xxPai6sCEdEZAxTBcB/+tOfsGTJEjz++OP46quvMGnSJMyaNQunTp1yuf2OHTtw++2346677kJRURFuuukm3HTTTfjaqbJXfn4+Kisru77efvvtwL8YVoAzrxCtFMdKb+bDinBERMYwVQD83HPPYcGCBZg/fz7Gjh2LdevWoV+/ftiwYYPL7V944QXk5+fjoYceQnZ2Np588klMmTIFv//97x22i4uLQ3p6etfXwIEDA/tCIiDjQNgK4UpxrPRmPszMQURkDNOcVtvb27Fnzx7k5eV1LbNarcjLy0NhYaHLfQoLCx22B4BZs2Z1276goACpqanIysrCz3/+c5w5c8ZjW9ra2tDQ0ODw5RPnjAPOX4A94wCFFk/jtg3mzXjS1laOJw01KjPH5MnAmTPA4cPyfcoUWc7MHERE/meaSXA1NTXo7OxEWlqaw/K0tDQcOnTI5T5VVVUut6+qqup6nJ+fj1tuuQUjRozAN998g0ceeQTXXnstCgsLERUV5fK4q1atwhNPPNHzF+NrxgEKDSFeKY6V3syLmTmIiILLNAFwoMyZM6fr5wkTJmDixIm45JJLUFBQgJkzZ7rcZ/ny5ViyZEnX44aGBgwdOtT7J9VnHAjxdFqkE+KV4ljpzdysVvnbqCC4rIxBMBFRoJgmAE5OTkZUVBSqq6sdlldXVyM9Pd3lPunp6T5tDwAjR45EcnIyjh496jYAjouLQ1xcnI+vwI0QTqdFOq7GbSv6cdsG9gKr8aTl5TJ+dMgQaVpzswS/HE8a2rxJX0dERP5hmo/C2NhYTJ06Fdu2betaZrPZsG3bNuTm5rrcJzc312F7ANi6davb7QHgxIkTOHPmDDIyMvzTcE9COJ0WOTHJuG2OJzUnpq8jIgou0/QAA8CSJUtw5513Ytq0aZg+fTrWrFmD5uZmzJ8/HwAwd+5cDB48GKtWrQIA/PKXv8SMGTPwu9/9Dtdffz3eeecd7N69G+vXrwcANDU14YknnsDs2bORnp6Ob775Br/61a9w6aWXYtasWYF/QSyDbB49GbcdoOEtnqq8ARxPajYsh0xEFHymCoBvu+02nD59Go899hiqqqpw2WWXYfPmzV0T3crKymDVfUJcccUV2LhxI37961/jkUcewahRo7Bp0yaMHz8eABAVFYX9+/fj9ddfR11dHTIzM3HNNdfgySef9N8QB3dYBtlcfK0UBwRkeIu3t8lZ6c08WA6ZiCj4TBUAA8CiRYuwaNEil+sKCgq6Lbv11ltx6623uty+b9++2LJliz+b5z2WQQ5vzsNb/HBho26T19TI20WN7y0qknG/HOJgTiyHTEQUfOxqNALLIIc/P1eLY5W38MVyyEREwccA2AgsgxzeAlAtjlXewhfLIRMRBR8D4GBjGeTwF4BqcazyFr5YDpmIKPhMNwbY9JzTabmi0mlxxov5BKhaHKu8hTeVvk5NcKyokL/nlCkS/HJsNxGRfzEADjaWQQ5vAaoWxypv4Y/p64iIgocBcLD1JJ0WmUMAq8WxyltkYPo6IqLgYABspAAVSiCDBHh4C2+TR4YLFTohIqLeYwBspAAUSiADBWF4C2+ThzdvC50QEVHvMAA2SgAKJZDBgjS8hbfJwxMLnRARBQ8jLqP4uVACEZkXC50QEQUXA2AjBKBQAhGZFwudEBEFFwNgIwSgUAIRmRcLnRARBRcD4GBzVyiBvcBEEUtf6MQVFjohIvIvBsDB5k2hBCKKKKrQSXm5ZEfUU4VOsrNZ6ISIyF8YAAeTq0IJ6ktfKIG9wEQRRRU6SU6WQif19XJTqL5eHrPQCRGRfzENWjAFuFACEZkXC50QEQUPA+BgCkKhBCIyLxY6ISIKDgbAwRSkQglEZF4sdEJEFHjsVzCKpsk9TucZL0QU8Ww24PhxmTN7/DinBRAR+Rt7gI2yfz/w2mvA/PnAxIlGt4aIQkRJiX0ccGurjAMeM0YmyXEcMBGRf7AH2AgqG8T+/cz6QERdSkqAtWslI2JysowHTk6Wx2vXup87S0REvmEAbASVC/iSS5j7l4gAyHXwe+8BNTXA2LFAQoLMiU1IkMc1NcCmTbxeJiLyB58D4MrKSrz55pv4+OOP0d7e7rCuubkZK1eu9FvjwpK+ElxmJivAEREAyfxw6JDUxLFYHNdZLJIcpqREtiMiot7xKQD+8ssvMXbsWNx333348Y9/jHHjxuHgwYNd65uamvDEE0/4vZFhxbkSHCvAEREk7Vlrq9TEcaV/f1nf2BjcdhERhSOfAuBHHnkEN998M86ePYvq6mr88Ic/xIwZM1BUVBSo9oUXfe9vfLwsi49nLzARIT5eJrw1N7te39ws69WpI2R0dACvvw588YV0T5eXd/86cULObydO2H+uqPD+u6bZM+f0Zpm3PwOuj6Nf7mkff67z1Jbe7qvWq7+Lq6xEzFhEYcqnLBB79uzBSy+9BKvVivj4eLz88ssYNmwYZs6ciS1btmAYC9V75tz7q+h7gZkRgigiDRsm2R6KimTMr34YhIpRpkzpfvow3IMPAi+/DAwYIHnOExJkucViD5oGDQJuuAF4/31ZfsMNwI4dwBVXePd9/nw51muv9W6Ztz9PnGjP1KM/jn65p338uQ5w3xb9up7sq9avXi1/l4ce6v4ZxIxFFKZ8ToPW2trq8HjZsmWIjo7GNddcgw0bNvitYe689NJLWL16NaqqqjBp0iS8+OKLmD59utvt3333XTz66KM4fvw4Ro0ahaeffhrXXXdd13pN0/D444/jlVdeQV1dHb773e/iD3/4A0aNGuXfhqve3/Z2uZep7+3t3196hbdsAcaPZ9knoghktUqqs/JyoLhYxvz27y89vydOSDaIm24KsdNDayvw5pty/jp7Fti9G4iLk0bqI/jERJnFd+SIBGlnzsi+hw8DLS3y/dw599//+lc53r59sqy1Fdi8WY61f799O1fL1L779zv+rN9Wv3zLFrkC+eQTx+fTL/e0j/OxfdnPed348fL7c9UW/boL7av/feg/Z2w2aesXX8i2mzc7fgY5Zyzi5xOFEZ8C4PHjx2PHjh2Y6HQV+OCDD8Jms+H222/3a+Oc/elPf8KSJUuwbt065OTkYM2aNZg1axZKS0uRmprabfsdO3bg9ttvx6pVq/CjH/0IGzduxE033YSvvvoK4/95cnjmmWewdu1avP766xgxYgQeffRRzJo1C8XFxejTp4//Gl9WBhw7Jicod7mMjh2T7VgGiigiZWcD999vzwNcUSHDHqZMkeA35PIAL1sG1NbaH7e2ypCIqCj7MqtVqmDu3i0vBgD27pXA7+uvgVGjPH+fNg0oKJBz58CBcpzLLwc++0yOlZQky6ZNc71M7XvJJY4/q22dlxcVyR+gqMjx+fTLPe3jfGxf9nNe9/XXEki7aot+3YX21f8+9HcbDxyQ/ZSCAiA/397T6ypjEXuBKUz4FADPnTsXBQUFuOeee7qt+9WvfgVN07Bu3Tq/Nc7Zc889hwULFmD+/PkAgHXr1uGjjz7Chg0bsGzZsm7bv/DCC8jPz8dDDz0EAHjyySexdetW/P73v8e6deugaRrWrFmDX//617jxxhsBAG+88QbS0tKwadMmzJkzx3+NHzIEuO8+oLPT/TZRUbIdEUWs7GzJ/1tWJhPe4uNl2EPIdbyp3l/nsaEdHXKeUw22WuWF2Gz2XuG2NuDbb2W7b7+VffSP9d8bGoCqKtkvPV2OU1cHnDoly1JTZVlDA1Bd7bisvt6+3bRp9p7OadOAnTul7Zdfbl9++eXS/f7aaxKsNzTYj5OUJMv79gUyMlzv06+frFPHnj7dvs7Tfq7WlZTYe5Lb27u3Ra07f97zvufP2/dtaJB9Vc/z5s1ylRUbK3+bigp7LzDgmLGouJi9wBRWfAqAf/azn+FnP/uZ2/UPP/wwHn744V43ypX29nbs2bMHy5cv71pmtVqRl5eHwsJCl/sUFhZiyZIlDstmzZqFTZs2AQCOHTuGqqoq5OXlda1PTExETk4OCgsL/RsAR0fL+DgioguwWk1wI8i591dP0yR4tVjkq71dvp87Jxf6mgZUVkqgevq09G6ePi1jhU+dAi66SB5nZMidsY4OOW5rq+xz/LgcX9PkmKmpjtupZWq7uDgJClXqzpISCcLVz2r5qVMS+O7aJT2dVVVynKoqOcbXXwMzZkigrd+nb1/ZR61Tx9Yfz9V+ntYNHWrvSU5JAUpL7W3JyLCvGzvW877JyY6vIyPD3vNcUCD7DRwo2549a+8FVr3HrjIW+akX2GZzf6Gn1tXX29cnJtqbo/ZTWVOam2WbIUNkyJCrdf7a11ObfFnn6fnUOnf76JeribGNjb5vq4ZZqe9qG5sNOHpUtr30Uvl+9Kgs79dPRi5ZLPLWb2mRt0tTk2ynrjmbm2W0U3W1/Ev/y78AV10l4VAo8KkZra2t+OSTT3D11Vcj3mkqckNDAwoKCjBr1izExcX5tZEAUFNTg87OTqSlpTksT0tLw6FDh1zuU1VV5XL7qn/2JqjvnrZxpa2tDW3qBAd57T7TNODkSbmydk76SUQRzVNgEBLc9f460zQJSlUg3NYGxMTIuo4O6clVvZqdnfJY0+zL29rkU1XT7MfIzLRnLLBY5NM3I6N7FgO1DJBAc+9e+3M7/xwdLb/go0ftwfuhQ7L8oovkE720VJZXVso2apzzkSPy3WaTc7rFYl+njmezdd/vQutyc+V4Npu9Vz0+Xi4MTp60