在看文章時，一篇文章提到了使用elman神經網絡來對癲癇病人的腦電信號與正常人的腦電信號進行區分，并且取得了較好的分類結果。于是就想自己寫一個elman神經網絡demo看看效果。

elman神經網絡和感知機的差別通過下面的圖片可以很明顯的看出哪里不一樣，elman在隱藏層多了一個“context units“，用來保存隱藏層的輸出，并作用到下一次隱藏層的計算中，關于elman原理的說明，大家可以自己查閱一些資料，這里不再贅述。（圖片來自維基百科https://en.wikipedia.org/wiki/Recurrent_neural_network）

""" coding: utf-8 @author: zhangxiang """ """ 在對腦電信號進行分類的時候，發現一篇文章對健康人，癲癇患者未發作時的腦電信號和癲癇發作時的腦電信號的分類使用了基于時序的 elman_RNN 神經網絡進行建模，于是想在預測麻醉深度類別及其它時序相關的分類問題上使用這一模型。 就寫了一個demo """ import numpy as npclass ELMAN_RNN(object):def __init__(self, input_num, hidden_num, output_num, learning_rate):self.input_num = input_numself.hidden_num = hidden_numself.output_num = output_numself.learning_rate = learning_rateself.hidden_weights = np.random.random((self.input_num, self.hidden_num))self.output_weights = np.random.random((self.hidden_num, self.output_num))self.rnn_weights = np.random.random((self.hidden_num, self.hidden_num))self.hidden_bias = np.random.rand(1)self.output_bias = np.random.rand(1)self.hidden_output = np.zeros((1, self.hidden_num))def training(self, train_input, train_output):"""training one time"""output = self.feed_forward(train_input)self.bptt(train_input, output, train_output)def calculate_the_cross_entropy(self, training_set):"""get the total error loss"""loss = 0for i in range(np.array(training_set).shape[0]):x, y = training_set[i]y = np.array(y).reshape(1,2)result = self.feed_forward(x)loss += self.get_the_total_error(y, result)return lossdef get_the_total_error(self, y, result):"""loss = -∑yi*ln(ai), y is the real label, result is the softmax result"""loss = -np.sum(y*np.log(result))return lossdef feed_forward(self, input):"""calculate feed_forward value"""self.hidden_output = self.sigmoid(np.dot(np.array(input).reshape(1,2), self.hidden_weights) + np.dot(self.hidden_output, self.rnn_weights) + self.hidden_bias)return self.softmax(np.dot(self.hidden_output, self.output_weights) + self.output_bias)def bptt(self,input, output, train_output):"""update the weights of all layers"""# claculate delta of output layersdelta_of_output_layers = [0]*self.output_numfor i in range(self.output_num):delta_of_output_layers[i] = self.calculate_output_wrt_rawout(output[0, i], train_output[i])# caculate delta of hidden layersdelta_of_hidden_layers = [0]*self.hidden_numfor i in range(self.hidden_num):d_error_wrt_hidden_output = 0.0for o in range(self.output_num):d_error_wrt_hidden_output += delta_of_output_layers[o]*self.output_weights[i, o]delta_of_hidden_layers[i] = d_error_wrt_hidden_output*self.calculate_output_wrt_netinput(self.hidden_output[0,i])# get the δw of output layers and update the weightsfor i in range(self.output_num):for weight_j in range(self.output_weights.shape[0]):delta_wrt_weight_j = delta_of_output_layers[i]*self.hidden_output[0,weight_j]self.output_weights[weight_j, i] -= self.learning_rate*delta_wrt_weight_j# get the δw of hidden layers and update the weightsfor i in range(self.hidden_num):for weight_j in range(self.hidden_weights.shape[0]):delta_wrt_weight_j = delta_of_hidden_layers[i]*input[weight_j]self.hidden_weights[weight_j, i] -= self.learning_rate*delta_wrt_weight_jdef sigmoid(self, x):"""activation function"""return 1.0/(1.0 + np.exp(-x))def softmax(self, x):"""the activation for multiple output function"""return np.exp(x)/np.sum(np.exp(x))def calculate_output_wrt_rawout(self, output, train_output):"""derivative of softmax function, actually in classification train_output equal to 1"""return (output - train_output)def calculate_output_wrt_netinput(self, output):"""the derivative of sigmoid function"""return output*(1 - output)if __name__ == "__main__":import matplotlib.pyplot as pltelman = ELMAN_RNN(input_num=2, hidden_num=4, output_num=2, learning_rate=0.02)train_x = [[1,2], [1,1], [1.5, 1.5], [2,1], [-1,-1], [-0.5, -0.5], [-1, -2], [-2, -1.5]]label_y = [[1,0], [1,0], [1,0], [1,0], [0,1], [0,1], [0,1], [0,1]]training_sets = [[[2,2],[1,0]], [[0.2, 0.8], [1,0]], [[-0.5, -0.8], [0, 1]], [[-1.2, -0.5], [0, 1]]]loss = []for i in range(1000):for x, y in zip(train_x, label_y):elman.training(x, y)loss.append(elman.calculate_the_cross_entropy(training_sets))plt.figure()plt.plot(loss)plt.title('the loss with the training')plt.show()print('training finished!')

loss函數的變化如下：

總結

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