支持向量机——线性分类SVM

模型原型
sklearn.svm.LinearSVC(penalty=’l2’,loss=’squared_hinge’,dual=True,tol=0.0001,C=1.0,multi_class=’ovr’, fit_intercept=True,intercept_scaling=1,class_weight=None,verbose=0,random_state=None,max_iter=1000)
参数

• penalty:罚项的范数
• loss:损失函数
  
  • ’hinge’:合页损失函数（标准SVM的损失函数）
  • ‘squared_hinge’:合页损失函数的平方
• dual:
  
  • True:解决对偶问题
  • False:解决原始问题
• tol
• C:罚项参数
• multi_class:指定多类分类问题的策略
  
  • ’ovr’:采用one-vs-rest分类策略
  • ‘crammer_singer’:多类联合分类，很少用（计算量大，且精度不会更佳）
• fit_intercept:是否计算截距（常数项）
• intercept_scaling:一个人工特征，该特征对所有实例都是常数值（人工特征也参与了罚项的计算）
• class_weight
• verbose:表示是否开启verbose输出
• random_state
• max_iter

属性

• coef_
• intercept_

方法

• fit(X,y)
• predict(X)
• score(X,y[,sample_weight])

import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets,linear_model,cross_validation,svm

加载数据

def load_data_classfication():
    iris=datasets.load_iris()
    X_train=iris.data
    y_train=iris.target
    return cross_validation.train_test_split(X_train,y_train,test_size=0.25,random_state=0,stratify=y_train)

使用LinearSVC类

def test_LinearSVC(*data):
    X_train,X_test,y_train,y_test=data
    cls=svm.LinearSVC()
    cls.fit(X_train,y_train)
    print('Coefficients:%s,intercept %s'%(cls.coef_,cls.intercept_))
    print('Score:%.2f'%cls.score(X_test,y_test))

X_train,X_test,y_train,y_test=load_data_classfication()
test_LinearSVC(X_train,X_test,y_train,y_test)

损失函数的影响

def test_LinearSVC_loss(*data):
    X_train,X_test,y_train,y_test=data
    losses=['hinge','squared_hinge']
    for loss in losses:
        cls=svm.LinearSVC(loss=loss)
        cls.fit(X_train,y_train)
        print('Loss:%s'%loss)
        print('Coefficients:%s,intercept %s'%(cls.coef_,cls.intercept_))
        print('Score:%.2f'%cls.score(X_test,y_test))

test_LinearSVC_loss(X_train,X_test,y_train,y_test)

罚项形式的影响

def test_LinearSVC_L12(*data):
    X_train,X_test,y_train,y_test=data
    L12=['l1','l2']
    for p in L12:
        cls=svm.LinearSVC(penalty=p,dual=False)
        cls.fit(X_train,y_train)
        print('penalty:%s'%p)
        print('Coefficients:%s,intercept %s'%(cls.coef_,cls.intercept_))
        print('Score:%.2f'%cls.score(X_test,y_test))

test_LinearSVC_L12(X_train,X_test,y_train,y_test)

罚项系数C的影响

def test_LinearSVC_C(*data):
    X_train,X_test,y_train,y_test=data
    Cs=np.logspace(-2,1)
    train_scores=[]
    test_scores=[]
    for C in Cs:
        cls=svm.LinearSVC(C=C)
        cls.fit(X_train,y_train)
        train_scores.append(cls.score(X_train,y_train))
        test_scores.append(cls.score(X_test,y_test))

    fig=plt.figure()
    ax=fig.add_subplot(1,1,1)
    ax.plot(Cs,train_scores,label='Training score')
    ax.plot(Cs,test_scores,label='Testing score')
    ax.set_xlabel(r'C')
    ax.set_ylabel(r'score')
    ax.set_xscale('log')
    ax.set_title('LinearSVC')
    ax.legend(loc='best')
    plt.show()

test_LinearSVC_C(X_train,X_test,y_train,y_test)