RxmXXy5jdF3tq3qA9ftWVkp09Oqr8vuxWiW4B+TipKIC+PhjOZZzxqLycr/1Ansq+Q3Iup07gX/8wx6gjRwJjBgh62tr5VegOv3T0uRlnDsnQVlbm+O61FS5vurtvseOuW+TL+tSUuTt5er5VFs6OuRP5ryPfnlUlD2gVG8Tb7dtbZU/saLa09kpz69CE/02ah81yklNZ7LZZD+bzf1pYe1aYPRomXP5ox95fn8Eg08B8H/8x3/ggw8+wA033NBtXUJCAtauXYuysjIsWrTIbw0MRatWrep9vmPOrCUiFzwFBiEzBthT768r6hNR9dCq4KmpSbqTmpvtXUl9+9q7ourq7D3JgHzqnj4ty9SxoqNlgp369Nc0CW5rauyPOztlv4svln0qKqSLXXVEDBsmUcOxY7I+IcG+XD1HRQUweLB9Lkdysqw7flweqx5n/Tq1reqhdl4HuF5XVWXvpW5tlS+1LiGhe892VZUEta72PXfOcV/Vm11UJG+u9HT73ykhQXqB//IX+f2PHev4d/RTL7Aq+V1TI4dUvY9FRfLRCEgzKivlz5qUJC/j0CHgq6/kzzthgj2w0zR5uZ2d9mAxKkoCNYtFtouLA7Zvl20nTpQAuKlJ1peVyfO0tMjbMSZG9lXXWH36AH//uyzr21eOrdpUUiJt0jR5Xqu1+zpAjqvW1dXJ2ys6Wh5HRcnz619HXZ0sS0x03EdJTJTXpH5HgLQ7I0N+BxUV9n+bxER5DZWV9mDWYpHnb2+X54uKkpEwZ8/KNtHRsk9np72HV987f/68fVSTtxnybDb5Gy5YALzyivFBsE+XcG+99RYWL17sdv3ixYvxxhtv9LZNLiUnJyMqKgrV6jLpn6qrq5Gu/wfWSU9P97i9+u7LMQFg+fLlqK+v7/oqLy/37cU4z6xl/l8igj0wKCqSmCUrS74XFclyd/Nng8rb3l9nKk/t+fP2XknVDaVp9gl0LS32T9jWVvmEbm+3RySqt7S93T7UQL9MfTLr7+KpYLi+3nEsbWOjLG9slAigoUGWt7TYl3d02Pc5d86+TXS0fKnH/fq5X9e3r/f7xcTIc6r8+i0t9nU2m31flTB6717ZPibmwvuq9SUlsn9zs32dWm+xAN98I73D/frZ19lsjhmLevi55ankd3a2xNYHDsifsqNDrg8SEqRH8+xZ+02Er7+WP0dGhtwUqKmR9SNGyPeaGlmXkSG/hq+/loAxLk6O39oq+6Wny7Z1dXJNVFcnAXN6uqxvbZXtY2Pl57o6aYtqU12dLG9rk+d1te7cOVmXmmofXqCC6dpaeX71fOp19Oljf8sPGGB/e3d22t/ira2Of76oKHku/U0Dta0afaS27eyUNkdH268Z9T3C6vG5c469xuqiQJ/C2lenTgEvvGAP3I3iUw/wkSNHMGnSJLfrJ06ciCNHjvS6Ua7ExsZi6tSp2LZtG2666SYAgM1mw7Zt29z2OOfm5mLbtm0OQfvWrVuRm5sLABgxYgTS09Oxbds2XHbZZQBkOMPOnTvx85//3G1b4uLiejfMgzNriciJc2Cgem8SEuRxcTGwaZMExYYOh/jP/5Sgqjf0wVNbm+MnqurxVQMK1XKLxf6prrrM1LGcl3V02INF1QMcHW0fNqBp3X9uarJ3daluRf1ym81+n1oNfQDsgeihQ7Id0H1daan7dc77qfvWLS0Srblap/ZVXYb9+tlLBHraV61vapLX09zsuE6/f0wMsGeP69KEvchY5Knkd0ODPWirqpKeT7VNe7u9xzEqSv40w4fL49ZW+zr10tTQ8z595Kuqyt5c9bMalaO2b262vzXVvqqXNTPT/lZU61Sb1FvWanW/Tj0XIEFlv37SVvXWVEO4VYDa3Gwfa9vYKN/79LEPi1L/Hvo/XXS0/W0QF9d9WzXqR71GNcolJsYeXKsbC+oaVbUPsI/Y8aXX1xWbTbL6ffEFcOWVPT9Ob/kUAHd0dOD06dNuC16cPn0aHQEM6ZcsWYI777wT06ZNw/Tp07FmzRo0Nzd3ZYWYO3cuBg8ejFWrVgEAfvnLX2LGjBn43e9+h+uvvx7vvPMOdu/ejfXr1wMALBYLFi9ejH//93/HqFGjutKgZWZmdgXZfqevBseZtUT0T54CA4tFJrSUlIRApsQ77pBb8IcOSSDc3Cyfzqq3Vn1yXnSRdF1ZLPb7vwMGyPeEBMcsEYmJ8mmdkGDPVKB+CerTNipKjllbKwMya2pk/UUXSZfZwIEy48ZikfV1dbIOkG2Tk+3Pqf8EV5FLWppERvroQL9c9WAD0pbMTPlZjbVNS7MHyIMHy3d1H1odQ41hVusA+35qXVSU/P6qqqQbsbpajj94sH2d2jc9XSLBjAz7oEz9vvrn1K9X46WtVvtxFbV/ZqZ00riasdSLjEWeSn6rANFmk7eSCtiA7r2F+pEx+nUqkNQvt1odA1F9khJv99UHfPrrLMD3dTabfeyv8+ggtU9np/zbnDtnD6bV/NGoKPvvSv87Uq8NkCDW07bqeTTNfl2l/5fwlLDKH0UB9eOejeJTADxu3Dj87W9/w9SpU12u/+STTzAugJkObrvtNpw+fRqPPfYYqqqqcNlll2Hz5s1dk9jKyspg1QWRV1xxBTZu3Ihf//rXeOSRRzBq1Chs2rSpKwcwIOnbmpubsXDhQtTV1eHKK6/E5s2b/ZsDWM+5GhyrwBERPAcGgCyvqLD38BgmKUlmsRD1gL7ktyoaqKgbq1arfRyuWuYch6tg0HldbKz9Z7VcHzyqoFBd53i7r/6iVK1T31Vg7e061VOsrmec26HvTbZapV36IF7d8AC6V73WX+c4b+tMtc1ms9dFUcdRz+duv96Ki5NrPyP5FAD/27/9G5YsWYJx48bhR06jlz/88EP85je/wXPPPefXBjpbtGiR2yEPBfqE3v9066234tZbb3V7PIvFgpUrV2LlypX+aqJ7+t7fAM2sJSJz8hQYALK8Tx/7qYPIjDyV/Fbjga1WGS9bXS0d2RaLPQgEJDAbNMjeg6qKDwL2mwyA7KOGl+u31/+sP66axKbft61Nttf3IKtAWe2rv1nhap0aN6uCeTX2d9Ag+b9W+6nA12qVbc6elZsY8fHSG1xTI+cA1SaLxfGCuKNDttU0Ob67bfVhhhrr27evY290377ys/7Gh2qf+rmnPcFWKzBpEvCd7/Rsf3/xKQBeuHAhPv/8c9xwww0YM2YMsrKyAACHDh3C4cOH8ZOf/AQLFy4MSEPDgnPvr8JeYKKI5ykw0DS5az1lSvfTB5GZXKjkt7pBe/as9IpWV0sw1toqo1xaWqQPacIEOYbKjJCcLEHqsWNykyI6WsbuAhJYjx5tL47nvG9Kihzz+PHu+8bHS1HCAwckoOzb1576ubXVnvFB0yRIPX1atjt3zr4OkHXqtage7nPnJDiNirI/n3oddXX2IQuNjY7BtbpIiIuT35P+wkAFvdHR9vHSKpNFXZ1jAKvPlHH+vH3sspqnqs8CATj2iusDe18D4dRU4Je/ND4fsM9P/+abb+LGG2/EW2+9hcOHD0PTNGRlZeGJJ57AT37yk0C0MTyo3t/2dvlv108C0c+sZS8wUUS6UGCQnCzlkHl6ILO7UMlvwDEPcH29Pa/uyJH2Hk79GFqVP1elDtSPMU1JkWHmN9zg+76pqbLvjTfK9iqfr2rT6NH2Njmv07fXed3w4RLgOj+fvi3nz0tA7byPWt7cLO1TQxw6OuRY7rZNTr5wHmAVgOvzAOuHhvQmD7DVKpN4n3nG+BRogI8BcGdnJ5599ll88MEHaG9vx49+9COsWLECfVVfOblXVmbP9egul1EvZtYSkfldKDAImTzARL10oZLfah0rwbESXKBYNM37zusnn3wSK1asQF5eHvr27YstW7bg9ttvx4YNGwLZxpDX0NCAxMRE1NfXI8HV4D1ALrdUJSF3oqLkvz5U3h1EZIieVoLz6lwUgH2JiPwpGOcjnyKtN954Ay+//DLuvvtuAMDf/vY3XH/99fjjH//okH2BXIiOBgKYIYOIwofVyhtBRESB5FPUWlZWhuuuu67rcV5eHiwWC07q6/ORdzRN7m/6I6EeEYUVm00m5Bw4IN9ZLJKIyL98LoThnB83JiYG5/WjqMk7+/cDr70GzJ/PzA9E1KWkxD4GWE3KGTNGJshxDDARkX/4FABrmoZ58+Y5lAFubW3FPffcg/667O3//d//7b8WhiOVEWL/fmZ+IKIuJSXA2rWS73PoUPvElKIiyQ5x//0MgomI/MGnAPjOO+/stuynP/2p3xoTMVQ+4EsuYf5fIgIg18XvvSfBrz4PcEKCPC4uBjZtknmyvF4mIuodnwLgV199NVDtiBz6anCZmfKpxl5goohXVibDHoYO7V5q1GKRlEYlJcyUSETkD4y4gs25Gpy+ChwRRazGRhnzqxtN5qB/f1mvL31KREQ9wwA4mPS9vyobdXy85AjesoVTvYkiWHy8THhrbna9vrlZ1qtTBxER9RwD4GBy7v1V2AtMFPGGDZNsD+Xl3bMjappUdMrO7n76ICIi3zEADhbV+9veLvcybTb7V//+0ivMXmCiiGW1Sqqz5GSZGlBfLzeH6uvlcXKylEPmVAEiot5jzd1gKSsDjh2T2SwlJa63OXaMM1yIIlh2tqQ6U3mAKypk2MOUKRL8MgUaEZF/MAAOliFDgPvuAzo73W8TFSXbEVHEys6WVGdlZTLhLT5ehj2w55eIyH8YAAdLdDQwbpzRrSAiE7BaeSOIiCiQ2KdgJE2Te5zOM16IKGLZbMDx4zJn9vhxTgsgIgoE9gAbaf9+4LXXgPnzWQmOiFBSYh//29oq43/HjJHJcRz/S0TkP+wBNorKCrF/P7M/mFWI9uCzB9GcSkqAtWslI2JysowDTk6Wx2vXup87S0REvmMPsFFUTuBLLrHnAGYvsLmEYA8+exDNyWaTv1tNDTB2rL0UckKCPC4uBjZtkqCYk+GIiHqPp1Ij6CvCZWayEpwZhWAPPnsQzausTC5ahg61B7+KxSLJYUpKZDsiIuo9BsBGcK4Ix0pw5uOqB99Azj2ICQmSVU/1INbUSA9iCMTp5EJjo/TY9+/ven3//rK+sTG47SIiClcMgINN3/sbHy/L4uPZC2wmIdiDzx5Ec4uPl+Eqzc2u1zc3y3p1yiAiot5hABxszr2/CnuBzSMEe/DZg2huw4bJWO3y8u5zKjUNOHFCxnA7nzaIiKhnGAAHk+o5bG+XiMRms3/17y89iuwFDm0h2oPPHkRzs1plomJyskx4q6+Xt1R9vTxOTpZSyJwAR0TkH8wCEUxlZcCxY3JP2t2MpGPHZDuWgQpN3vTgG5ARQvUgFhU5ZhEA7D2IU6awBzGUZWcD999vz+JRUSEXLVOmSPDLLB5ERP5jmgC4trYWv/jFL/Dhhx/CarVi9uzZeOGFFzBgwAC3+7S2tmLp0qV455130NbWhlmzZuHll19GWlpa1zYW5wGTAN5++23MmTPH/y9iyBDgvvuAzk7320RFyXYUelz14Cv6Hvzx44PeVad6EMvLpcdwyBBpUnOzBL/sQTSH7GzJ3lFWJsNV4uPlooV/NyIi/zJNAHzHHXegsrISW7duxfnz5zF//nwsXLgQGzdudLvPAw88gI8++gjvvvsuEhMTsWjRItxyyy3Yvn27w3avvvoq8vPzux4nJSUF5kVERwPjxgXm2BQYmgacPCmT3UK8B/9CPYhZWVIYg4FVaLNaeQOIiCjQLJoWYmWsXCgpKcHYsWPx5ZdfYtq0aQCAzZs347rrrsOJEyeQmZnZbZ/6+nqkpKRg48aN+PGPfwwAOHToELKzs1FYWIjvfOc7AKQH+L333sNNN93U4/Y1NDQgMTER9fX1SEhI8G1nfYDlojeaDLZvn73YxdixQGnphXvws7LkYscgNlv3HsTSUhbIMANXfztfLlJ6cy7q1XmMiMiPgnE+MkUPcGFhIZKSkrqCXwDIy8uD1WrFzp07cfPNN3fbZ8+ePTh//jzy8vK6lo0ZMwbDhg1zCIAB4L777sPPfvYzjBw5Evfccw/mz5/vcmiE0tbWhra2tq7HDQ0NPX9xIVhNjP7JudjF+PGm6MF37kFUBTJqamSoshoaUVQkQybuv59BcChgFT8iouAxxQ3QqqoqpKamOiyLjo7GoEGDUFVV5Xaf2NjYbsMZ0tLSHPZZuXIl/vznP2Pr1q2YPXs27r33Xrz44ose27Nq1SokJiZ2fQ0dOrRnLywEq4mRTogVu+gJFsgwB1bxIyIKLkMD4GXLlsFisXj8OnToUEDb8Oijj+K73/0uJk+ejIcffhi/+tWvsHr1ao/7LF++HPX19V1f5eXlPXvyMAiwwlYIFrvoCRbICH28SCEiCj5Dh0AsXboU8+bN87jNyJEjkZ6ejlOnTjks7+joQG1tLdLT013ul56ejvb2dtTV1Tn0AldXV7vdBwBycnLw5JNPoq2tDXFxcS63iYuLc7vOa84BVnGxYRkEyAVPxS5MNFTFmwIZFRUskGEkXy5SODmOiMg/DA2AU1JSkJKScsHtcnNzUVdXhz179mDq1KkAgE8//RQ2mw05OTku95k6dSpiYmKwbds2zJ49GwBQWlqKsrIy5Obmun2uvXv3YuDAgb0PcC8kTAKssOSu2EV5uekuUvQFMlzNI2CBDOPxIoWIKPhM8SmenZ2N/Px8LFiwALt27cL27duxaNEizJkzpysDREVFBcaMGYNdu3YBABITE3HXXXdhyZIl+Oyzz7Bnzx7Mnz8fubm5XRPgPvzwQ/zxj3/E119/jaNHj+IPf/gDfvvb3+IXv/hFYF9QiFYTo38Ko3LVLLEb+ljFj4go+EyRBQIA3nrrLSxatAgzZ87sKoSxdu3arvXnz59HaWkpWlpaupY9//zzXdvqC2EoMTExeOmll/DAAw9A0zRceumleO6557BgwYLAvpgQrSZGCOliFz3BAhmhj1X8iIiCzxR5gEOdT/nqbDbgd78Ddu6UTztnJSXA9OnA0qWMSoxw/DjwzDPA6dPut0lJAX71K1MNyHSVYis7myV2Q4U+VZ2rixRvU9UxDzARhQPmAQ5HIV5NLOKFablqltgNbReq4seLFCIi/2IAHGxhGmCZmr4aXxiXq75Qid3eViGj3uFFChFR8DAADjZ3ARZLIhuH1fhYhcxgzhcf48Yx8CUiCiQGwKGCQZgxXJU7jrDIg6WSjcWLDyKi4IusT/pQxZLIxonwanysQmYslkAmIjIGA+BQEOFBmGHCpNxxb7BUsnF48UFEZBwGwEZjEGYcT9X4IoQ3VchaW1mFLBB48UFEZBwGwEZjEGYMVuMDwCpkRuLFBxGRcRgAG4lBmHHCqNxxb7BUsnF48UFEZBwGwEZiEGYMV+WO1Ze+3HEEXICoUsnJyVIqub5err/q6+UxSyUHDi8+iIiMwzRoRnEVhCn6ICwC03IFHKvxOWAVMmOoi4/ycrnYcFUCmRcfRESBwQDYKAzCgktfaITV+Lq5UBUyVokLDF58EBEZgwGwUdwFYZoGnDoFpKZK1bgICsICyrnQSJiWO+4Nd6WSWaghcGw2oG9f4PrrgauukouLxEReYBARBRoDYKO4K4m8bx/w8ccSqDFI8w9We+sxVokLHE8XFnx7EhEFFk+zoYQV4QKDhUZ6hIUaAocV4IiIjMUAOJQwUPM/FhrpMRZqCAxeWBARGY8BcKhgoBYYLDTSYyzUEBi8sCAiMh4D4FDBQM3/WGikV1ioITB4YUFEZDwGwKGAgVpgsNBIr7BQQ2DwwoKIyHgMgEMBAzX/Y7W3XmOVuMDghQURkfGYBs1orAjnH/pCFxYLC434ibeFGlgow3usAEdEZDwGwEbzFKhpmgwGZKB2Yc6FLljtzW8uVCWOhTJ8o4pf5OcDf/87UFXFCnBERMHGANhongK10lLg/feBvDwGap64KnThrtAI9YinKnEslOE954uFuDggPR248kpg0iT2nBMRBQsDYKO5C9RsNgnmKiuBb77hp6InrvInT5xodKvCnnM+W5XSS+WzLS6WfLZZWXz7Au4vFo4fB5qagNGj+XsiIgoWnm5DFYtieIf5kw3DfLbeY/ELIqLQwgA4FDGo8x7zJxuG+Wy9x4sFIqLQwgA4FDGo8w7zJxuK+Wy9x4sFIqLQYpoAuLa2FnfccQcSEhKQlJSEu+66C01NTR73Wb9+Pb7//e8jISEBFosFdXV1fjluQDGo8x7zJxuK+Wy9x4sFIqLQYpoA+I477sDBgwexdetW/OUvf8Hnn3+OhQsXetynpaUF+fn5eOSRR/x63IBiUOcdFrowHAtleI8XC0REocUUWSBKSkqwefNmfPnll5g2bRoA4MUXX8R1112HZ599FpmZmS73W7x4MQCgoKDAr8cNGBbF8Exf7IKFLkKCN4UyWCSDxS+IiEKNKQLgwsJCJCUldQWpAJCXlwer1YqdO3fi5ptvDupx29ra0NbW1vW4oaGhR8/fjTdFMf7xj8gN6vTFLsaOZaGLEOGpUAaLZAgWvyAiCi2mCICrqqqQmprqsCw6OhqDBg1CVVVV0I+7atUqPPHEEz1+XrcuVBTjgw+AH/4wMoM6V8UuWOgiZLgqlMEiGYLFL4iIQo+hp91ly5bBYrF4/Dp06JCRTXRp+fLlqK+v7/oqLy/3z4FVUYyJEx2/xo+XbPknT0ZuUQzmRTYV5r0V6iKgqEiGOWRlASkp8u+8eTNw7lxk/jsTERnN0B7gpUuXYt68eR63GTlyJNLT03Hq1CmH5R0dHaitrUV6enqPn7+nx42Li0NcXFyPn9dnkV7pzDkvcnFxZI+FNgFf8t6G62geVsojIgpdhgbAKSkpSElJueB2ubm5qKurw549ezB16lQAwKeffgqbzYacnJweP3+gjutXDP4850WOpAsBE/Em721FRXjnveVFABFR6DJFBJWdnY38/HwsWLAAu3btwvbt27Fo0SLMmTOnK1NDRUUFxowZg127dnXtV1VVhb179+Lo0aMAgAMHDmDv3r2ora31+riGi/SiGMyLbErMe8viF0REocwUATAAvPXWWxgzZgxmzpyJ6667DldeeSXWr1/ftf78+fMoLS1FS0tL17J169Zh8uTJWLBgAQDgqquuwuTJk/HBBx94fVxDRWLwp2nSNaiSpTIvsil5m/d2yBAZD3vggHwPp7c0LwKIiEKXKbJAAMCgQYOwceNGt+uHDx8OzemTdsWKFVixYkWvjmsod8HfkCHAjh3ANdfINPJwok91Nn488yKblDd5bydMAJ55JnxTpA0ZAqSlAfv2yetJSrIPhVAXAVOmsPgFEZERTBMARxxPRTGamqTn87XXgN/9LnyCP+dUZwMGsNiFiXkqkjFhAvDRR+GbIk2lPjt8WBK3lJZKQDxhguQDZvELIiJjMQAOVe6KYmiafKrW1wNffCH3jUeONKyZfuWc7WLmTBa7MDlXRTKGDJGe33DNjqDPf