{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# 파이썬 2와 파이썬 3 지원\n", "from __future__ import division, print_function, unicode_literals\n", "\n", "# 공통\n", "import numpy as np\n", "import os\n", "\n", "# 일관된 출력을 위해 유사난수 초기화\n", "np.random.seed(42)\n", "\n", "# 맷플롯립 설정\n", "%matplotlib inline\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['axes.labelsize'] = 14\n", "plt.rcParams['xtick.labelsize'] = 12\n", "plt.rcParams['ytick.labelsize'] = 12\n", "\n", "# 한글출력\n", "plt.rcParams['font.family'] = 'AppleGothic'\n", "plt.rcParams['axes.unicode_minus'] = False" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# CHAPTER 5. 서포트 벡터 머신" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- **서포트 벡터 머신**Support Vector Machine(SVM) : 매우 강력하고 선형이나 비선형 분류, 회귀, 이상치 탐색에도 사용할 수 있는 다목적 머신러닝 모델
\n", "- 특히 복잡한 분류 문제에 잘 들어맞으며 작거나 중간 크기의 데이터셋에 적합" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## 5.1 선형 SVM 분류" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**그림 5-1 라지 마진 분류**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- SVM의 기본 아이디어 ([그림 5-1]은 붓꽃 데이터셋의 일부)
\n", " - 왼쪽 그래프에 세 개의 선형 분류기에서 만들어진 결정 경계가 보임\n", " - 점선 모델은 클래스를 적절하게 분류하지 못하고 있고, 다른 두 모델은 결정 경계가 샘플에 너무 가까워 새로운 샘플에 대해서는 잘 작동하지 못할 것\n", " - 오른쪽 그래프에 있는 실선은 SVM 분류기의 결정 경계\n", " - 이 직선은 두 개의 클래스를 나누고 있고 제일 가까운 훈련 샘플로부터 가능한 한 멀리 떨어져 있음\n", " - SVM 분류기를 클래스 사이에 가장 폭이 넓은 도로를 찾는 것으로 생각할 수 있음. 그래서 **라지 마진 분류**large margin classification라고 함\n", " - 도로 바깥쪽에 훈련 샘플을 추가해도 결정 경계에는 영향을 미치지 않음\n", " - 도로 경계에 위치한 샘플에 의해 전적으로 결정됨. 이런 샘플을 **서포트 벡터**support vector라고 함([그림 5-1]에 동그라미 표시)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- SVM은 특성의 스케일에 민감\n", "- 특성의 스케일을 조정하면 결정 경계가 훨씬 좋아짐([그림 5-2]의 오른쪽 그래프)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**그림 5-2 특성 스케일에 따른 민감성**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.1.1 소프트 마진 분류" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- **하드 마진 분류**hard margin classification : 모든 샘플이 도로 바깥쪽에 올바르게 분류됨\n", "- 하드 마진 분류의 두 가지 문제점\n", " - 데이터가 선형적으로 구분될 수 있어야 제대로 작동\n", " - 이상치에 민감\n", " - [그림 5-3]의 왼쪽 그래프에서는 이상치가 하나 있어 하드 마진을 찾을 수 없고, 오른쪽 그래프의 결정 경계는 [그림 5-1]과 매우 다르고 일반화가 잘될 것 같지 않음" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**그림 5-3 이상치에 민감한 하드 마진**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 이런 문제를 피하려면 좀 더 유연한 모델이 필요함\n", "- 도로의 폭을 가능한 한 넓게 유지, **마진 오류**margin violation(즉, 샘플이 도로 중간이나 심지어 반대쪽에 있는 경우) 사이에 적절한 균형을 잡아야 함\n", "- 이를 **소프트 마진 분류**soft margin classification라고 함" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 사이킷런의 SVM 모델에서는 C 하이퍼파라미터를 사용해 이 균형을 조절할 수 있음\n", "- C 값을 줄이면 도로의 폭이 넓어지지만 마진 오류도 커짐\n", "- [그림 5-4]의 왼쪽을 보면 큰 C 값을 사용해 분류기가 마진 오류를 적게 냈지만 마진이 좁아졌음\n", "- 오른쪽에서는 작은 C 값을 사용해 마진이 넓어졌지만 많은 샘플이 도로 안에 포함되었음. 그러나 더 잘 일반화될 것 같아 보임\n", "- 대부분의 마진 오류는 결정 경계를 기준으로 올바른 클래스로 분류되기 때문에 이 훈련 세트에서 예측 에러는 마진 오류보다 작음" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**그림 5-4 좁은 마진과 넓은 마진**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "다음 코드는 붓꽃 데이터셋을 적재하고, 특성 스케일을 변경하고, Iris-Virginia 품종을 감지하기 위해 선형 SVM 모델을 훈련시킴
