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這篇文章主要介紹Python如何實(shí)現(xiàn)三層BP神經(jīng)網(wǎng)絡(luò)算法示例,文中介紹的非常詳細(xì),具有一定的參考價(jià)值,感興趣的小伙伴們一定要看完!
下面是運(yùn)行演示函數(shù)的截圖,你會(huì)發(fā)現(xiàn)預(yù)測的結(jié)果很驚人!
提示:運(yùn)行演示函數(shù)的時(shí)候,可以嘗試改變隱藏層的節(jié)點(diǎn)數(shù),看節(jié)點(diǎn)數(shù)增加了,預(yù)測的精度會(huì)否提升
import math import random import string random.seed(0) # 生成區(qū)間[a, b)內(nèi)的隨機(jī)數(shù) def rand(a, b): return (b-a)*random.random() + a # 生成大小 I*J 的矩陣,默認(rèn)零矩陣 (當(dāng)然,亦可用 NumPy 提速) def makeMatrix(I, J, fill=0.0): m = [] for i in range(I): m.append([fill]*J) return m # 函數(shù) sigmoid,這里采用 tanh,因?yàn)榭雌饋硪葮?biāo)準(zhǔn)的 1/(1+e^-x) 漂亮些 def sigmoid(x): return math.tanh(x) # 函數(shù) sigmoid 的派生函數(shù), 為了得到輸出 (即:y) def dsigmoid(y): return 1.0 - y**2 class NN: ''' 三層反向傳播神經(jīng)網(wǎng)絡(luò) ''' def __init__(self, ni, nh, no): # 輸入層、隱藏層、輸出層的節(jié)點(diǎn)(數(shù)) self.ni = ni + 1 # 增加一個(gè)偏差節(jié)點(diǎn) self.nh = nh self.no = no # 激活神經(jīng)網(wǎng)絡(luò)的所有節(jié)點(diǎn)(向量) self.ai = [1.0]*self.ni self.ah = [1.0]*self.nh self.ao = [1.0]*self.no # 建立權(quán)重(矩陣) self.wi = makeMatrix(self.ni, self.nh) self.wo = makeMatrix(self.nh, self.no) # 設(shè)為隨機(jī)值 for i in range(self.ni): for j in range(self.nh): self.wi[i][j] = rand(-0.2, 0.2) for j in range(self.nh): for k in range(self.no): self.wo[j][k] = rand(-2.0, 2.0) # 最后建立動(dòng)量因子(矩陣) self.ci = makeMatrix(self.ni, self.nh) self.co = makeMatrix(self.nh, self.no) def update(self, inputs): if len(inputs) != self.ni-1: raise ValueError('與輸入層節(jié)點(diǎn)數(shù)不符!') # 激活輸入層 for i in range(self.ni-1): #self.ai[i] = sigmoid(inputs[i]) self.ai[i] = inputs[i] # 激活隱藏層 for j in range(self.nh): sum = 0.0 for i in range(self.ni): sum = sum + self.ai[i] * self.wi[i][j] self.ah[j] = sigmoid(sum) # 激活輸出層 for k in range(self.no): sum = 0.0 for j in range(self.nh): sum = sum + self.ah[j] * self.wo[j][k] self.ao[k] = sigmoid(sum) return self.ao[:] def backPropagate(self, targets, N, M): ''' 反向傳播 ''' if len(targets) != self.no: raise ValueError('與輸出層節(jié)點(diǎn)數(shù)不符!') # 計(jì)算輸出層的誤差 output_deltas = [0.0] * self.no for k in range(self.no): error = targets[k]-self.ao[k] output_deltas[k] = dsigmoid(self.ao[k]) * error # 計(jì)算隱藏層的誤差 hidden_deltas = [0.0] * self.nh for j in range(self.nh): error = 0.0 for k in range(self.no): error = error + output_deltas[k]*self.wo[j][k] hidden_deltas[j] = dsigmoid(self.ah[j]) * error # 更新輸出層權(quán)重 for j in range(self.nh): for k in range(self.no): change = output_deltas[k]*self.ah[j] self.wo[j][k] = self.wo[j][k] + N*change + M*self.co[j][k] self.co[j][k] = change #print(N*change, M*self.co[j][k]) # 更新輸入層權(quán)重 for i in range(self.ni): for j in range(self.nh): change = hidden_deltas[j]*self.ai[i] self.wi[i][j] = self.wi[i][j] + N*change + M*self.ci[i][j] self.ci[i][j] = change # 計(jì)算誤差 error = 0.0 for k in range(len(targets)): error = error + 0.5*(targets[k]-self.ao[k])**2 return error def test(self, patterns): for p in patterns: print(p[0], '->', self.update(p[0])) def weights(self): print('輸入層權(quán)重:') for i in range(self.ni): print(self.wi[i]) print() print('輸出層權(quán)重:') for j in range(self.nh): print(self.wo[j]) def train(self, patterns, iterations=1000, N=0.5, M=0.1): # N: 學(xué)習(xí)速率(learning rate) # M: 動(dòng)量因子(momentum factor) for i in range(iterations): error = 0.0 for p in patterns: inputs = p[0] targets = p[1] self.update(inputs) error = error + self.backPropagate(targets, N, M) if i % 100 == 0: print('誤差 %-.5f' % error) def demo(): # 一個(gè)演示:教神經(jīng)網(wǎng)絡(luò)學(xué)習(xí)邏輯異或(XOR)------------可以換成你自己的數(shù)據(jù)試試 pat = [ [[0,0], [0]], [[0,1], [1]], [[1,0], [1]], [[1,1], [0]] ] # 創(chuàng)建一個(gè)神經(jīng)網(wǎng)絡(luò):輸入層有兩個(gè)節(jié)點(diǎn)、隱藏層有兩個(gè)節(jié)點(diǎn)、輸出層有一個(gè)節(jié)點(diǎn) n = NN(2, 2, 1) # 用一些模式訓(xùn)練它 n.train(pat) # 測試訓(xùn)練的成果(不要吃驚哦) n.test(pat) # 看看訓(xùn)練好的權(quán)重(當(dāng)然可以考慮把訓(xùn)練好的權(quán)重持久化) #n.weights() if __name__ == '__main__': demo()
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