3zJJUBGhry1T5yQAhjjxwPf+Q6LXxARGYkBcKhyVxSjtBTYsAEYNUruG9fVGdI8v3OV7WLbNmDpUnNGQdTFuUjG8ePhmx3BVeqzhAQZClFXJ68rKwt46CFJ+01ERMZgZBGqXBXFUAUxBgyQe6n9+0uQGA4zhyI920UECefsCO5Sn1kswMCB8i9dVSW9wUREZBwGwGYSrkFiJGa7iGDhnB0hnIN7IqJwwgDYLDwFiZs3u843FaqY6iyihWuKNJtNhuafOydVy139O5o5uCciCicchWYWnoLEzz6T9Q89ZI7KaEx1FtHCMUWayvpQUiLB+v79MgEuOxtQxS6Z+oyIKHQwADYDTynR+vWT3tQjR6QnONQDRaY6I4RXijR91oehQ4ErrwS2b5dkLTU1wBVXMPUZEVGoYQBsBu5SogEytbyuTgLJ7duB/PzQ7gVmqjP6p3BIkeYu68P3vif/qt98I/+Wl10mwT1TnxERhQYGwGbgLiWazQa8/rp86l56KXD6dGgPF2CqM3Ji9hRp7rI+pKRIb+/w4fJveffd0hPMtzkRUWhgAGwGKiWas337gOpquWccHy/3WYuKpJc1OVmCTOcoIlg0TWYC6dvgKYtFKPdaU9B4k0WhokImmx0/bu85HjYs+MGlzSbBb1UVkJgob3nn1GeZmVK4MTGRwS8RUShhAGxW7rJClJfLBDNNA/7t34wLLPUT3SZO9NzeUO61pqDSp0hLSOi+vrkZaGsD3nxTrv2MmiCnJr3t3i21acrLJdgdM8Y+6U21l1kfiIhCDyMOs3KXFWLIEKCgACgsNC6HrvNEN5uNqc7IKxdKkVZcLD2ux47JTY6sLPleVCQT0dzNo/QnNemtqAi4+GKpRN7ZKTc8du6UIQ+qvSqlG7M+EBGFFgbAZuQqK4T6amqSGTkA8NVXgQ8snXP6At0nuu3f7769+lRnoZ7olQJOpUhLTpZgt75eUl3X1wMHD8p8z6QkGRGUkCDzI9UEuZoa4L//G/jHPwKXO9h50ltionxPSJAhD/X10u66OvnOrA9ERKGJQyDMyF1WCE2T3EuaJp/UDQ324QUWS/cxuf7gaaiDmuj2pz9JRMBUZ+QFdynSRo6Ut9Ull7ieINevH/D//h+wZ48Mm/fn0AibzT7hbfdu6flVbUhJAXJyZN3JkxKADxwIXH45sz4QEYUqBsBm5C4rRGkpsGGD5FwaMACIi7MPL9A0x0DVH5yHOowf73qi2/HjwK23SqYKd5jqjHRcpUirrwd+8xvXE+ROn5a3Xk2NvA2HD/df7mA13ldNeCstBc6elZ5fNd5XZX04c0ZSci9cCFxzDXt+iYhCFQNgM3KVFcJmsxeWGDnSvryiAvjrX6W7Sh+oWq2uMzW4WuZuuauhDlu3dp/o1tkpCVF5L5h84CpFmqsJcpomwWljo/S8XnSR49CI4mIZGnH77bKvPmuE6tnVZ5MA7Muqq6VX+cwZuZZLTJSAuqJC1ufk2INgiwWIiQHS0qTnmW91IqLQxQA4XHiaZFZQIJ/OKlBVacechy8Arpe5Wu5qqMPrr0sXmaeJbkx3Rj2kJsgVFTkWyaivt088S0mRIFXxNDRC/Qvoyy0PGiT71dYC584BR4/KW/yqqySg1jR5u588CbS0yL7JyfI8LHVMRGQe7KMIB54mxalSySdOABkZMqNoyxb57pypwVX2Bv3xPWV1UNknamo40Y0Cwt0EuTNnJGCNj5fAVn/jQj80on9/e9aI//kf4OGH5bvKJmGxAB9+CHzwgfycni4p19ragF275FgWizyHekufPCnPrya/cdIbEZE5sAc4HHhTKnngQPmUVr2x773nOHxBjRN2XjZxondDHWw2uSfc2SmRgKuJdpzoRr3kaoJcR4f0/E6Y4JiD193QiPh4eevW10uQq97CJ07IsHnVkztqlD0QPnPG3turJr0VF8uEtyNHZNgDSx0TEZkHA+Bw4G2p5IQE6ZoqK5PhDH372ocvbN4sn/z6IQ1btsi9Zm+GOiQkAN/9rnSTzZkDjB7dvZ2c6EZ+4DxBrn9/4O23gb17HauxuRsaUV8vAW1qqvQM19fL8poae0W3mhrJ9BAdLQF2QoJ926QkOd6kSRJYL1wovcJGVKMjIqKeYQAcDrwtlaz06SP3dGfMkMdDhwKffSY/jx1rX6bvKdYPdfjsM+kKGzXKcUjDxRfLwMhjx4BbbmE0QAHjPEHulluk17a4WN6i/fvbh0akpjoOjWhrk6A2Pl6yObS1yfKODpnEBkhgHRsrb/PKSuk9bmy0b6vSX19+ObM9EBGZEQPgcOVqXDBgz+bQ2Smf7CNGSOaIkydl3fTpsl18vL2nuF8/DnWgkObL0Ii4OLlmbGmR73Fxsjw6Wm50aJrjZLn6ernhER0tNzHq6yXY5nhfIiLzYgAcrtyNC66rk0GL/frJz/X1MgVedW2dOiUDGgEZIqHvKQY41IFClrdDIxITpUf38GHZXg2NUL29KtNDYqLsM3068Pnn0jtcXS3/FhzvS0RkbgyAw5WrccE2G/DGG/LzyJHy6d6/v0xys1jk68gRiQQAe09xRYVj6SsOdaAQ5c3QiOZmCWYTE6VXt6FBlg8ZIrmGNQ0YPFje+s3Ncq135ZXAj38s14b6PMJERGRODIDDlatxwcePS29vUpIMjgSku+z4cXsPcFubDH4EJMBV+8XFdS/BxaEOFOLclVX+/vdlaITKA6yW33CDBMC1tdJD3KcPe3uJiMKRaQLg2tpa/OIXv8CHH34Iq9WK2bNn44UXXsCAAQPc7rN+/Xps3LgRX331FRobG3H27FkkJSU5bDN8+HB8++23DstWrVqFZcuWBeJlGMtVr3BHhwS4aoywvgtNLVfLop3eLhzqQCbgqqyy6sG97jrPleDY20tEFJ5MEwDfcccdqKysxNatW3H+/HnMnz8fCxcuxMaNG93u09LSgvz8fOTn52P58uVut1u5ciUWLFjQ9ThenzEhnLjLFjFliuvt3S0nMhnnoREXWs6bGkRE4c0UAXBJSQk2b96ML7/8EtOmTQMAvPjii7juuuvw7LPPIjMz0+V+ixcvBgAUFBR4PH58fDzS09P92WQiIiIiClGmuLFXWFiIpKSkruAXAPLy8mC1WrFz585eH/+pp57CRRddhMmTJ2P16tXo6Ojo9TGJiIiIKDSZoge4qqoKqampDsuio6MxaNAgVFVV9erY999/P6ZMmYJBgwZhx44dWL58OSorK/Hcc8+53aetrQ1tatIYgIaGhl61gYiIiIiCx9AAeNmyZXj66ac9blOiz2EbAEuWLOn6eeLEiYiNjcXdd9+NVatWIU5lyHeyatUqPPHEE92WMxAmIiOpc5CmaT7vq/bheYyIjNabc5m3DA2Aly5dinnz5nncZuTIkUhPT8epU6cclnd0dKC2ttbvY3dzcnLQ0dGB48ePIysry+U2y5cvdwicKyoqMHbsWAwdOtSvbSEi6onGxkYkqgofPuwDgOcxIgoZPTmXecvQADglJQUp+hqlbuTm5qKurg579uzB1KlTAQCffvopbDYbcnJy/NqmvXv3wmq1dhtyoRcXF+fQOzxgwAAUFxdj7NixKC8vR0JCgl/bFAwNDQ0YOnQo228Qs7cfMP9rCJf2FxcXu50Y7ElmZqbpz2NA+Pwd2X5jmL39gPlfQ2/PZd4yxRjg7Oxs5OfnY8GCBVi3bh3Onz+PRYsWYc6cOV2/nIqKCsycORNvvPEGpk+fDkDGDldVVeHo0aMAgAMHDiA+Ph7Dhg3DoEGDUFhYiJ07d+Lqq69GfHw8CgsL8cADD+CnP/0pBg4c6HX7rFYrBg8eDABISEgw5RtOYfuNZfb2A+Z/DWZv/+DBg2HtQeLicDqPAeZ/DWy/sczefsD8r6Gn5zJvmSILBAC89dZbGDNmDGbOnInrrrsOV155JdavX9+1/vz58ygtLUVLS0vXsnXr1mHy5MldOX6vuuoqTJ48GR988AEA6cl95513MGPGDIwbNw6/+c1v8MADDzgcl4iIiIjCiyl6gAFg0KBBHoteDB8+vNtg6RUrVmDFihVu95kyZQq++OILfzWRiIiIiEzAND3AoS4uLg6PP/6428wRoY7tN5bZ2w+Y/zWw/eb/HQDmfw1sv7HM3n7A/K8hWO23aIHMMUFEREREFGLYA0xEREREEYUBMBERERFFFAbARERERBRRGAB7qba2FnfccQcSEhKQlJSEu+66C01NTR73Wb9+Pb7//e8jISEBFosFdXV13bYZPnw4LBaLw9dTTz1lmvb35LjBfA2tra247777cNFFF2HAgAGYPXs2qqurHbZx/v1bLBa88847vW7vSy+9hOHDh6NPnz7IycnBrl27PG7/7rvvYsyYMejTpw8mTJiAjz/+2GG9pml47LHHkJGRgb59+yIvLw9HjhzpdTuD1f558+Z1+z3n5+cHrP2Ab6/h4MGDmD17dtf/5Jo1a3p9zN7yd/tXrFjR7W+QlJTEc1kPjxus9ht5HgN4LjP6XMbzmCNX57ExY8b43jCNvJKfn69NmjRJ++KLL7T//d//1S699FLt9ttv97jP888/r61atUpbtWqVBkA7e/Zst20uvvhibeXKlVplZWXXV1NTk2na35PjBvM13HPPPdrQoUO1bdu2abt379a+853vaFdccYXDNgC0V1991eFvcO7cuV619Z133tFiY2O1DRs2aAcPHtQWLFigJSUladXV1S633759uxYVFaU