\n", "(C=1, **힌지 손실**hinge loss함수를 적용한 LinearSVC 클래스를 사용)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Pipeline(memory=None,\n", " steps=[('scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('linear_svc', LinearSVC(C=1, class_weight=None, dual=True, fit_intercept=True,\n", " intercept_scaling=1, loss='hinge', max_iter=1000, multi_class='ovr',\n", " penalty='l2', random_state=42, tol=0.0001, verbose=0))])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "from sklearn import datasets\n", "from sklearn.pipeline import Pipeline\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.svm import LinearSVC\n", "\n", "iris = datasets.load_iris()\n", "X = iris[\"data\"][:, (2, 3)] # 꽃잎 길이, 꽃잎 너비\n", "y = (iris[\"target\"] == 2).astype(np.float64) # Iris-Virginica\n", "\n", "svm_clf = Pipeline([\n", " (\"scaler\", StandardScaler()),\n", " (\"linear_svc\", LinearSVC(C=1, loss=\"hinge\", random_state=42)),\n", " ])\n", "\n", "svm_clf.fit(X, y)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "svm_clf.predict([[5.5, 1.7]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- LinearSVC는 규제에 편향을 포함. 그래서 훈련 세트에서 평균을 빼서 중앙에 맞춰야 함\n", "- StandardScaler를 사용하여 데이터 스케일을 맞추면 자동으로 됨\n", "- loss 매개변수를 \"hinge\"로 지정해야 함(기본값은 \"squared_hinge\")\n", "- 훈련 샘플보다 특성이 많지 않다면 성능을 높이기 위해 dual 매개변수를 False로 지정" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## 5.2 비선형 SVM 분류" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 비선형 데이터셋을 다루는 한 가지 방법은 다항 특성과 같은 특성을 더 추가하는 것\n", "- [그림 5-5]의 왼쪽 그래프는 하나의 특성 x1만을 가짐. 이 데이터셋은 선형적으로 구분이 안 됨\n", "- 하지만 두 번째 특성 x2 = (x1)2을 추가하여 만들어진 2차원 데이터셋은 선형적으로 구분할 수 있음" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**그림 5-5 특성을 추가하여 선형적으로 구분되는 데이터셋 만들기**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 사이킷런의 PolynomialFeatures를 사용해 특성을 추가\n", "- 이를 moons 데이터셋에 적용(사이킷런의 make_moons 함수를 사용해서 만든 두 개의 반달 모양 데이터셋)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "사이킷런 0.20 버전부터는 LinearSVC가 max_iter 반복 안에 수렴하지 않을 경우 반복 횟수 증가 경고가 나옵니다. 경고 메세지를 피하기 위해 max_iter 매개변수의 기본값을 1,000에서 2,000으로 증가시킵니다." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Pipeline(memory=None,\n", " steps=[('poly_features', PolynomialFeatures(degree=3, include_bias=True, interaction_only=False)), ('scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('svm_clf', LinearSVC(C=10, class_weight=None, dual=True, fit_intercept=True,\n", " intercept_scaling=1, loss='hinge', max_iter=2000, multi_class='ovr',\n", " penalty='l2', random_state=42, tol=0.0001, verbose=0))])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.datasets