写了个多层感知器，用bp梯度下降更新，拟合正弦曲线，效果凑合。

# -*- coding: utf-8 -*-import numpy as npimport matplotlib.pyplot as plt def sigmod(z): return 1.0 / (1.0 + np.exp(-z)) class mlp(object): def __init__(self, lr=0.1, lda=0.0, te=1e-5, epoch=100, size=None): self.learningRate = lr self.lambda_ = lda self.thresholdError = te self.maxEpoch = epoch self.size = size self.W = [] self.b = [] self.init() def init(self): for i in xrange(len(self.size)-1): self.W.append(np.mat(np.random.uniform(-0.5, 0.5, size=(self.size[i+1], self.size[i])))) self.b.append(np.mat(np.random.uniform(-0.5, 0.5, size=(self.size[i+1], 1)))) def forwardPropagation(self, item=None): a = [item] for wIndex in xrange(len(self.W)): a.append(sigmod(self.W[wIndex]*a[-1]+self.b[wIndex])) """ print "-----------------------------------------" for i in a: print i.shape, print for i in self.W: print i.shape, print for i in self.b: print i.shape, print print "-----------------------------------------" """ return a def backPropagation(self, label=None, a=None): # print "backPropagation--------------------begin" delta = [(a[-1]-label)*a[-1]*(1.0-a[-1])] for i in xrange(len(self.W)-1): abc = np.multiply(a[-2-i], 1-a[-2-i]) cba = np.multiply(self.W[-1-i].T*delta[-1], abc) delta.append(cba) """ print "++++++++++++++delta++++++++++++++++++++" print "len(delta):", len(delta) for ii in delta: print ii.shape, print "\n=======================================" """ for j in xrange(len(delta)): ads = delta[j]*a[-2-j].T # print self.W[-1-j].shape, ads.shape, self.b[-1-j].shape, delta[j].shape self.W[-1-j] = self.W[-1-j]-self.learningRate*(ads+self.lambda_*self.W[-1-j]) self.b[-1-j] = self.b[-1-j]-self.learningRate*delta[j] """print "=======================================1234" for ij in self.b: print ij.shape, print """ # print "backPropagation--------------------finish" error = 0.5*(a[-1]-label)**2 return error def train(self, input_=None, target=None, show=10): for ep in xrange(self.maxEpoch): error = [] for itemIndex in xrange(input_.shape[1]): a = self.forwardPropagation(input_[:, itemIndex]) e = self.backPropagation(target[:, itemIndex], a) error.append(e[0, 0]) tt = sum(error)/len(error) if tt < self.thresholdError: print "Finish {0}: ".format(ep), tt return elif ep % show == 0: print "epoch {0}: ".format(ep), tt def sim(self, inp=None): return self.forwardPropagation(item=inp)[-1] if __name__ == "__main__": tt = np.arange(0, 6.28, 0.01) labels = np.zeros_like(tt) print tt.shape """ for po in xrange(tt.shape[0]): if tt[po] < 4: labels[po] = 0.0 elif 8 > tt[po] >= 4: labels[po] = 0.25 elif 12 > tt[po] >= 8: labels[po] = 0.5 elif 16 > tt[po] >= 12: labels[po] = 0.75 else: labels[po] = 1.0 """ tt = np.mat(tt) labels = np.sin(tt)*0.5+0.5 labels = np.mat(labels) model = mlp(lr=0.2, lda=0.0, te=1e-5, epoch=500, size=[1, 6, 6, 6, 1]) print tt.shape, labels.shape print len(model.W), len(model.b) print model.train(input_=tt, target=labels, show=10) sims = [model.sim(tt[:, idx])[0, 0] for idx in xrange(tt.shape[1])] xx = tt.tolist()[0] plt.figure() plt.plot(xx, labels.tolist()[0], xx, sims, 'r') plt.show()

效果图：

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