{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Майнор по Анализу Данных, Группа ИАД-4\n", "## 07/09/2017 Метод Опорных Векторов" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.figsize'] = (12,5)\n", "\n", "# Для кириллицы на графиках\n", "font = {'family': 'Verdana',\n", " 'weight': 'normal'}\n", "plt.rc('font', **font)\n", "\n", "try:\n", " from ipywidgets import interact, IntSlider, fixed, FloatSlider\n", "except ImportError:\n", " print(u'Так надо')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Вспоминаем про линейные модели" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Уравнение прямой задаётся как: $$g(x) = w_0 + w_1x_1 + w_2x_2 = w_0 + \\langle w, x \\rangle = w_0 + w^\\top x $$\n", "\n", "* Если $g(x^*) > 0$, то $y^* = \\text{'черный'} = +1$\n", "* Если $g(x^*) < 0$, то $y^* = \\text{'белый'} = -1$\n", "* Если $g(x^*) = 0$, то мы находимся на линии\n", "* т.е. решающее правило: $y^* = sign(g(x^*))$\n", "\n", "Некоторые геометрические особенности\n", "* $\\frac{|g(x)|}{||w||}$ - расстояние от точки $x$ до гиперплоскости, степень \"уверенности\" в классификациий\n", "* Величину $M = y(\\langle w, x \\rangle + w_0) = y \\cdot g(x)$ называют **отступом**(margin)\n", "\n", "Если для какого-то объекта $x_i$ его отступ $M_i \\geq 0$, то его классификация выполнена успешно." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$L(w) = \\sum_i [y^{(i)} (\\langle w, x^{(i)} \\rangle + w_0) < 0] \\rightarrow \\min_{w, w_0}$$\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Линейноразделимый случай с двумя классами\n", "* Заметим что $g(x) = w_0 + \\langle w, x \\rangle$ и $g'(x) = c \\cdot (w_0 + \\langle w, x \\rangle)$, $\\forall c>0$ задают одну и ту же гиперплоскость\n", "* Подберем $c$ таким образом, чтобы $\\min\\limits_i M_i = \\min\\limits_i y^{(i)} \\cdot g(x^{(i)}) = 1$\n", "* Объекты $x^{(i)}$ для которых $M^*_i = 1$ будем называть опорными\n", "
\n", "* Таким образом выполняются следующие неравенства:\n", " * $w_0 + \\langle w, x^{(i)} \\rangle \\geq 1$, если $y^{(i)} = + 1$\n", " * $w_0 + \\langle w, x^{(i)} \\rangle \\leq - 1$, если $y^{(i)} = - 1$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Разделяющая полоса: $ -1 \\leq w_0 + \\langle w, x \\rangle \\leq +1$\n", "* Ширина разделяющей полосы:\n", " $$\\langle (x^{+} - x^{-}) , \\frac{w}{||w||}\\rangle = \\frac{\\langle w, x^{+} \\rangle - \\langle w, x^{-} \\rangle }{||w||} = \\frac{2}{||w||} \\rightarrow \\max$$\n", " \n", " \n", "* Таким образом мы придем к оптимизационной задаче:\n", "$$\n", "\\begin{cases} \n", " \\frac{1}{2} ||w||^2 \\rightarrow \\min \\\\\n", " y^{(i)}(\\langle w, x^{(i)} \\rangle + w_0 ) \\geq 1 \\quad i=1\\dots n\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.datasets.samples_generator import make_classification\n", "\n", "from sklearn.svm import SVC\n", "from sklearn.linear_model import LogisticRegression\n", "\n", "def plot_svc_decision_function(clf1, ax=None):\n", " if ax is None:\n", " ax = plt.gca()\n", " x = np.linspace(plt.xlim()[0], plt.xlim()[1], 30)\n", " y = np.linspace(plt.ylim()[0], plt.ylim()[1], 30)\n", " XX, YY = np.meshgrid(x, y)\n", " XY = np.c_[XX.ravel(), YY.ravel()]\n", " P1 = clf1.decision_function(XY)\n", " P1 = P1.reshape(XX.shape)\n", " \n", " # plot the margins\n", " cplot = ax.contour(XX, YY, P1, colors='k', label='svm',\n", " levels=[-1, 0, 1], alpha=0.5,\n", " linestyles=['--', '-', '--'])\n", " ax.clabel(cplot, inline=1, fontsize=10)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-3, 4)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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wOOVVubHfd+wrz4oSR1VjWNb1lyxX1w+Sn//Pw5LSalonXu//YZrVxGIfvKLvqapnUdUI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\n3/2gG0QXkqQQDK7A51vP8PDDJOIKlkSP+WIkYq6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LwnwTtzKFWRNT3+pLpJhLY2OYH38c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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "class_sep = 1.4\n", "\n", "X, y = make_classification(n_samples=100, n_features=2, n_informative=2, class_sep=class_sep, scale=1,\n", " n_redundant=0, n_clusters_per_class=1, random_state=31)\n", "\n", "lin_svm = SVC(kernel='linear', C=100).fit(X, y)\n", "\n", "# Plotting the splitting hyperplane and support vectors\n", "plt.figure(figsize=(10,7))\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=70, cmap='autumn')\n", "plot_svc_decision_function(lin_svm)\n", "plt.scatter(lin_svm.support_vectors_[:, 0], lin_svm.support_vectors_[:, 1],\n", " s=200, facecolors='none')\n", "\n", "plt.xlabel('$x_1$')\n", "plt.ylabel('$x_2$')\n", "\n", "plt.xlim(-1, 5)\n", "plt.ylim(-3, 4)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.50589936 1.36629804]]\n", "0.0\n" ] } ], "source": [ "print(lin_svm.coef_) # w1, w2\n", "\n", "print(lin_svm.coef0) # w0" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([10, 41, 54], dtype=int32)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lin_svm.support_vectors_ # Координаты опорных векторов\n", "lin_svm.support_ # индексы опорных векторов в X" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# lin_svm.predict_proba(X) #SVM не умеет предсказывать вероятности\n", "y_hat = lin_svm.predict(X) # метка класса" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 1, 1, 0, 1, 0, 1, 0, 0, 0])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y_hat[:10]" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "y_hat_score = lin_svm.decision_function(X) \n", "# \"Расстояние\" от\n", "# гиперплоскости до объекта" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-5.36885256, 2.61733817, 2.44638215, -3.34662808, 1.49461987,\n", " -1.94482004, 1.62022006, -2.22515071, -4.18415577, -4.00759831])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y_hat_score[:10]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Неразделимый случай \n", "\n", "Будем допускать пропуск объектов за разделительную линию\n", "* Вместо условия $y^{(i)}(\\langle w, x^{(i)} \\rangle + w_0 ) \\geq 1$\n", "* Будет условие $y^{(i)}(\\langle w, x^{(i)} \\rangle + w_0 ) \\geq 1 - \\xi_i, \\quad \\xi_i \\geq 0$\n", "\n", "
\n", "\n", "А целевой функционал заменим на \n", "\n", "$$ \\frac{1}{2} ||w||^2 + C\\sum\\limits_i\\xi_i \\rightarrow \\min\\limits_{w,w_0,\\xi} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Таким образом мы придем к оптимизационной задаче:\n", "$$\n", "\\begin{cases} \n", " \\frac{1}{2} ||w||^2 + C\\sum\\limits_i\\xi_i \\rightarrow \\min\\limits_{w,w_0,\\xi} \\\\\n", " y^{(i)}(\\langle w, x^{(i)} \\rangle + w_0 ) \\geq 1 - \\xi_i \\quad i=1\\dots n \\\\\n", " \\xi_i \\geq 0 \\quad i=1\\dots n\n", "\\end{cases}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-3, 4)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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sL/re74e3H93hJ5OB117L8OqrFzNnTn4Rd1tbG7/+9a/RdZ3m5mbe8573oCgK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\nkupYuucZ991HxsMP9+s5oTlzqHv5ZfSOZraRSITq6moqKyvx+Xw0NTV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "class_sep = 1.4\n", "\n", "X, y = make_classification(n_samples=100, n_features=2, n_informative=2, class_sep=class_sep, scale=1,\n", " n_redundant=0, n_clusters_per_class=1, random_state=31)\n", "\n", "lin_svm = SVC(kernel='linear', C=0.1).fit(X, y)\n", "\n", "# Plotting the splitting hyperplane and support vectors\n", "plt.figure(figsize=(10,7))\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=70, cmap='autumn')\n", "plot_svc_decision_function(lin_svm)\n", "plt.scatter(lin_svm.support_vectors_[:, 0], lin_svm.support_vectors_[:, 1],\n", " s=200, facecolors='none')\n", "\n", "plt.xlabel('$x_1$')\n", "plt.ylabel('$x_2$')\n", "\n", "plt.xlim(-1, 5)\n", "plt.ylim(-3, 4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ядра и спрямляющие