import make_moons\n", "from sklearn.pipeline import Pipeline\n", "from sklearn.preprocessing import PolynomialFeatures\n", "\n", "X, y = make_moons(n_samples=100, noise=0.15, random_state=42)\n", "\n", "polynomial_svm_clf = Pipeline([\n", " (\"poly_features\", PolynomialFeatures(degree=3)),\n", " (\"scaler\", StandardScaler()),\n", " (\"svm_clf\", LinearSVC(C=10, loss=\"hinge\", max_iter=2000, random_state=42))\n", " ])\n", "\n", "polynomial_svm_clf.fit(X, y)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_dataset(X, y, axes):\n", " plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n", " plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n", " plt.axis(axes)\n", " plt.grid(True, which='both')\n", " plt.xlabel(r\"$x_1$\", fontsize=20)\n", " plt.ylabel(r\"$x_2$\", fontsize=20, rotation=0)\n", " \n", "def plot_predictions(clf, axes):\n", " x0s = np.linspace(axes[0], axes[1], 100)\n", " x1s = np.linspace(axes[2], axes[3], 100)\n", " x0, x1 = np.meshgrid(x0s, x1s)\n", " X = np.c_[x0.ravel(), x1.ravel()]\n", " y_pred = clf.predict(X).reshape(x0.shape)\n", " y_decision = clf.decision_function(X).reshape(x0.shape)\n", " plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)\n", " plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)\n", "\n", "plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])\n", "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2.1 다항식 커널" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 낮은 차수의 다항식은 매우 복잡한 데이터셋을 잘 표현하지 못함\n", "- 높은 차수의 다항식은 굉장히 많은 특성을 추가하므로 모델을 느리게 만듦\n", "- SVM을 사용할 땐 **커널 트릭**kernel trick이라는 수학적 기교를 적용하여 특성을 추가하지 않으면서 다항식 특성을 많이 추가한 것과 같은 결과를 얻을 수 있음" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Pipeline(memory=None,\n", " steps=[('scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('svm_clf', SVC(C=5, cache_size=200, class_weight=None, coef0=1,\n", " decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\n", " kernel='poly', max_iter=-1, probability=False, random_state=None,\n", " shrinking=True, tol=0.001, verbose=False))])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.svm import SVC\n", "\n", "poly_kernel_svm_clf = Pipeline([\n", " (\"scaler\", StandardScaler()),\n", " (\"svm_clf\", SVC(kernel=\"poly\", degree=3, coef0=1, C=5))\n", " ])\n", "poly_kernel_svm_clf.fit(X, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 매개변수 coef0는 모델이 높은 차수와 낮은 차수에 얼마나 영향을 받을지 조절\n", "- coef0 매개변수는 [식 5-10]의 다항식 커널에 있는 상수항 r\n", "- 다항식 커널은 차수가 높아질수록 1보다 작은 값과 1보다 큰 값의 차이가 크게 벌어지므로 coef0을 적절한 값으로 지정하면 고차항의 영향을 줄일 수 