{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "这一节我们使用 sklearn 中提供的 SVM 方法来解决一个简单的二分类问题。sklearn 自带了一个鸢尾花的数据集，这个数据集是 Fisher 在 1936 年收集整理的，是一类多重变量分析的数据集，数据集共包含 150 条数据记录，分为 3 类，每类 50 个数据，每条数据包含 4 个属性。可通过花萼长度，花萼宽度，花瓣长度，花瓣宽度 4 个属性预测鸢尾花卉属于（Setosa，Versicolour，Virginica）三个种类中的哪一类。\n", "\n", "由于我们想使用 SVM 解决二分类问题，所以这里我们只取鸢尾花的两种类型，每种类型只取两个特征：" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn import datasets\n", "\n", "iris = datasets.load_iris();\n", "\n", "X = iris.data\n", "y = iris.target\n", "\n", "X = X[y < 2, :2]\n", "y = y[y < 2]\n", "\n", "plt.scatter(X[y == 0, 0], X[y == 0, 1], color='red')\n", "plt.scatter(X[y == 1, 0], X[y == 1, 1], color='blue')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "图中可以看出数据非常明显的分为两类。通过 sklearn 中提供的 `LinearSVC` 类，可以非常方便的训练出模型，这里的参数 C 取一个很大的数字，这样得到的接近于硬间隔支持向量机。我们输入两个测试数据：`(6,2)` 和 `(4,3)` 得到的结果正好是 1 和 0。" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 0]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/aneasystone/anaconda3/lib/python3.7/site-packages/sklearn/svm/base.py:922: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n", " \"the number of iterations.\", ConvergenceWarning)\n" ] } ], "source": [ "from sklearn.svm import LinearSVC\n", "\n", "svc = LinearSVC(C=1e9)\n", "svc.fit(X, y)\n", "results = svc.predict([[6,2], [4, 3]])\n", "print(results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "不过这里我们看到了警告信息：`Liblinear failed to converge, increase the number of iterations`，这句话的意思是算法没有达到收敛，需要增加迭代次数，sklearn 默认的迭代次数是 1000，我们将其加到 40000 才收敛：" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 0]\n" ] } ], "source": [ "from sklearn.svm import LinearSVC\n", "\n", "svc = LinearSVC(C=1e9, max_iter=40000)\n", "svc.fit(X, y)\n", "results = svc.predict([[6,2], [4, 3]])\n", "print(results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "迭代次数越多很显然算法性能就越低，解决这个问题的令一个办法是数据归一化，使用 `preprocessing` 模块提供的 `scale` 方法将数据移到靠近中心的位置，让其符合正态分布，可以看出不用增加迭代次数算法也可以很快收敛：" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 0]\n" ] }, { "data": { "image/png": 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fKTHXeH5RMHf9E5unANAW1tgbR03xyPnz0sLCcCNvYWH4HJhnM+vHjnzo/T1y/rz02GOj5zdujJ5fvNhPTEDfWIqpEDXFIwsLw2S+12AgXb8++3iAkliKaRi9v0fGJfXDjgPzgMReIWqKRwaDtOPAPCCxV4ia4pGdvYWux4F5QGKvEL2/Ry5elM6dG12hDwbD52ycYp6xeQoAlWDzNEXjReGNn17z5xcF81yRLren5n6EainQeKPpxk+v+fOLgnmOQbQU6KjxovDGT6/584uCeY6BfuxdNd5ouvHTa/78omCeY2CNvavGi8IbP73mzy8K5rkuJPbGi8IbP73mzy8K5rkyXRbicz9CbZ66N99ouvHTa/78omCe+yc2TwGgLayxA40oVT9OXXq76McOBFaq9z49/dvGUgwQWKn6cerS68RSDNCAUr336enftqkSu5l92sxeMbMXzexJM7sjV2AAytWPU5fetmmv2J+R9IC7v0vS9yU9On1IAHaUqh+nLr1tUyV2d/+6u+98suTzku6ePiQAO0r13qenf9uybZ6a2b9L+ld3f+KAr69KWpWkpaWlU5vjdm4AAAfqunl6ZLmjmV2SdOeYL11w96e2X3NB0nVJB1bCuvuapDVpWBVz1PcFAEzmyMTu7mcO+7qZfVjSw5JOex+1kwCAXaa6QcnMzkr6hKQ/dPetPCEBAKYxbVXMZyW9TdIzZvaCmX0+Q0wAgClMdcXu7u/IFQgAIA/uPAWAxpDYAaAxJHYAaAyJfQ7QdxuYL/Rjbxx9t4H5wxV74y5cGCX1HVtbw+MA2kRibxx9t4H5Q2JvHH23gflDYm8cfbeB+UNibxx9t4H5Q1XMHFhZIZED84QrdgBoDIkdABpDYgeAxpDYAaAxJHYAaAyJHQAaQ2IHgMaQ2AGgMebus/+mZtckbd5y6Ncl/WzmgdSBuTkc83Mw5uZwNc7PCXdfPOpFvST2fUGYbbj7ct9xRMTcHI75ORhzc7iW54elGABoDIkdABoTJbGv9R1AYMzN4ZifgzE3h2t2fkKssQMA8olyxQ4AyITEDgCNCZPYzezTZvaKmb1oZk+a2R19xxSFmX3QzF42s5tm1mR5ViozO2tmr5rZa2b2yb7jicTMHjezn5rZS33HEo2Z3WNm3zCzK9u/U4/0HVMJYRK7pGckPeDu75L0fUmP9hxPJC9J+lNJz/UdSARmNpD0OUl/JOl+SX9uZvf3G1Uo/yjpbN9BBHVd0sfd/T5J75H00RbfO2ESu7t/3d2vbz99XtLdfcYTibtfcfdX+44jkN+X9Jq7/8Dd/0/Sv0j6k55jCsPdn5P0877jiMjdf+Lu393+719KuiLprn6jyi9MYt/jLyT9Z99BIKy7JP3oludX1eAvJ8oys5OS3i3pO/1Gkt9MP8zazC5JunPMly64+1Pbr7mg4f8urc8ytr51mRu8ycYco24XnZnZWyV9WdLH3P0XfceT20wTu7ufOezrZvZhSQ9LOu1zVmB/1Nxgl6uS7rnl+d2SftxTLKiMmd2mYVJfd/ev9B1PCWGWYszsrKRPSPpjd9/qOx6E9t+SfsfM3m5mb5H0Z5L+reeYUAEzM0lfkHTF3T/TdzylhEnskj4r6W2SnjGzF8zs830HFIWZfcDMrkp6UNLXzOzpvmPq0/Ym+19KelrDza8vufvL/UYVh5l9UdK3Jb3TzK6a2Uf6jimQ90r6kKT3beeZF8zsob6Dyo2WAgDQmEhX7ACADEjsANAYEjsANIbEDgCNIbEDQGNI7ADQGBI7ADTm/wFmtHNBW1/OsAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.svm import LinearSVC\n", "from sklearn import preprocessing\n", "\n", "X_scaled = preprocessing.scale(X)\n", "svc = LinearSVC(C=1e9)\n", "svc.fit(X_scaled, y)\n", "results = svc.predict(preprocessing.scale([[6,2], [4, 3]]))\n", "print(results)\n", "\n", "plt.scatter(X_scaled[y == 0, 0], X_scaled[y == 0, 1], color='red')\n", "plt.scatter(X_scaled[y == 1, 0], X_scaled[y == 1, 1], color='blue')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "最后我们在图中画出划分超平面，也就是决策边界，决策边界为一条直线：\n", "\n", "$$\n", "w_1x + w_2y + b = 0\n", "$$\n", "\n", "这里的 $w$ 为特征系数，可以通过 `svc.coef_` 取得，$b$ 为截距，可以通过 `intercept_` 取得：" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w = [[ 4.03244052 -2.50699934]]\n", "b = [0.92733476]\n" ] } ], "source": [ "print('w = ', svc.coef_)\n", "print('b = ', svc.intercept_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "从而得到直线方程：\n", "\n", "$$\n", "y = -\\frac{w_1x+b}{w_2}\n", "$$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_svc_decision_boundary(model):\n", " w = model.coef_[0]\n", " b = model.intercept_[0]\n", " x = np.linspace(-3, 3, 200)\n", " y = - (w[0]*x+b) / w[1]\n", " plt.plot(x, y, color='black')\n", "\n", "plot_svc_decision_boundary(svc)\n", "plt.scatter(X_scaled[y == 0, 0], X_scaled[y == 0, 1], color='red')\n", "plt.scatter(X_scaled[y == 1, 0], X_scaled[y == 1, 1], color='blue')\n", "plt.show()" ] } ], "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 2 }