988wzWnFxsfbrX/9ai4mJ0Q4cONC1zVNPPaUlJiZqmzZt0vbt26fdcMMN2ogRI3rd1mC1/84779Ty8/Mdfs+1tbV+b3tPX8OuXbu0Bx98UHv77be19PR07fnnn+/1MUOt/Y8//rg2YMAAbdy4cdpHH32kbdq0SRsxYgTPZT08brDab9R5TNN4LjP6XMbzWPf2P/7449q4ceMcfv+nT5/2uW0MgL1QXFysAdC+/PLLrmV//etfNYvFolVUVFxw/88++8zjh4arP7A/Bar9vT2uL3ryXHV1dVpMTIz27rvvdi0rKSnRAGiFhYVdywBo7733nl/bO336dO2+++7retzZ2allZmZqq1atcrn9T37yE+366693WJaTk6PdfffdmqZpms1m09LT07XVq1d3ra+rq9Pi4uK0t99+269tD0T7NU0+NG688Ua/t9UdX1+Dnrv/y94c01eBaP+9997Lc5mB5zKzncc0jecy5/ZrWnDPZTyPPd9t+eOPP65NmjSp123jEAgvFBYWIikpCdOmTetalpeXB6vVip07d/b6+E899RQuuugiTJ48GatXr0ZHR0evj6kXqPYH+vfS2+fas2cPzp8/j7y8vK5lY8aMwbBhw1BYWOiw7X333Yfk5GRMnz4dGzZs6FZUxRft7e3Ys2ePw/NarVbk5eV1e17969NvDwCzZs3q2v7YsWOoqqpy2CYxMRE5OTlujxlK7VcKCgqQmpqKrKws/PznP8eZM2f82nalJ6/BiGMG+7lOnDgBALjhhhswcuRI3HHHHRg9ejTPZUE6l5npPAbwXOaq/UowzmU8j7l35MgRZGZmdp3HysrKfD6GaSrBGamqqgqpqakOy6KjozFo0CBUVVX16tj3338/pkyZgkGDBmHHjh1Yvnw5Kisr8dxzz/XquHqBan8gfy/+eK6qqirExsYiKSnJYXlaWprDPitXrsQPfvAD9OvXD5988gnuvfdeNDU14f777+9RW2tqatDZ2Ym0tLRuz3vo0CG3bXW1vWqn+u5pG38JRPsBID8/H7fccgtGjBiBb775Bo888giuvfZaFBYWIioqyvDXYMQxg/1cAwcOREZGBjZv3ozKyko88cQTuPrqqzFw4ECey4JwLjPTeQzgucxd24J1LuN5zLWcnBy89tpryMrK6jqPfe9738PXX3+N+Ph4r48T0QHwsmXL8PTTT3vcpqSkJKBtWLJkSdfPEydORGxsLO6++26sWrXqglVQQqH9vRUKr+HRRx/t+nny5Mlobm7G6tWre/XBQd3NmTOn6+cJEyZg4sSJuOSSS1BQUICZM2ca2DLzc/V/9MADD+CBBx7oelxSUoLRo0ejsLAQEydOxMSJE5GTk4OLL7641z2FQGSfy0Kh/TyPBQ/PZca69tpru37Wn8f+/Oc/46677vL6OBEdAC9duhTz5s3zuM3IkSORnp6OU6dOOSzv6OhAbW0t0tPT/dqmnJwcdHR04Pjx48jKyvK4rdHt98dxA/ka0tPT0d7ejrq6Oofek+rqao/ty8nJwZNPPom2trYelWJMTk5GVFRUt1nanp43PT3d4/bqe3V1NTIyMhy2ueyyy3xuoyeBaL8rI0eORHJyMo4ePer3D42evAYjjumv53L+P5o5cybmzp2LO++8s2uZq/+jpKQkjBo1Cl999RXPZb04bjiexwCey7zZHgjcuSzSzmM9lZSUhNGjR+Po0aM+7RfRY4BTUlIwZswYj1+xsbHIzc1FXV0d9uzZ07Xvp59+CpvNhpycHL+2ae/evbBard1uk4Vi+/1x3EC+hqlTpyImJgbbtm3rWlZaWoqysjLk5ua6bdPevXsxcODAHn9oxMbGYurUqQ7Pa7PZsG3bNrfPm5ub67A9AGzdurVr+xEjRiA9Pd1hm4aGBuzcudPjawmV9rty4sQJnDlzxuFD0F968hqMOKa/nsv5/ygmJgZpaWkX/D9qampCaWkpAPBc1ovjhuN5DOC5zFX7XQnUuSzSzmM91dTUhG+++cb333+vp9FFiPz8fG3y5Mnazp07tb///e/aqFGjHFLXnDhxQsvKytJ27tzZtayyslIrKirSXnnlFQ2A9vnnn2tFRUXamTNnNE3TtB07dmjPP/+8tnfvXu2bb77R3nzzTS0lJUWbO3euKdrvzXGNfg333HOPNmzYMO3TTz/Vdu/ereXm5mq5ubld6z/44APtlVde0Q4cOKAdOXJEe/nll7V+/fppjz32WK/a+s4772hxcXHaa6+9phUXF2sLFy7UkpKStKqqKk3TNO1f//VftWXLlnVtv337di06Olp79tlntZKSEu3xxx93mTooKSlJe//997X9+/drN954Y0BTB/mz/Y2NjdqDDz6oFRYWaseOHdP+9re/aVOmTNFGjRqltba2+r39PXkNbW1tWlFRkVZUVKRlZGRoDz74oFZUVKQdOXLE62OGevuXLl2qTZ8+XRs3bpz2yiuvaNOmTdOsVqt2yy23dG3Dc1lgz2VmOo9pGs9lRp/LeB5zfR4rKCjQjh07pm3fvl3Ly8vTkpOTtVOnTvnUNgbAXjpz5ox2++23awMGDNASEhK0+fPna42NjV3rjx07pgHQPvvss65ljz/+uAag29err76qaZqm7dmzR8vJydESExO1Pn36aNnZ2dpvf/vbgPwTBaL93hzX6Ndw7tw57d5779UGDhyo9evXT7v55pu1ysrKrvV//etftcsuu0wbMGCA1r9/f23SpEnaunXrtM7Ozl6398UXX9SGDRumxcbGatOnT9e++OKLrnUzZszQ7rzzToft//znP2ujR4/WYmNju/K06tlsNu3RRx/V0tLStLi4OG3mzJlaaWlpr9sZjPa3tLRo11xzjZaSkqLFxMRoF198sbZgwYKAnHB7+hrU+8f5a8aMGV4fM9Tbf9ttt2lpaWma1WrVLBaLFhMTo/34xz/mucyL4xrZfiPPY5rGc5nR5zKex7qfxzIyMrTY2Fht8ODB2m233aYdPXrU53ZZNM0Psx+IiIiIiEwioscAExEREVHkYQBMRERERBGFATARERERRRQGwEREREQUURgAExEREVFEYQBMRERERBGFATARERERRRQGwEREREQUURgAExEREVFEYQBMFCDz5s2DxWKBxWJBbGwsLr30UqxcuRIdHR0AAE3TsH79euTk5GDAgAFISkrCtGnTsGbNGrS0tAAADh48iNmzZ2P48OGwWCxYs2aNga+IiCIRz2UUjhgAEwVQfn4+KisrceTIESxduhQrVqzA6tWrAQD/+q//isWLF+PGG2/EZ599hr179+LRRx/F+++/j08++QQA0NLSgpEjR+Kpp55Cenq6kS+FiCIYz2UUbiyapmlGN4IoHM2bNw91dXXYtGlT17JrrrkGjY2NeOCBB3Dbbbdh06ZNuPHGGx320zQNDQ0NSExMdFg+fPhwLF68GIsXLw5C64mIBM9lFI7YA0wURH379kV7ezveeustZGVldfvAAACLxdLtA4OIKJTwXEZmxwCYKAg0TcPf/vY3bNmyBT/4wQ9w5MgRZGVlGd0sIiKf8FxG4YIBMFEA/eUvf8GAAQPQp08fXHvttbjtttuwYsUKcOQREZkJz2UUbqKNbgBROLv66qvxhz/8AbGxscjMzER0tPzLjR49GocOHTK4dURE3uG5jMINe4CJAqh///649NJLMWzYsK4PDAD4P//n/+Dw4cN4//33u+2jaRrq6+uD2UwiIo94LqNwwwCYyAA/+clPcNttt+H222/Hb3/7W+zevRvffvst/vKXvyAvLw+fffYZAKC9vR179+7F3r170d7ejoqKCuzduxdHjx41+BUQEfFcRubFNGhEAeIqdZCezWbD+vXrsWHDBhw8eBDR0dEYNWoU5s6diwULFqBv3744fvw4RowY0W3fGTNmoKCgILAvgIgIPJdReGIATEREREQRhUMgiIiIiCiiMAAmIiIioojCAJiIiIiIIgoDYCIiIiKKKAyAiYiIiCiiMAAmIiIioojCAJiIiIiIIgoDYCIiIiKKKAyAiYiIiCiiMAAmIiIioojCAJiIiIiIIgoDYCIiIiKKKP8fWT0tlZbJ1pYAAAAASUVORK5CYII=\n" }, "metadata": {} } ], "source": [ "X_kpca = rbf_kernel_pca(X, gamma=15, n_components=2)\n", "\n", "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))\n", "ax[0].scatter(X_kpca[y==0, 0], X_kpca[y==0, 1],\n", " color='red', marker='^', alpha=0.5)\n", "ax[0].scatter(X_kpca[y==1, 0], X_kpca[y==1, 1],\n", " color='blue', marker='o', alpha=0.5)\n", "\n", "ax[1].scatter(X_kpca[y==0, 0], np.zeros((50, 1))+0.02,\n", " color='red', marker='^', alpha=0.5)\n", "ax[1].scatter(X_kpca[y==1, 0], np.zeros((50, 1))-0.02,\n", " color='blue', marker='o', alpha=0.5)\n", "\n", "ax[0].set_xlabel('PC1')\n", "ax[0].set_ylabel('PC2')\n", "ax[1].set_ylim([-1, 1])\n", "ax[1].set_yticks([])\n", "ax[1].set_xlabel('PC1')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('images/05_14.