있음" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Pipeline(memory=None,\n", " steps=[('scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('svm_clf', SVC(C=5, cache_size=200, class_weight=None, coef0=100,\n", " decision_function_shape='ovr', degree=10, gamma='auto_deprecated',\n", " kernel='poly', max_iter=-1, probability=False, random_state=None,\n", " shrinking=True, tol=0.001, verbose=False))])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "poly100_kernel_svm_clf = Pipeline([\n", " (\"scaler\", StandardScaler()),\n", " (\"svm_clf\", SVC(kernel=\"poly\", degree=10, coef0=100, C=5))\n", " ])\n", "poly100_kernel_svm_clf.fit(X, y)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(11, 4))\n", "\n", "plt.subplot(121)\n", "plot_predictions(poly_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])\n", "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n", "plt.title(r\"$d=3, r=1, C=5$\", fontsize=18)\n", "\n", "plt.subplot(122)\n", "plot_predictions(poly100_kernel_svm_clf, [-1.5, 2.5, -1, 1.5])\n", "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n", "plt.title(r\"$d=10, r=100, C=5$\", fontsize=18)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 왼쪽 그래프는 3차 다항식 커널을 사용한 SVM 분류기, 오른쪽은 10차 다항식 커널을 사용한 SVM 분류기\n", "- 모델이 과대적합이라면 다항식의 차수를 줄이고 과소적합이라면 차수를 늘려야 함" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2.2 유사도 특성 추가" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 비선형 특성을 다루는 또 다른 기법은 각 샘플이 특정 **랜드마크**landmark와 얼마나 닮았는지 측정하는 **유사도 함수**similarity function로 계산한 특성을 추가하는 것\n", "- [그림 5-8]의 왼쪽 그래프는 두 개의 랜드마크 x1 = -2와 x2 = 1을 추가" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**그림 5-8 가우시안 RBF를 사용한 유사도 특성**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**식 5-1 가우시안 RBF**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- $\\gamma$ = 0.3인 가우시안 **방사 기저 함수**Radial Basis Function(RBF)를 유사도 함수로 정의\n", "- 이 함수의 값은 0부터 1까지 변화하며 종 모양으로 나타남\n", "- [식 5-1]의 $\\ell$이 랜드마크 지점. $\\gamma$는 0보다 커야 하며 값이 작을수록 폭이 넓은 종 모양\n", "- [그림 5-8]의 x1 = -1 샘플을 살펴보면,\n", " - 첫 번째 랜드마크에서 1만큼 떨어져 있고 두 번째 랜드마크에서 2만큼 떨어져 있음\n", " - 그러므로 새로 만든 특성은 x2 = exp(-0.3 × 12) ≈ 0.74와 x3 = exp(-0.3 × 22) ≈ 0.30" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 랜드마크를 선택하는 간단한 방법은 데이터셋에 있는 모든 샘플 위치에 랜드마크를 설정하는 것\n", "- 이렇게 하면 차원이 매우 커져 변환된 훈련 세트가 선형적으로 구분될 가능성이 높음\n", "- 단점은 훈련 세트에 있는 n개의 특성을 가진 m개의 샘플이 m개의 특성을 가진 m개의 샘플로 변환됨(원본 특성은 제외한다고 가정)\n", "- 훈련 세트가 매우 클 경우 동일한 크기의 아주 많은 특성이 만들어짐" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2.3 가우시안 RBF 커널" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 유사도 특성 방식에서 추가 특성을 모두 계산하려면 연산 비용이 많이 듦\n", "- 하지만 커널 트릭을 적용하면 유사도 특성을 많이 추가하는 것과 같은 비슷한 결과를 실제로 특성을 추가하지 않고 얻을 수 있음" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "SVC 모델에 가우시안 RBF 커널을 적용" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Pipeline(memory=None,\n", " steps=[('scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('svm_clf', SVC(C=0.001, cache_size=200, class_weight=None, coef0=0.0,\n", " decision_function_shape='ovr', degree=3, gamma=5, kernel='rbf',\n", " max_iter=-1, probability=False, random_state=None, shrinking=True,\n", " tol=0.001, verbose=False))])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rbf_kernel_svm_clf = Pipeline([\n", " (\"scaler\", StandardScaler()),\n", " (\"svm_clf\", SVC(kernel=\"rbf\", gamma=5, C=0.001))\n", " ])\n", "rbf_kernel_svm_clf.fit(X, y)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.svm import SVC\n", "\n", "gamma1, gamma2 = 0.1, 5\n", "C1, C2 = 0.001, 1000\n", "hyperparams = (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)\n", "\n", "svm_clfs = []\n", "for gamma, C in hyperparams:\n", " rbf_kernel_svm_clf = Pipeline([\n", " (\"scaler\", StandardScaler()),\n", " (\"svm_clf\", SVC(kernel=\"rbf\", gamma=gamma, C=C))\n", " ])\n", " rbf_kernel_svm_clf.fit(X, y)\n", " svm_clfs.append(rbf_kernel_svm_clf)\n", "\n", "plt.figure(figsize=(11, 7))\n", "\n", "for i, svm_clf in enumerate(svm_clfs):\n", " plt.subplot(221 + i)\n", " plot_predictions(svm_clf, [-1.5, 2.5, -1, 1.5])\n", " plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n", " gamma, C = hyperparams[i]\n", " plt.title(r\"$\\gamma = {}, C = {}$\".format(gamma, C), fontsize=16)\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- gamma 증가\n", " - 종 모양 그래프가 좁아져서([그림 5-8] 참고) 각 샘플의 영향 범위가 작아짐\n", " - 결정 경계가 조금 더 불규칙해지고 각 샘플을 따라 구불구불하게 휘어짐\n", "- gamma 감소\n", " - 넒은 종 모양 그래프를 만들며 샘플이 넓은 범위에 걸쳐 영향을 주므로 결정 경계가 더 부드러워짐\n", "- 결국 하이퍼파라미터 $\\gamma$가 규제의 역할\n", "- 모델이 과대적합일 경우엔 감소, 과소적합일 경우엔 증가(하이퍼파라미터 C와 비슷)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 다른 커널은 거의 사용되지 않고 어떤 커널은 특정 데이터 구조에 특화되어 있음\n", "- **문자열 커널**이 가끔 텍스트 문서나 DNA 서열을 분류할 때 사용\n", " - e.g. **문자열 서브시퀀스 커널**string subsequence kernel이나 **레벤슈타인 거리**Levenshtein distance기반의 커널" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 여러 가지 커널 중 어떤 것을 사용해야 할지에 대한 TIP\n", " - 선형 커널을 가장 먼저 시도(LinearSVC가 SVC(kernel=\"linear\")보다 훨씬 빠름)\n", " - 특히 훈련 세트가 아주 크거나 특성 수가 많을 경우\n", " - 훈련 세트가 너무 크지 않다면 가우시안 RBF 커널을 시도. 대부분의 경우 이 커널이 잘 들어맞음\n", " - 시간과 컴퓨팅 성능이 충분하다면 교차 검증과 그리드 탐색을 사용해 다른 커널을 좀 더 시도" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2.4 계산 복잡도" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- LinearSVC 파이썬 클래스\n", " - 선형 SVM을 위한 최적화된 알고리즘을 구현한 liblinear 라이브러리를 기반\n", " - 커널 트릭을 지원하지 않지만 훈련 샘플과 특성 수에 거의 선형적으로 늘어남\n", " - 훈련 시간 복잡도는 대략 O(m × n)           m: 훈련 샘플 수, n: 특성 수\n", "

\n", "- 정밀도precision를 높이면 알고리즘의 수행 시간이 길어짐\n", "- 이는 허용오차 하이퍼파라미터 ε으로 조절(사이킷런에서는 매개변수 tol)\n", "- 대부분의 분류 문제는 허용오차를 기본값으로 두면 잘 작동\n", "

