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对偶感知机算法实现

李航老师《统计学习方法》第二章笔记。 关于感知机学习算法对偶形式的简单实现。

算法原理

算法实现

import numpy as np
from matplotlib import pyplot as plt


# S1-->随机生成训练集并标注

# train matrix
def get_train_data():
    M1 = np.random.random((100, 2))
    M11 = np.column_stack((M1, np.ones(100)))

    M2 = np.random.random((100, 2)) - 0.7
    M22 = np.column_stack((M2, np.ones(100) * (-1)))
    # 合并两类,并将位置索引加到最后
    MA = np.vstack((M11, M22))
    MA = np.column_stack((MA, range(0, 200)))

    # 作图操作
    plt.plot(M1[:, 0], M1[:, 1], 'ro')
    plt.plot(M2[:, 0], M2[:, 1], 'go')
    # 为了美观,根据数据点限制之后分类线的范围
    min_x = np.min(M2)
    max_x = np.max(M1)
    # 分隔x,方便作图
    x = np.linspace(min_x, max_x, 100)
    # 此处返回 x 是为了之后作图方便
    return MA, x


# S2-->GRAM计算
def get_gram(MA):
    GRAM = np.empty(shape=(200, 200))
    for i in range(len(MA)):
        for j in range(len(MA)):
            GRAM[i, j] = np.dot(MA[i,][:2], MA[j,][:2])
    return GRAM


# S3-->训练模型

# 模型实现
def func(alpha, b, xi, yi, yN, index, GRAM):
    pa1 = alpha * yN
    pa2 = GRAM[:, index]
    num = yi * (np.dot(pa1, pa2) + b)
    return num


# 训练training data
def train(MA, alpha, b, GRAM, yN):
    # M 存储每次处理后依旧处于误分类的原始数据
    M = []
    for sample in MA:
        xi = sample[0:2]
        yi = sample[-2]
        index = int(sample[-1])
        # 如果为误分类,改变alpha,b
        # n 为学习率
        if func(alpha, b, xi, yi, yN, index, GRAM) <= 0:
            alpha[index] += n
            b += n * yi
            M.append(sample)
    if len(M) > 0:
        train(M, alpha, b, GRAM, yN)
    return alpha, b


# 作出分类线的图
def plot_classify(w, b, x, rate0):
    y = (w[0] * x + b) / ((-1) * w[1])
    plt.plot(x, y)
    plt.title('Accuracy = ' + str(rate0))


# S4-->生成测试集并测试模型准确性

# 随机生成testing data 并作图
def get_test_data():
    M = np.random.random((50, 2))
    plt.plot(M[:, 0], M[:, 1], '*y')
    return M


# 对传入的testing data 的单个样本进行分类
def classify(w, b, test_i):
    if np.sign(np.dot(w, test_i) + b) == 1:
        return 1
    else:
        return 0


# 测试数据,返回正确率
def test(w, b, test_data):
    right_count = 0
    for test_i in test_data:
        classx = classify(w, b, test_i)
        if classx == 1:
            right_count += 1
    rate = right_count / len(test_data)
    return rate


# 作出学习率——准确率的图
def plot_n_rate(rate_l):
    # plot n-rate
    n_l = sorted([float(x) for x in rate_l.keys()])
    y = [float(rate_l[n_l[i]]) for i in range(len(n_l))]
    print(n_l, '\n', y)
    plt.plot(n_l, y, 'ro-')
    plt.title("n-accuracy")
    plt.show()



if __name__ == "__main__":
    MA, x = get_train_data()
    test_data = get_test_data()
    GRAM = get_gram(MA)
    yN = MA[:, 2]
    xN = MA[:, 0:2]
    # 定义初始值
    alpha = [0] * 200
    b = 0
    n = 1
    # 初始化最优的正确率
    rate0 = 0
    rate_l = {}

    #    print(alpha,b)
    #    循环不同的学习率n,寻求最优的学习率,即最终的rate0
    #    w0,b0为对应的最优参数
    for i in np.linspace(0.01, 1, 1000):
        n = i
        alpha, b = train(MA, alpha, b, GRAM, yN)
        alphap = np.column_stack((alpha * yN, alpha * yN))
        w = sum(alphap * xN)
        rate = test(w, b, test_data)
        # print(w,b)
        rate = test(w, b, test_data)
        if rate > rate0:
            rate_l[n] = rate
            rate0 = rate
            w0 = w
            b0 = b
            print('Until now, the best result of the accuracy on test data is ' + str(rate))
            print('with w=' + str(w0) + ' b=' + str(b0))
            print("n=", n)
            print('---------------------------------------------')
            #     在选定最优的学习率后,作图
    plot_classify(w0, b0, x, rate0)
    plt.show()

    # 作出学习率——准确率的图
    plot_n_rate(rate_l)

输出:


最后更新: 2023年1月29日