支持向量机（SVM）算法的Python实现

更多机器学习算法的实现，详见 https://github.com/WiseDoge/ML-by-Python

import numpy as npclass SVC(object):    """    支持向量机(Support Vector Machine)二分类器, 默认的核函数是    多项式函数。    使用时，正类用1表示，负类用-1表示。    如果有必要，可自行编写新的核函数。    """    def __init__(self, C, e=0.3, kernel='poly'):        '''        :param C: 常数C，用来控制非线性部分的权重        :param e: 误差，做为训练停止的条件        :param kernel: 核函数，默认为多项式函数        '''        self.kernel = self.poly_kern        self.e = e        self.C = C        self.bias = 0    def poly_kern(self, x, z, p=1):        '''        :param x: 第一个向量        :param z: 第二个向量        :param p: 指数，默认为1，代表线性。        :return: (np.dot(x, z) + 1) ** p        '''        return (np.dot(x, z) + 1) ** p    def fit(self, train_x, train_y):        '''        :param train_x: 训练集X        :param train_y: 训练集Y        :return: None        拟合SVM        '''        self.train_x = train_x        self.train_y = train_y        self.alpha = np.zeros(train_x.shape[0])        while True:            index1, index2 = self.choose_alpha()            if index1 == -1:                break            if self.train(index1, index2):                break    def get_index_two(self, index1):        '''        :param index1: alpha1的下标        :return: alpha2的下标        SMO算法的步骤，给定alpha1的坐标，通过MAX|E1 - E2|来获取alpha2的下标        '''        errors = np.array([abs(self.error(i) - self.error(index1)) for i in range(self.train_x.shape[0])])        return np.where(errors == errors.max())[0][0]    def choose_alpha(self):        '''        :return: alpha1和alpha2的下标        SMO算法的步骤，用来选取alpha1        '''        for i in range(self.alpha.shape[0]):            if 0 < self.alpha[i] < self.C:                if 1 - self.e <= self.train_y[i] * self.g(self.train_x[i]) <= 1 + self.e:                    index2 = self.get_index_two(i)                    return i, index2        for i in range(self.alpha.shape[0]):            if 0 < self.alpha[i] < self.C:                continue            if self.alpha[i] == 0:                if self.train_y[i] * self.g(self.train_x[i]) < 1:                    index2 = self.get_index_two(i)                    return i, index2            else:                if self.train_y[i] * self.g(self.train_x[i]) > 1:                    index2 = self.get_index_two(i)                    return i, index2        return -1, -1    def train(self, i1, i2):        '''        :param i1: alpha1        :param i2: alpha2        :return: 停止训练返回True，继续训练返回False        采用SMO训练alpha，同时更新bias的值        '''        x1 = self.train_x[i1]        x2 = self.train_x[i2]        y1 = self.train_y[i1]        y2 = self.train_y[i2]        old_alpha = self.alpha.copy()        eta = self.kernel(x1, x1) \              + self.kernel(x2, x2) \              - 2.0 * self.kernel(x1, x2)        alpha2 = self.alpha[i2] \                 + self.train_y[i2] * (self.error(i1) - self.error(i2)) / eta        if y1 == y2:            l = max(0, self.alpha[i2] + self.alpha[i1] - self.C)            h = min(self.C, self.alpha[i2] + self.alpha[i1])        else:            l = max(0, self.alpha[i2] - self.alpha[i1])            h = min(self.C, self.C + self.alpha[i2] - self.alpha[i1])        if alpha2 > h:            alpha2 = h        elif alpha2 < l:            alpha2 = l        alpha_old_1 = self.alpha[i1]        self.alpha[i1] += y1 * y2 * (self.alpha[i2] - alpha2)        self.alpha[i2] = alpha2        b1 = -1 * self.error(i1) \             - y1 * self.kernel(x1, x1) * (self.alpha[i1] - alpha_old_1) \             - y2 * self.kernel(x2, x1) * (self.alpha[2] - alpha2) \             + self.bias        b2 = -1 * self.error(i2) \             - y1 * self.kernel(x1, x2) * (self.alpha[i1] - alpha_old_1) \             - y2 * self.kernel(x2, x2) * (self.alpha[2] - alpha2) \             + self.bias        if 0 < self.alpha[i1] < self.C:            self.bias = b1        elif 0 < self.alpha[i2] < self.C:            self.bias = b2        else:            self.bias = 0.5 * (b1 + b2)        if np.linalg.norm(old_alpha - self.alpha) < self.e:            return True        else:            return False    def error(self, index):        '''        :param index: 要计算的训练集下标        :return: E(X)        求E(X) = g(x) - y，即预测值与真实值的偏差        '''        return self.g(self.train_x[index]) - self.train_y[index]    def g(self, x):        '''        :param x: 样本        :return: g(x)        预测函数 g(x) = Σ(alpha[i] * y[i] * k(x, xi)) + bias        '''        ans = 0.0        for i in range(self.train_x.shape[0]):            ans += self.alpha[i] * self.train_y[i] * self.kernel(x, self.train_x[i])        return ans + self.bias    def predict_one(self, x):        '''        :param x: 测试样本.        :return: 样本所属类别        预测单个样本        '''        return 1 if self.g(x) >= 0 else -1    def predict(self, test_x):        '''        :param test_x: 测试集        :return: 测试集样本的类别        '''        return np.array([self.predict_one(x) for x in test_x])