пространства" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "code_folding": [] }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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h/uEPoaxfDx4MQtjtSMyeDf/tt8NobweEgGPp0gzxnXqursPy1ltQ1qxB4rjj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\noml9t1uWj1jsDOzCUYehwZwwgfTDDyOuvRZl40bkaBQrFCI9bRpdt96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rLqRwGHnLFkRz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\nPy6XC7qudxsci6Jo/jFWx2VZzpiqYnS39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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets.samples_generator import make_circles\n", "from mpl_toolkits import mplot3d\n", "\n", "X, y = make_circles(n_samples=100, factor=0.1, \n", " noise=0.1, random_state=0)\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(1, 2, 1)\n", "\n", "ax.scatter(X[:, 0], X[:, 1], c=y, s=70, cmap='autumn')\n", "ax.set_xlabel('$x_1$')\n", "ax.set_ylabel('$x_2$')\n", "\n", "r = X[:, 0] ** 2 + X[:, 1] ** 2\n", "\n", "ax = fig.add_subplot(1, 2, 2)\n", "\n", "ax = fig.add_subplot(1, 2, 2, projection='3d')\n", "ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=70, cmap='autumn')\n", "ax.view_init(elev=30, azim=30)\n", "ax.set_xlabel('$x_1$')\n", "ax.set_ylabel('$x_2$')\n", "ax.set_zlabel('$x_1^2 + x_2^2$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* $\\psi: X \\rightarrow H$\n", "* $H$ - пространство большей размерности, в котором классы становятся линейноразделимыми называется **спрямляющим**.\n", "* Разделяющся гиперплоскость в таком пространстве будет линейной, но при проекции на исходное пространство $X$ - нет" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Представим, что мы как-то перешли в спрямляющее пространство и хотим строить SVM там? Что изменится в задаче оптимизации?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Наиболее популярны следующие ядра:\n", "\n", "1. Линейное (linear): $$\\langle x, y\\rangle$$\n", "2. Полиномиальное (polynomial): $$(\\gamma \\langle x, y\\rangle + с)^d,$$ \n", "3. Radial basis function kernel (rbf): $$e^{(-\\gamma \\cdot \\|x - y\\|^2)},$$ \n", "4. Sigmoid: $$\\tanh(\\gamma \\langle x,y \\rangle + r)$$ " ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from IPython.display import YouTubeVideo" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/jpeg": 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xMfC4sbEx0O17KsvxNXKsVisTJkzg4MGDQHsrn8vlwmaz0dra2mW2X1BQQEFB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\n2Lt3LyRJg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "class_sep = 1.4\n", "\n", "X, y = make_circles(n_samples=100, factor=0.1, \n", " noise=0.1, random_state=0)\n", "\n", "lin_svm = SVC(kernel='rbf', C=1.0, gamma=60).fit(X, y)\n", "\n", "# Plotting the splitting hyperplane and support vectors\n", "plt.figure(figsize=(10,7))\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=70, cmap='autumn')\n", "plot_svc_decision_function(lin_svm)\n", "plt.scatter(lin_svm.support_vectors_[:, 0], lin_svm.support_vectors_[:, 1],\n", " s=200, facecolors='none')\n", "\n", "plt.xlabel('$x_1$')\n", "plt.ylabel('$x_2$')\n", "\n", "plt.xlim(-1, 1)\n", "plt.ylim(-1, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Метод опорных векторов для регрессии?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Практика" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Загрузите текстовые данные [отсюда](https://archive.ics.uci.edu/ml/machine-learning-databases/00331/). Архив должен содержать 3 файла с положительными и отрицательными отзывами с ресурсов\n", "* imdb.com\n", "* amazon.com\n", "* yelp.com\n", "\n", "Формат файла следующий:\n", "<отзыв>\\t<метка>\\n\n", "\n", "\n", "### Задача\n", "1. Загрузите тексты и метки классов в разные переменные\n", "2. Выберите меру качества классификации\n", "3. Обучите линейный SVM (без подбора гиперпараметров). Тексты представляются в виде