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "MhgMuq_2EjG7" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "EWhZCKfMEjG7" }, "source": [ "### 예제 2: 동심원 분리하기" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:34.204102Z", "iopub.status.busy": "2021-10-23T05:55:34.179005Z", "iopub.status.idle": "2021-10-23T05:55:34.361782Z", "shell.execute_reply": "2021-10-23T05:55:34.362406Z" }, "id": "PHt9XURIEjG7", "outputId": "533836a4-6baf-4c70-c111-55e1bbc6be40" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "from sklearn.datasets import make_circles\n", "\n", "X, y = make_circles(n_samples=1000, random_state=123, noise=0.1, factor=0.2)\n", "\n", "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='red', marker='^', alpha=0.5)\n", "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='blue', marker='o', alpha=0.5)\n", "\n", "plt.tight_layout()\n", "# plt.savefig('images/05_15.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 307 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:34.374986Z", "iopub.status.busy": "2021-10-23T05:55:34.373310Z", "iopub.status.idle": "2021-10-23T05:55:34.592865Z", "shell.execute_reply": "2021-10-23T05:55:34.593320Z" }, "id": "vAzJy-ojEjG7", "outputId": "f5fbf5cc-72ac-4e07-fb0a-a29b0f19c810" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "scikit_pca = PCA(n_components=2)\n", "X_spca = scikit_pca.fit_transform(X)\n", "\n", "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))\n", "\n", "ax[0].scatter(X_spca[y == 0, 0], X_spca[y == 0, 1],\n", " color='red', marker='^', alpha=0.5)\n", "ax[0].scatter(X_spca[y == 1, 0], X_spca[y == 1, 1],\n", " color='blue', marker='o', alpha=0.5)\n", "\n", "ax[1].scatter(X_spca[y == 0, 0], np.zeros((500, 1)) + 0.02,\n", " color='red', marker='^', alpha=0.5)\n", "ax[1].scatter(X_spca[y == 1, 0], np.zeros((500, 1)) - 0.02,\n", " color='blue', marker='o', alpha=0.5)\n", "\n", "ax[0].set_xlabel('PC1')\n", "ax[0].set_ylabel('PC2')\n", "ax[1].set_ylim([-1, 1])\n", "ax[1].set_yticks([])\n", "ax[1].set_xlabel('PC1')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('images/05_16.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 307 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:34.602221Z", "iopub.status.busy": "2021-10-23T05:55:34.601414Z", "iopub.status.idle": "2021-10-23T05:55:35.270552Z", "shell.execute_reply": "2021-10-23T05:55:35.271118Z" }, "id": "lnVjnP93EjG7", "outputId": "0794029a-14d3-4e08-be27-681a09d962f4" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "X_kpca = rbf_kernel_pca(X, gamma=15, n_components=2)\n", "\n", "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(7, 3))\n", "ax[0].scatter(X_kpca[y == 0, 0], X_kpca[y == 0, 1],\n", " color='red', marker='^', alpha=0.5)\n", "ax[0].scatter(X_kpca[y == 1, 0], X_kpca[y == 1, 1],\n", " color='blue', marker='o', alpha=0.5)\n", "\n", "ax[1].scatter(X_kpca[y == 0, 0], np.zeros((500, 1)) + 0.02,\n", " color='red', marker='^', alpha=0.5)\n", "ax[1].scatter(X_kpca[y == 1, 0], np.zeros((500, 1)) - 0.02,\n", " color='blue', marker='o', alpha=0.5)\n", "\n", "ax[0].set_xlabel('PC1')\n", "ax[0].set_ylabel('PC2')\n", "ax[1].set_ylim([-1, 1])\n", "ax[1].set_yticks([])\n", "ax[1].set_xlabel('PC1')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('images/05_17.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "X7mOuyN_EjG7" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "4-NJGCOhEjG7" }, "source": [ "## 5.3.3 새로운 데이터 포인트 투영하기" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:35.281007Z", "iopub.status.busy": "2021-10-23T05:55:35.280202Z", "iopub.status.idle": "2021-10-23T05:55:35.282915Z", "shell.execute_reply": "2021-10-23T05:55:35.283419Z" }, "id": "I6mzj4vMEjG7" }, "outputs": [], "source": [ "from scipy.spatial.distance import pdist, squareform\n", "from numpy import exp\n", "from scipy.linalg import eigh\n", "import numpy as np\n", "\n", "def rbf_kernel_pca(X, gamma, n_components):\n", " \"\"\"\n", " RBF 커널 PCA 구현\n", "\n", " 매개변수\n", " ------------\n", " X: {넘파이 ndarray}, shape = [n_samples, n_features]\n", "\n", " gamma: float\n", " RBF 커널 튜닝 매개변수\n", "\n", " n_components: int\n", " 반환할 주성분 개수\n", "\n", " Returns\n", " ------------\n", " alphas: {넘파이 ndarray}, shape = [n_samples, k_features]\n", " 투영된 데이터셋\n", "\n", " lambdas: list\n", " 고윳값\n", "\n", " \"\"\"\n", " # MxN 차원의 데이터셋에서 샘플 간의 유클리디안 거리의 제곱을 계산합니다.\n", " sq_dists = pdist(X, 'sqeuclidean')\n", "\n", " # 샘플 간의 거리를 정방 대칭 행렬로 변환합니다.\n", " mat_sq_dists = squareform(sq_dists)\n", "\n", " # 커널 행렬을 계산합니다.\n", " K = exp(-gamma * mat_sq_dists)\n", "\n", " # 커널 행렬을 중앙에 맞춥니다.