python实现基本的机器学习算法系列（3）：感知机

from sklearn.datasets import make_blobs
from sklearn.model_selection import train_test_split
import numpy as np
import matplotlib.pyplot as plt


X, y = make_blobs(n_samples=1000, centers=2)
# y = y[:, np.newaxis]

y[np.where(y==0)]=-1
# y = np.where(y==0, -1, 1)

x_train, x_test, y_train, y_test = train_test_split(X, y)
x_train = np.c_[x_train, np.ones(x_train.shape[0])]
x_test = np.c_[x_test, np.ones(x_test.shape[0])]

class Perception:
    def __init__(self):
        self.W = None

    def Heaviside_Step(self, z):    # sign()
        # return 1 if z>=0 else -1
        return np.where(z>=0, 1, -1)
        # return np.sign(z)   sign在z==0时，输出值为0

    # def fit(self, x_train, y_train, epoch, learning_rate):
    #     n_samples, n_feature = x_train.shape
    #     self.W = np.random.randn(n_feature)
    #     losses=[]
    #
    #     for i in range(epoch):
    #         y_pred = np.dot(x_train, self.W)
    #         # if y_train.dot(y_pred)<=0:  # 这是在给很多样本的预期值和真实值做求和运算，会导致有的样本对了但有的样本错了，加和后总体结果又会对了。
    #         loss = np.max(0.0, -y_train.dot(y_pred))
    #         losses.append(loss)
    #
    #         dw = -x_train.T.dot(y_train) # 问题在这里！！！！！！！！！！，dw的值恒定了，没有更新。
    #         self.W -= learning_rate*dw
    #         if i % 10 == 0:
    #             print(f"After {i} epoch, loss is {loss}")
    #
    #     return self.W, losses


    def fit(self, x_train, y_train, epoch, learning_rate):
        n_samples, n_feature = x_train.shape
        self.W = np.random.randn(n_feature)
        losses=[]
        for i in range(epoch):
            y_pred = x_train.dot(self.W)
            loss = sum(np.maximum(0, -y_train * y_pred)) / n_samples
            losses.append(loss)
            if i % 1 == 0:
                print(f"After {i} epoch, loss is {loss}.")

            idx = np.argmax(np.maximum(0, -y_train*y_pred))
            if y_train[idx]*y_pred[idx] > 0:
                break
            dw = x_train[idx]*y_train[idx]    # 找出分类错误的样本，更新权重
            self.W += learning_rate*dw

        return self.W, losses


    def predition(self, x_test, y_test):
        y_ = self.Heaviside_Step(x_test.dot(self.W))
        score = len(np.where(y_ == y_test)[0])/len(y_test)*100
        print(f"The test data score is {score}%")
        return y_

def plot_hyperplane(X, y, Weight):
    xmin = np.min(X[:, 0])
    xmax = np.max(X[:, 0])
    x_hyperplane = np.array([xmin, xmax])
    y_hyperplane = -(x_hyperplane*Weight[0]+Weight[-1])/Weight[1]
    plt.figure(figsize=(8, 6))
    plt.scatter(X[:,0], X[:,1], c=y)
    plt.plot(x_hyperplane, y_hyperplane, c='b', linewidth=2)
    plt.xlabel('first feature', fontsize=12)
    plt.ylabel('second feature', fontsize=12)
    plt.title("Data and hyperplane", fontsize=16)
    plt.show()


if __name__ == "__main__":
    P = Perception()
    epoch = 1000
    lr = 0.1
    Weight, losses = P.fit(x_train, y_train, epoch, lr)
    y_pred = P.predition(x_test, y_test)

    plot_hyperplane(X, y, Weight)
    plt.plot(range(len(losses)), losses)
    plt.show()