[深度学习PART I] 单层感知器

1. 原理

单层感知器的原始形式如下：

如果把偏置项当作特殊权值，则单层感知器可以改为如下形式：

感知器的学习规则

学习率：

（1）学习率太大，容易造成权值调整不稳定。

（2）学习率太小，权值调整太慢，迭代次数太多。

收敛条件：

（1）误差小于某个预先设定的较小的值。

（2）两次迭代之间的权值变化已经很小。

（3）设定最大迭代次数，当迭代次数超过最大次数就停止。

2. 样例代码

Perceptron.py

# -*- encoding: utf-8 -*-import numpy as npclass Perceptron:    def __init__(self):        self.W = None        self.trainTimes = 0    def train(self, X, Y, n, learningRate):        '''training'''        # random W        row, column = X.shape        self.W = (np.random.random(column) - 0.5) * 2        # training for n times        for i in range(n):            # training            self.trainTimes += 1            output = np.sign(np.dot(X, self.W.T))            gain = learningRate * ((Y - output).dot(X)) / row            self.W += gain            # check            newOutput = np.sign(np.dot(X, self.W.T))            if (newOutput == Y).all():                break    def getW(self):        return self.W    def getTrainTimes(self):        return self.trainTimes    def predict(self, x):        return np.sign(np.dot(x, self.W.T))

Test4Perceptron.py

# -*- encoding: utf-8 -*-from Perceptron import *import numpy as npimport matplotlib.pyplot as pltdef test():    # training data    X = np.array([[1, 3, 3], [1, 4, 3], [1, 1, 1]])    Y = np.array([1, 1, -1])    learningRate = 0.1    learningTimes = 100    # training    perceptron = Perceptron()    perceptron.train(X, Y, learningTimes, learningRate)    W = perceptron.getW()    trainTimes = perceptron.getTrainTimes()    print W    print trainTimes    # plot the training data    X1 = [3, 4]    Y1 = [3, 3]    X2 = [1]    Y2 = [1]    k = -W[1] / W[2]    d = -W[0] / W[2]    x = np.linspace(0, 5)   # generate arithmetic sequence    # plot    plt.figure()    plt.plot(x, x*k+d, 'r')    plt.plot(X1, Y1, 'bo')    plt.plot(X2, Y2, 'yo')    plt.show()    # predict    test = np.array([[1, 2, 3], [1, 6, 2], [1, 3, 3], [1, 7, 5], [1, 5, 7], [1, 9, 2]])    testResult = perceptron.predict(test)    print testResult    testX1 = []    testY1 = []    testX2 = []    testY2 = []    for i in range(len(testResult)):        if testResult[i] >= 0:            testX1.append(test[i][1])            testY1.append(test[i][2])        else:            testX2.append(test[i][1])            testY2.append(test[i][2])    plt.figure()    plt.plot(x, x*k+d, 'r')    plt.plot(testX1, testY1, 'bo')    plt.plot(testX2, testY2, 'yo')    plt.show()if __name__ == '__main__':    test()