感知机算法python实现

1. 感知机

在机器学习中，感知机（Perceptron）是二分类的线性分类模型，属于监督学习算法。输入为实例的特征向量，输出为实例的类别（取+1和-1）。感知机对应于输入空间中将实例划分为两类的分离超平面。感知机旨在求出该超平面，为求得超平面导入了基于误分类的损失函数，利用随机梯度下降法（SGD）对损失函数进行最优化。

2. 感知机python实现

2.1 数据

在二维坐标图中表示如下：

2.2 python实现

#!/usr/bin/python3# -*- coding: utf-8 -*-# @Time    : 2017/11/17 20:06# @Author  : Z.C.Wang# @Email   : [e-mail]# @File    : PLA.py# @Software: PyCharm Community Edition"""Description :Perceptron learning algorithm"""import numpy as npimport matplotlib.pyplot as plt# load data from txtdata_set = []data_label = []file = open('DataSet_linear_separable.txt')for line in file:    line = line.split('\t')    for i in range(len(line)):        line[i] = float(line[i])    data_set.append(line[0:2])    data_label.append(int(line[-1]))file.close()data = np.array(data_set)label = np.array(data_label)# 初始化w, b, alphaw = np.array([0, 0])b = 0alpha = 1# 计算 y*(w*x+b)f = (np.dot(data, w.T) + b) * labelidx = np.where(f <= 0)# 使用随机梯度下降法求解w, biteration = 1while f[idx].size != 0:    point = np.random.randint((f[idx].shape[0]))    x = data[idx[0][point], :]    y = label[idx[0][point]]    w = w + alpha * y * x    b = b + alpha * y    print('Iteration:%d  w:%s  b:%s' % (iteration, w, b))    f = (np.dot(data, w.T) + b) * label    idx = np.where(f <= 0)    iteration = iteration + 1# 绘图显示x1 = np.arange(0, 6, 0.1)x2 = (w[0] * x1 + b) / (-w[1])idx_p = np.where(label == 1)idx_n = np.where(label != 1)data_p = data[idx_p]data_n = data[idx_n]plt.scatter(data_p[:, 0], data_p[:, 1], color='red')plt.scatter(data_n[:, 0], data_n[:, 1], color='blue')plt.plot(x1, x2)plt.show()print('\nPerceptron learning algorithm is over')

2.3 运行结果

结果如下：

Iteration:1  w:[-4.2 -5. ]  b:-1Iteration:2  w:[-2.2 -3.5]  b:0Iteration:3  w:[-0.2 -2. ]  b:1Iteration:4  w:[ 2.2 -0.7]  b:2Iteration:5  w:[-0.4 -3.7]  b:1Iteration:6  w:[ 1.4 -2.2]  b:2Iteration:7  w:[ 0.9 -3.2]  b:1Iteration:8  w:[ 3.3 -1.9]  b:2Iteration:9  w:[ 1.65 -3.8 ]  b:1Iteration:10  w:[ 4.65 -1.6 ]  b:2Iteration:11  w:[ 2.05 -4.6 ]  b:1Iteration:12  w:[ 4.05 -3.1 ]  b:2Iteration:13  w:[ 2.4 -5. ]  b:1Iteration:14  w:[ 5.5 -2.2]  b:2Iteration:15  w:[ 3.85 -4.1 ]  b:1Perceptron learning algorithm is over