\n", "- SVC 파이썬 클래스\n", " - 커널 트릭 알고리즘을 구현한 libsvm 라이브러리를 기반\n", " - 훈련 시간 복잡도는 보통 O(m2 × n)과 O(m3 × n) 사이\n", " - 이는 훈련 샘플 수가 커지면 엄청나게 느려진다는 것을 의미\n", " - 복잡하지만 작거나 중간 규모의 훈련 세트에 이 알고리즘이 잘 맞음\n", " - 하지만 특성의 개수에는, 특히 **희소 특성**sparse features(즉, 각 샘플에 0이 아닌 특성이 몇 개 없는 경우)인 경우에는 잘 확장\n", " - 이런 경우 알고리즘의 성능이 샘플이 가진 0이 아닌 특성의 평균 수에 거의 비례" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**표 5-1 SVM 분류를 위한 사이킷런 파이썬 클래스 비교**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## 5.3 SVM 회귀" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- SVM 알고리즘은 선형, 비선형 분류뿐만 아니라 선형, 비선형 회귀에도 사용할 수 있음\n", "- 일정한 마진 오류 안에서 두 클래스 간의 도로 폭이 가능한 한 최대가 되도록 하는 대신, SVM 회귀는 제한된 마진 오류 안에서 도로 안에 가능한 한 많은 샘플이 들어가도록 학습\n", "- 도로의 폭은 하이퍼파라미터 ε으로 조절\n", "- 마진 안에서는 훈련 샘플이 추가되어도 모델의 예측에는 영향이 없음\n", "- 그래서 이 모델을 **ε에 민감하지 않다**ε-insensitive고 말함" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "사이킷런의 LinearSVR을 사용해 선형 SVM 회귀를 적용" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "np.random.seed(42)\n", "m = 50\n", "# 무작위 선형 데이터셋 생성\n", "X = 2 * np.random.rand(m, 1)\n", "y = (4 + 3 * X + np.random.randn(m, 1)).ravel()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.svm import LinearSVR\n", "\n", "svm_reg1 = LinearSVR(epsilon=1.5, random_state=42)\n", "svm_reg2 = LinearSVR(epsilon=0.5, random_state=42)\n", "svm_reg1.fit(X, y)\n", "svm_reg2.fit(X, y)\n", "\n", "def find_support_vectors(svm_reg, X, y):\n", " y_pred = svm_reg.predict(X)\n", " off_margin = (np.abs(y - y_pred) >= svm_reg.epsilon)\n", " return np.argwhere(off_margin)\n", "\n", "svm_reg1.support_ = find_support_vectors(svm_reg1, X, y)\n", "svm_reg2.support_ = find_support_vectors(svm_reg2, X, y)\n", "\n", "eps_x1 = 1\n", "eps_y_pred = svm_reg1.predict([[eps_x1]])\n", "\n", "\n", "def plot_svm_regression(svm_reg, X, y, axes):\n", " x1s = np.linspace(axes[0], axes[1], 100).reshape(100, 1)\n", " y_pred = svm_reg.predict(x1s)\n", " plt.plot(x1s, y_pred, \"k-\", linewidth=2, label=r\"$\\hat{y}$\")\n", " plt.plot(x1s, y_pred + svm_reg.epsilon, \"k--\")\n", " plt.plot(x1s, y_pred - svm_reg.epsilon, \"k--\")\n", " plt.scatter(X[svm_reg.support_], y[svm_reg.support_], s=180, facecolors='#FFAAAA')\n", " plt.plot(X, y, \"bo\")\n", " plt.xlabel(r\"$x_1$\", fontsize=18)\n", " plt.legend(loc=\"upper left\", fontsize=18)\n", " plt.axis(axes)\n", "\n", "plt.figure(figsize=(9, 4))\n", "plt.subplot(121)\n", "plot_svm_regression(svm_reg1, X, y, [0, 2, 3, 11])\n", "plt.title(r\"$\\epsilon = {}$\".format(svm_reg1.epsilon), fontsize=18)\n", "plt.ylabel(r\"$y$\", fontsize=18, rotation=0)\n", "#plt.plot([eps_x1, eps_x1], [eps_y_pred, eps_y_pred - svm_reg1.epsilon], \"k-\", linewidth=2)\n", "plt.annotate(\n", " '', xy=(eps_x1, eps_y_pred), xycoords='data',\n", " xytext=(eps_x1, eps_y_pred - svm_reg1.epsilon),\n", " textcoords='data', arrowprops={'arrowstyle': '<->', 'linewidth': 1.5}\n", " )\n", "plt.text(0.91, 5.6, r\"$\\epsilon$\", fontsize=20)\n", "plt.subplot(122)\n", "plot_svm_regression(svm_reg2, X, y, [0, 2, 3, 11])\n", "plt.title(r\"$\\epsilon = {}$\".format(svm_reg2.epsilon), fontsize=18)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 비선형 회귀 작업을 처리하려면 커널 SVM 모델을 사용\n", "- SVR은 SVC의 회귀 버전이고 LinearSVR은 LinearSVC의 회귀 버전\n", "- LinearSVr은 (LinearSVC처럼) 필요한 시간이 훈련 세트의 크기에 비례해서 선형적으로 늘어남\n", "- 하지만 SVR은 (SVC처럼) 훈련 세트가 커지면 훨씬 느려짐" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "다음 코드는 (커널 트릭을 제공하는) 사이킷런의 SVR을 사용
