支持向量机(SVM)——python代码实现

数据集

• 数据集：ris鸢尾花数据集，它包含3个不同品种的鸢尾花：[Setosa，Versicolour，and Virginica]数据，特征：[‘sepal length’, ‘sepal width’, ‘petal length’, ‘petal width’],一共150个数据。由于这是2分类问题，所以选择前两类数据进行算法测试。

代码实现

import numpy as np
import pandas as pd
from sklearn.datasets import load_iris
from sklearn.model_selection import  train_test_split
import matplotlib.pyplot as plt

#加载数据
def create_data():
    iris = load_iris()
    #选取前两类作为数据
    Data=np.array(iris["data"])[:100]
    Label=np.array(iris["target"])[:100]
    Label=Label*2-1
    print("dara shape:",Data.shape)
    print("label shape:",Label.shape)
    return Data, Label

class SVM:
    def __init__(self, max_iter=100, kernel='linear'):
        self.max_iter = max_iter
        self._kernel = kernel

    #参数初始化
    def init_args(self, features, labels):
        self.m, self.n = features.shape
        self.X = features
        self.Y = labels
        self.b = 0.0
        self.alpha = np.ones(self.m)
        self.computer_product_matrix()#为了加快训练速度创建一个内积矩阵
        # 松弛变量
        self.C = 1.0
        # 将Ei保存在一个列表里
        self.create_E()

    #KKT条件判断
    def judge_KKT(self, i):
        y_g = self.function_g(i) * self.Y[i]
        if self.alpha[i] == 0:
            return y_g >= 1
        elif 0 < self.alpha[i] < self.C:
            return y_g == 1
        else:
            return y_g <= 1

    #计算内积矩阵#如果数据量较大，可以使用系数矩阵
    def computer_product_matrix(self):
        self.product_matrix = np.zeros((self.m,self.m)).astype(np.float)
        for i in range(self.m):
            for j in range(self.m):
                if self.product_matrix[i][j]==0.0:
                    self.product_matrix[i][j]=self.product_matrix[j][i]= self.kernel(self.X[i], self.X[j])

    # 核函数
    def kernel(self, x1, x2):
        if self._kernel == 'linear':
            return np.dot(x1,x2)
        elif self._kernel == 'poly':
            return (np.dot(x1,x2) + 1) ** 2
        return 0

    #将Ei保存在一个列表里
    def create_E(self):
        self.E=(np.dot((self.alpha * self.Y),self.product_matrix)+self.b)-self.Y

    # 预测函数g(x)
    def function_g(self, i):
        return self.b+np.dot((self.alpha * self.Y),self.product_matrix[i])

    #选择变量
    def select_alpha(self):
        # 外层循环首先遍历所有满足0
        index_list = [i for i in range(self.m) if 0 < self.alpha[i] < self.C]
        # 否则遍历整个训练集
        non_satisfy_list = [i for i in range(self.m) if i not in index_list]
        index_list.extend(non_satisfy_list)
        for i in index_list:
            if self.judge_KKT(i):
                continue
            E1 = self.E[i]
            # 如果E2是+，选择最小的；如果E2是负的，选择最大的
            if E1 >= 0:
                j =np.argmin(self.E)
            else:
                j = np.argmax(self.E)
            return i, j

    #剪切
    def clip_alpha(self, _alpha, L, H):
        if _alpha > H:
            return H
        elif _alpha < L:
            return L
        else:
            return _alpha
    #训练函数，使用SMO算法
    def Train(self, features, labels):
        self.init_args(features, labels)
        #SMO算法训练
        for t in range(self.max_iter):
            i1, i2 = self.select_alpha()

            # 边界
            if self.Y[i1] == self.Y[i2]:
                L = max(0, self.alpha[i1] + self.alpha[i2] - self.C)
                H = min(self.C, self.alpha[i1] + self.alpha[i2])
            else:
                L = max(0, self.alpha[i2] - self.alpha[i1])
                H = min(self.C, self.C + self.alpha[i2] - self.alpha[i1])

            E1 = self.E[i1]
            E2 = self.E[i2]
            # eta=K11+K22-2K12
            eta = self.kernel(self.X[i1], self.X[i1]) + self.kernel(self.X[i2], self.X[i2]) - 2 * self.kernel(
                self.X[i1], self.X[i2])
            if eta <= 0:
                # print('eta <= 0')
                continue

            alpha2_new_unc = self.alpha[i2] + self.Y[i2] * (E1 - E2) / eta  # 此处有修改，根据书上应该是E1 - E2，书上130-131页
            alpha2_new = self.clip_alpha(alpha2_new_unc, L, H)

            alpha1_new = self.alpha[i1] + self.Y[i1] * self.Y[i2] * (self.alpha[i2] - alpha2_new)

            b1_new = -E1 - self.Y[i1] * self.kernel(self.X[i1], self.X[i1]) * (alpha1_new - self.alpha[i1]) - self.Y[
                i2] * self.kernel(self.X[i2], self.X[i1]) * (alpha2_new - self.alpha[i2]) + self.b
            b2_new = -E2 - self.Y[i1] * self.kernel(self.X[i1], self.X[i2]) * (alpha1_new - self.alpha[i1]) - self.Y[
                i2] * self.kernel(self.X[i2], self.X[i2]) * (alpha2_new - self.alpha[i2]) + self.b

            if 0 < alpha1_new < self.C:
                b_new = b1_new
            elif 0 < alpha2_new < self.C:
                b_new = b2_new
            else:
                # 选择中点
                b_new = (b1_new + b2_new) / 2

            # 更新参数
            self.alpha[i1] = alpha1_new
            self.alpha[i2] = alpha2_new
            self.b = b_new

            self.create_E()#这里与书上不同，，我选择更新全部E

    def predict(self, data):
        r = self.b
        for i in range(self.m):
            r += self.alpha[i] * self.Y[i] * self.kernel(data, self.X[i])

        return 1 if r > 0 else -1

    def score(self, X_test, y_test):
        right_count = 0
        for i in range(len(X_test)):
            result = self.predict(X_test[i])
            if result == y_test[i]:
                right_count += 1
        return right_count / len(X_test)

if __name__ == '__main__':
    svm = SVM(max_iter=200)
    X, y = create_data()
    X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.333, random_state=23323)
    svm.Train(X_train, y_train)
    print(svm.score(X_test, y_test))

结果：
	dara shape: (100, 4)
	label shape: (100,)
	0.9705882352941176