Python_ support vector machine classifier

SVM ( Support the Vector Machine, SVM ) are a class by supervised learning ( Supervised Learning ) mode data binary classification of generalized linear classifiers ( Generalized Linear classifier ), whose decision boundary is the largest margin of solving learning samples hyperplane ( maximum-margin hyperplane )

SVM using a hinge loss function ( Hinge Loss ) calculated empirical risk ( Empirical Risk ) was added and the regularization term risk to optimize the structure (in the solution system Structural Risk ), it is a sparse and robust classifier. SVM by nuclear methods ( Kernel Method, nonlinear classification), is a common core of learning ( Kernel Learning one) method.

SVM was proposed in 1964 , at the twentieth century 90 after years of rapid development and derive a series of improvements and expansion algorithm in face recognition , text classification such as pattern recognition ( pattern Recognition has been applied) problems.

import numpy as np
from scipy import io as spio
from matplotlib import pyplot as plt
from sklearn import svm


def SVM():
    '''data1——线性分类'''
    data1 = spio.loadmat('data1.mat')
    X = data1['X']
    y = data1['y']
    y = np.ravel(y)
    plot_data(X, y)

    model = svm.SVC(C=1.0, kernel='linear').fit(X, y)  # 指定核函数为线性核函数
    plot_decisionBoundary(X, y, model)  # 画决策边界
    '''data2——非线性分类'''
    data2 = spio.loadmat('data2.mat')
    X = data2['X']
    y = data2['y']
    y = np.ravel(y)
    plt = plot_data(X, y)
    plt.show()

    model = svm.SVC(gamma=100).fit(X, y)  # gamma为核函数的系数，值越大拟合的越好
    plot_decisionBoundary(X, y, model, class_='notLinear')  # 画决策边界


# 作图
def plot_data(X, y):
    plt.figure(figsize=(10, 8))
    pos = np.where(y == 1)  # 找到y=1的位置
    neg = np.where(y == 0)  # 找到y=0的位置
    p1, = plt.plot(np.ravel(X[pos, 0]), np.ravel(X[pos, 1]), 'ro', markersize=8)
    p2, = plt.plot(np.ravel(X[neg, 0]), np.ravel(X[neg, 1]), 'g^', markersize=8)
    plt.xlabel("X1")
    plt.ylabel("X2")
    plt.legend([p1, p2], ["y==1", "y==0"])
    return plt


# 画决策边界
def plot_decisionBoundary(X, y, model, class_='linear'):
    plt = plot_data(X, y)

    # 线性边界        
    if class_ == 'linear':
        w = model.coef_
        b = model.intercept_
        xp = np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), 100)
        yp = -(w[0, 0] * xp + b) / w[0, 1]
        plt.plot(xp, yp, 'b-', linewidth=2.0)
        plt.show()
    else:  # 非线性边界
        x_1 = np.transpose(np.linspace(np.min(X[:, 0]), np.max(X[:, 0]), 100).reshape(1, -1))
        x_2 = np.transpose(np.linspace(np.min(X[:, 1]), np.max(X[:, 1]), 100).reshape(1, -1))
        X1, X2 = np.meshgrid(x_1, x_2)
        vals = np.zeros(X1.shape)
        for i in range(X1.shape[1]):
            this_X = np.hstack((X1[:, i].reshape(-1, 1), X2[:, i].reshape(-1, 1)))
            vals[:, i] = model.predict(this_X)

        plt.contour(X1, X2, vals, [0, 1], color='blue')
        plt.show()


if __name__ == "__main__":
    SVM()

Author: WangB