\n", " N = K.shape[0]\n", " one_n = np.ones((N, N)) / N\n", " K = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n)\n", "\n", " # 중앙에 맞춰진 커널 행렬의 고윳값과 고유 벡터를 구합니다.\n", " # scipy.linalg.eigh 함수는 오름차순으로 반환합니다.\n", " eigvals, eigvecs = eigh(K)\n", " eigvals, eigvecs = eigvals[::-1], eigvecs[:, ::-1]\n", "\n", " # 최상위 k 개의 고유 벡터를 선택합니다(투영 결과).\n", " alphas = np.column_stack([eigvecs[:, i]\n", " for i in range(n_components)])\n", "\n", " # 고유 벡터에 상응하는 고윳값을 선택합니다.\n", " lambdas = [eigvals[i] for i in range(n_components)]\n", "\n", " return alphas, lambdas" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:35.294416Z", "iopub.status.busy": "2021-10-23T05:55:35.290250Z", "iopub.status.idle": "2021-10-23T05:55:35.317555Z", "shell.execute_reply": "2021-10-23T05:55:35.315854Z" }, "id": "BSuLhPTBEjG8" }, "outputs": [], "source": [ "X, y = make_moons(n_samples=100, random_state=123)\n", "alphas, lambdas = rbf_kernel_pca(X, gamma=15, n_components=1)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:35.329412Z", "iopub.status.busy": "2021-10-23T05:55:35.327166Z", "iopub.status.idle": "2021-10-23T05:55:35.336760Z", "shell.execute_reply": "2021-10-23T05:55:35.334567Z" }, "id": "-DYnonckEjG8", "outputId": "cf3c528d-044d-4802-b6bc-6af2905e50b9" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([1.8713, 0.0093])" ] }, "metadata": {}, "execution_count": 58 } ], "source": [ "x_new = X[25]\n", "x_new" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:35.345934Z", "iopub.status.busy": "2021-10-23T05:55:35.344707Z", "iopub.status.idle": "2021-10-23T05:55:35.351033Z", "shell.execute_reply": "2021-10-23T05:55:35.352106Z" }, "id": "t2lcwezdEjG8", "outputId": "0491ad8f-f64d-4d83-855e-f896ddfccf63" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([0.0788])" ] }, "metadata": {}, "execution_count": 59 } ], "source": [ "x_proj = alphas[25] # 원본 투영\n", "x_proj" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2021-10-23T05:55:35.368945Z", "iopub.status.busy": "2021-10-23T05:55:35.366960Z", "iopub.status.idle": "2021-10-23T05:55:35.379713Z", "shell.execute_reply": "2021-10-23T05:55:35.374085Z" }, "id": "K67SPqwPEjG8", "outputId": "f7bdd23e-f1d7-427c-c86f-029da1d5d87c" }, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([0.0788])" ] }, "metadata": {}, "execution_count": 60 } ], "source": [ "def project_x(x_new, X, gamma, alphas, lambdas):\n", " pair_dist = np.array([np.sum((x_new - row)**2) for row in X])\n", " k = np.exp(-gamma * pair_dist)\n", " return k.dot(alphas / lambdas)\n", "\n", "# 새로운 데이터포인트를 투영합니다.\n", "x_reproj = project_x(x_new, X, gamma=15, alphas=alphas, lambdas=lambdas)\n", "x_reproj" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:35.395440Z", "iopub.status.busy": "2021-10-23T05:55:35.393348Z", "iopub.status.idle": "2021-10-23T05:55:35.559154Z", "shell.execute_reply": "2021-10-23T05:55:35.559650Z" }, "id": "NqAizbQcEjG8", "outputId": "24032614-50e8-4b66-ea2e-a96f05b077fb" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ], "source": [ "plt.scatter(alphas[y == 0, 0], np.zeros((50)),\n", " color='red', marker='^', alpha=0.5)\n", "plt.scatter(alphas[y == 1, 0], np.zeros((50)),\n", " color='blue', marker='o', alpha=0.5)\n", "plt.scatter(x_proj, 0, color='black',\n", " label='Original projection of point X[25]', marker='^', s=100)\n", "plt.scatter(x_reproj, 0, color='green',\n", " label='Remapped point X[25]', marker='x', s=500)\n", "plt.yticks([], [])\n", "plt.legend(scatterpoints=1)\n", "\n", "plt.tight_layout()\n", "# plt.savefig('images/05_18.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "kifU6Zl1EjG8" }, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": { "id": "QRFvGBFJEjG8" }, "source": [ "## 5.3.4 사이킷런의 커널 PCA" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:35.569746Z", "iopub.status.busy": "2021-10-23T05:55:35.568622Z", "iopub.status.idle": "2021-10-23T05:55:35.805594Z", "shell.execute_reply": "2021-10-23T05:55:35.806058Z" }, "id": "9oStyswlEjG9", "outputId": "cb982d58-31cf-4909-fe2b-7371dddb082d" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "from sklearn.decomposition import KernelPCA\n", "\n", "X, y = make_moons(n_samples=100, random_state=123)\n", "scikit_kpca = KernelPCA(n_components=2, kernel='rbf', gamma=15)\n", "X_skernpca = scikit_kpca.fit_transform(X)\n", "\n", "plt.scatter(X_skernpca[y == 0, 0], X_skernpca[y == 0, 1],\n", " color='red', marker='^', alpha=0.5)\n", "plt.scatter(X_skernpca[y == 1, 0], X_skernpca[y == 1, 1],\n", " color='blue', marker='o', alpha=0.5)\n", "\n", "plt.xlabel('PC1')\n", "plt.ylabel('PC2')\n", "plt.tight_layout()\n", "# plt.savefig('images/05_19.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "0aHpcz4zEjG9" }, "source": [ "사이킷런의 매니폴드 알고리즘을 반달 모양 데이터셋과 동심원 데이터셋에 적용해 보겠습니다. 