мешка слов\n", "4. Выведите наиболее значимые слова из текста\n", "5. С помощью кросс-валидации и валидационных кривых исследуйте, как различные комбинции параметров влияют на качество" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "amazon_cells_labelled.txt readme.txt\r\n", "imdb_labelled.txt yelp_labelled.txt\r\n" ] } ], "source": [ "!ls ./sentiment\\ labelled\\ sentences" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "texts, labels = [], []\n", "\n", "for line in open('./sentiment labelled sentences/amazon_cells_labelled.txt'):\n", " text, label = line.strip('\\n').split('\\t')\n", " texts.append(text)\n", " labels.append(int(label))" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "from sklearn.feature_extraction.text import TfidfVectorizer\n", "from sklearn.pipeline import Pipeline\n", "\n", "model = Pipeline(\n", "[\n", " ('vect', TfidfVectorizer()),\n", " ('svm', SVC(kernel='linear'))\n", "])" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Pipeline(steps=[('vect', TfidfVectorizer(analyzer=u'word', binary=False, decode_error=u'strict',\n", " dtype=, encoding=u'utf-8', input=u'content',\n", " lowercase=True, max_df=1.0, max_features=None, min_df=1,\n", " ngram_range=(1, 1), norm=u'l2', preprocessor=None, smooth_idf=True...,\n", " max_iter=-1, probability=False, random_state=None, shrinking=True,\n", " tol=0.001, verbose=False))])" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.fit(texts, labels)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": true }, "outputs": [], "source": [ "weights = model.steps[1][1].coef_.toarray()[0]\n", "words = model.steps[0][1].get_feature_names()" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": true }, "outputs": [], "source": [ "coefs = pd.Series(index=words, data=weights)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "not -3.507181\n", "first -1.975821\n", "poor -1.965497\n", "doesn -1.505776\n", "bad -1.485459\n", "if -1.456254\n", "none -1.446073\n", "difficult -1.376058\n", "disappointed -1.374236\n", "then -1.372565\n", "unreliable -1.359178\n", "old -1.344775\n", "worst -1.294790\n", "disappointing -1.292949\n", "terrible -1.290509\n", "hear -1.255339\n", "money -1.162993\n", "however -1.148374\n", "don -1.145519\n", "horrible -1.063185\n", "problem -1.036764\n", "within -1.013970\n", "return -1.007565\n", "waste -1.005096\n", "stay -1.003578\n", "buying -0.996052\n", "sucks -0.976878\n", "experience -0.958927\n", "off -0.953516\n", "crap -0.947778\n", " ... \n", "all 1.077599\n", "car 1.091398\n", "rocks 1.125765\n", "happy 1.163118\n", "awesome 1.169940\n", "beautiful 1.170902\n", "any 1.173849\n", "seems 1.181771\n", "setup 1.185614\n", "definitely 1.194722\n", "worthwhile 1.198160\n", "pleased 1.216341\n", "exactly 1.236538\n", "and 1.242878\n", "sturdy 1.324035\n", "glad 1.324793\n", "perfectly 1.472077\n", "without 1.489238\n", "comfortable 1.565059\n", "well 1.579040\n", "recommend 1.776462\n", "than 1.781467\n", "easy 1.834265\n", "excellent 1.876684\n", "nice 1.923456\n", "love 1.954578\n", "works 2.188037\n", "best 2.503786\n", "good 2.569317\n", "great 3.112906\n", "dtype: float64" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coefs.sort_values()" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda root]", "language": "python", "name": "conda-root-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" }, "toc": { "colors": { "hover_highlight": "#DAA520", "navigate_num": "#000000", "navigate_text": "#333333", "running_highlight": "#FF0000", "selected_highlight": "#FFD700", "sidebar_border": "#EEEEEE", "wrapper_background": "#FFFFFF" }, "moveMenuLeft": true, "nav_menu": { "height": "179px", "width": "252px" }, "navigate_menu": true, "number_sections": false, "sideBar": true, "threshold": 4, "toc_cell": false, "toc_section_display": "block", "toc_window_display": false, "widenNotebook": false } }, "nbformat": 4, "nbformat_minor": 2 }