\n", "임의의 2차방정식 형태의 훈련 세트에 2차 다항 커널을 사용한 SVM 회귀를 보여줌" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "np.random.seed(42)\n", "m = 100\n", "X = 2 * np.random.rand(m, 1) - 1\n", "y = (0.2 + 0.1 * X + 0.5 * X**2 + np.random.randn(m, 1)/10).ravel()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.svm import SVR\n", "\n", "svm_poly_reg1 = SVR(kernel=\"poly\", gamma='auto', degree=2, C=100, epsilon=0.1)\n", "svm_poly_reg2 = SVR(kernel=\"poly\", gamma='auto', degree=2, C=0.01, epsilon=0.1)\n", "svm_poly_reg1.fit(X, y)\n", "svm_poly_reg2.fit(X, y)\n", "\n", "plt.figure(figsize=(9, 4))\n", "plt.subplot(121)\n", "plot_svm_regression(svm_poly_reg1, X, y, [-1, 1, 0, 1])\n", "plt.title(r\"$degree={}, C={}, \\epsilon = {}$\".format(svm_poly_reg1.degree, svm_poly_reg1.C, svm_poly_reg1.epsilon), fontsize=18)\n", "plt.ylabel(r\"$y$\", fontsize=18, rotation=0)\n", "plt.subplot(122)\n", "plot_svm_regression(svm_poly_reg2, X, y, [-1, 1, 0, 1])\n", "plt.title(r\"$degree={}, C={}, \\epsilon = {}$\".format(svm_poly_reg2.degree, svm_poly_reg2.C, svm_poly_reg2.epsilon), fontsize=18)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**NOTE_** SVM을 이상치 탐지에도 사용할 수 있음.
\n", "https://scikit-learn.org/stable/modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## 5.4 SVM 이론" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "이 절에서 SVM의 예측은 어떻게 이뤄지는지, 그리고 SVM의 훈련 알고리즘이 어떻게 작동하는지 설명함
\n", "편향을 b라 하고 특성의 가중치 벡터를 **w**라 하겠음" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.4.1 결정 함수와 예측" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 선형 SVM 분류기 모델은 단순히 결정 함수 **w**T · **x** + b = w1x1 + ··· + wnxn + b를 계산해서 새로운 샘플 **x**의 클래스를 예측\n", "- 결괏값이 0보다 크면 예측된 클래스 $\\hat{y}$은 양성 클래스(1), 그렇지 않으면 음성 클래스(0)가 됨. [식 5-2] 참조" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**식 5-2 선형 SVM 분류기의 예측**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 아래 [그림 5-12]는 특성이 두 개(꽃잎의 너비와 길이)인 데이터셋이기 때문에 모델의 결정 함수가 2차원 평면임\n", "- 결정 경계는 결정 함수의 값이 0인 점들로 이루어져 있음\n", "- 이는 두 평면의 교차점으로 직선임(굵은 실선)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
**그림 5-12 iris 데이터셋의 결정 함수**
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 점선은 결정 함수의 값이 1 또는 -1인 점들을 나타냄\n", "- 이 선분은 결정 경계에 나란하고 일정한 거리만큼 떨어져서 마진을 형성하고 있음\n", "- 선형 SVM 분류기를 훈련한다는 것: 마진 오류를 하나도 발생하지 않거나(하드 마진) 제한적인 마진 오류를 가지면서(소프트 마진) 가능한 한 마진을 크게 하는 **w**와 b를 찾는 것" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.5.4" } }, "nbformat": 4, "nbformat_minor": 2 }