먼저 변환된 2차원 데이터셋을 그래프로 그리기 위한 간단한 함수를 정의합니다." ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "execution": { "iopub.execute_input": "2021-10-23T05:55:35.812832Z", "iopub.status.busy": "2021-10-23T05:55:35.809522Z", "iopub.status.idle": "2021-10-23T05:55:35.815424Z", "shell.execute_reply": "2021-10-23T05:55:35.814770Z" }, "id": "4siFOwEDEjG9" }, "outputs": [], "source": [ "def plot_manifold(X, y, savefig_name):\n", "\n", " plt.scatter(X[y == 0, 0], X[y == 0, 1],\n", " color='red', marker='^', alpha=0.5)\n", " plt.scatter(X[y == 1, 0], X[y == 1, 1],\n", " color='blue', marker='o', alpha=0.5)\n", "\n", " plt.xlabel('PC1')\n", " plt.ylabel('PC2')\n", " plt.tight_layout()\n", " # plt.savefig(savefig_name, dpi=300)\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "DqzS7onvEjG9" }, "source": [ "지역 선형 임베딩(Locally Linear Embedding)은 이웃한 샘플 간의 거리를 유지하는 저차원 투영을 찾습니다. 지역 선형 임베딩을 구현한 사이킷런의 `LocallyLinearEmbedding` 클래스를 앞에서 적재한 반달 모양 데이터셋에 적용해 보겠습니다." ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:35.823203Z", "iopub.status.busy": "2021-10-23T05:55:35.821880Z", "iopub.status.idle": "2021-10-23T05:55:36.042562Z", "shell.execute_reply": "2021-10-23T05:55:36.043038Z" }, "id": "fbIHXIAsEjG9", "outputId": "e0bd45ba-48bd-497b-b0fe-32203afc3077" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "from sklearn.manifold import LocallyLinearEmbedding\n", "\n", "lle = LocallyLinearEmbedding(n_components=2, random_state=1)\n", "X_lle = lle.fit_transform(X)\n", "\n", "plot_manifold(X_lle, y, 'images/05_lle_moon.png')" ] }, { "cell_type": "markdown", "metadata": { "id": "2pGF6ts1EjG9" }, "source": [ "t-SNE(t-distributed Stochastic Neighbor Embedding)는 데이터 포인트 간의 유사도를 결합 확률(joint probability)로 변환하고, 저차원과 고차원의 확률 사이에서 쿨백-라이블러(Kullback-Leibler) 발산을 최소화합니다. t-SNE는 특히 고차원 데이터셋을 시각화하는데 뛰어난 성능을 냅니다. 사이킷런에는 `TSNE` 클래스에 구현되어 있습니다." ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 486 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:36.052171Z", "iopub.status.busy": "2021-10-23T05:55:36.048529Z", "iopub.status.idle": "2021-10-23T05:55:36.681559Z", "shell.execute_reply": "2021-10-23T05:55:36.680928Z" }, "id": "pqZx-bjGEjG9", "outputId": "911acca2-9715-46cc-8e4e-0dcf1933c0f8" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "from sklearn.manifold import TSNE\n", "\n", "tsne = TSNE(n_components=2, random_state=1)\n", "X_tsne = tsne.fit_transform(X)\n", "\n", "plot_manifold(X_tsne, y, 'images/05_tsne_moon.png')" ] }, { "cell_type": "markdown", "metadata": { "id": "UtmSZYnKEjG9" }, "source": [ "위와 비슷한 방식으로 `KernelPCA`, `LocallyLinearEmbedding`, `TSNE`를 동심원 데이터셋에 적용해 보겠습니다." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:36.688774Z", "iopub.status.busy": "2021-10-23T05:55:36.687040Z", "iopub.status.idle": "2021-10-23T05:55:37.010873Z", "shell.execute_reply": "2021-10-23T05:55:37.011314Z" }, "id": "iRCNOjo6EjG-", "outputId": "f1589f62-88a2-460d-b83a-71666acbbba6", "scrolled": true }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "from sklearn.datasets import make_circles\n", "\n", "X, y = make_circles(n_samples=1000, random_state=123, noise=0.1, factor=0.2)\n", "\n", "scikit_kpca = KernelPCA(n_components=2, kernel='rbf', gamma=15)\n", "X_skernpca = scikit_kpca.fit_transform(X)\n", "\n", "plot_manifold(X_skernpca, y, 'images/05_kpca_circles.png')" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:37.015316Z", "iopub.status.busy": "2021-10-23T05:55:37.014510Z", "iopub.status.idle": "2021-10-23T05:55:37.381273Z", "shell.execute_reply": "2021-10-23T05:55:37.381723Z" }, "id": "Awt6SJtlEjG-", "outputId": "636018d4-e27a-44a3-a6fe-4707fa9cdab8" }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "from sklearn.manifold import LocallyLinearEmbedding\n", "\n", "lle = LocallyLinearEmbedding(n_components=2, random_state=1)\n", "X_lle = lle.fit_transform(X)\n", "\n", "plot_manifold(X_lle, y, 'images/05_lle_circles.png')" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 486 }, "execution": { "iopub.execute_input": "2021-10-23T05:55:37.390092Z", "iopub.status.busy": "2021-10-23T05:55:37.389230Z", "iopub.status.idle": "2021-10-23T05:55:40.151106Z", "shell.execute_reply": "2021-10-23T05:55:40.150117Z" }, "id": "j2LjGy2nEjG-", "outputId": "a108fc4d-ec64-4c90-da50-75b38ac11b63", "scrolled": true }, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ], "source": [ "from sklearn.manifold import TSNE\n", "\n", "tsne = TSNE(n_components=2, random_state=1)\n", "X_tsne = tsne.fit_transform(X)\n", "\n", "plot_manifold(X_tsne, y, 'images/05_tsne_circles.png')" ] } ], "metadata": { "anaconda-cloud": {}, "colab": { "name": "ch05.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" }, "toc": { "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 0 }