延续上一篇进行修改，可用于多层卷积网络，按mini batch传播，正确率96%左右。
存在的问题是卷积速度过慢，学习率更新方式。
下一篇将使用im2col。
# coding:utf8 import cPickle import numpy as np from scipy.signal.signaltools import convolve2d class ConvPoolLayer(object): def __init__(self, image_shape,filter_shape,poolsize=(2,2)): self.filter_shape = filter_shape self.image_shape = image_shape self.w = np.random.normal(loc=0, scale=np.sqrt(1.0/np.prod(filter_shape[1:])), size=filter_shape) self.b = np.random.normal(loc=0, scale=0.2, size=(filter_shape[0],)) self.poolsize = poolsize self.samp_shape=(image_shape[-2] - filter_shape[-2] + 1,image_shape[-1] - filter_shape[-1] + 1) self.out_shape=(self.samp_shape[0]/poolsize[0],self.samp_shape[1]/poolsize[1]) def conv(self,a, v,b=0,mod=-1,r1=0,r2=0): n, m, h, w = np.shape(a) vn, vm, vh, vw = np.shape(v) assert m == vm, 'wrong filter shape' d, s = h + mod*(vh - 1), w + mod*(vw - 1) z = np.zeros((n, vn, d, s)) for i in range(n): for j in range(vn): for k in range(m): if mod==-1: z[i][j] += convolve2d(a[i][k], np.rot90(v[j][k],r1), mode='valid') else: z[i][j] += convolve2d(a[i][k], np.rot90(v[j][k],r1), mode='full') if r2==1: z[i][j]=np.rot90(z[i][j],2) if type(b)!=int: z[i]+=b[j] return z def feedforward(self, a): self.out = self.relu(self.conv(a, self.w,self.b)) return np.array(self.pool2d(self.out)) def backprop(self, x, dnext,eta=0.001): if dnext.ndim<3: dnext = np.reshape(dnext,(self.image_shape[0],self.filter_shape[0], self.out_shape[0], self.out_shape[1])) u = self.relu_prime(self.out) delta = np.multiply(u,self.up(dnext,self.poolsize[0])) delta=np.rollaxis(delta,1,0) out_delta = self.conv(np.rollaxis(delta, 1, 0), np.rollaxis(self.w, 1, 0), mod=1,r1=2) b = np.array([np.sum(d_) for d_ in delta]) w = np.array(self.conv(np.rollaxis(x,1,0), delta,r1=2,r2=1)) w = np.rollaxis(w,1,0) self.w -= eta * w/self.image_shape[0] self.b -= eta * b/self.image_shape[0] return out_delta def pool2d(self,input, ds=(2, 2), mode='max'): fun = np.max if mode == 'sum': fun = np.sum elif mode == 'average': fun = np.average n, m, h, w = np.shape(input) d, s = ds zh = h / d + h % d zw = w / s + w % s z = np.zeros((n, m, zh, zw)) for k in range(n): for o in range(m): for i in range(zh): for j in range(zw): z[k, o, i, j] = fun(input[k, o, d * i:min(d * i + d, h), s * j:min(s * j + s, w)]) return z def up(self,a,l): b=np.ones((l,l)) return np.kron(a,b) def relu(self,z): return np.maximum(z, 0.0) def relu_prime(self,z): z[z>0]=1 return z class SoftmaxLayer(object): def __init__(self, in_num=100,out_num=10): self.weights = np.random.randn(in_num, out_num)/np.sqrt(out_num) def feedforward(self, input): self.out=self.softmax(np.dot(input, self.weights)) return self.out def backprop(self, input, y,eta=0.001): o=self.out delta =o-y out_delta=np.dot(delta,self.weights.T) w = np.dot(input.T,delta) self.weights-=eta*(w) return out_delta def softmax(self,a): m = np.exp(a) return m / (np.sum(m,axis=1)[:,np.newaxis]) class FullLayer(object): def __init__(self, in_num=720,out_num=100): self.in_num=in_num self.out_num=out_num self.biases = np.random.randn(out_num) self.weights = np.random.randn(in_num, out_num)/np.sqrt(out_num) def feedforward(self, x): if x.ndim>2: x = np.reshape(x, (len(x), self.in_num)) self.out = self.sigmoid(np.dot(x, self.weights)+self.biases) return self.out def backprop(self, x,delta,eta=0.001): if x.ndim>2: x = np.reshape(x, (len(x), self.in_num)) sp=self.sigmoid_prime(self.out) delta = delta * sp out_delta = np.dot(delta, self.weights.T) w = np.dot( x.T,delta) self.weights-=eta*w self.biases -= eta*np.sum(delta,0) return out_delta def sigmoid(self,z): return 1.0/(1.0+np.exp(-z)) def sigmoid_prime(self,z): return z*(1-z) class Network(object): def __init__(self, layers): self.layers=layers self.num_layers = len(layers) self.a=[] def feedforward(self, x): self.a.append(x) for layer in self.layers: x=layer.feedforward(x) self.a.append(x) return x def SGD(self, training_data, test_data,epochs, mini_batch_size, eta=0.001): self.n = len(training_data[0]) self.mini_batch_size=mini_batch_size self.eta = eta cx=range(epochs) for j in cx: for k in xrange(0, self.n , mini_batch_size): batch_x = np.array(training_data[0][k:k + mini_batch_size]) batch_y = training_data[1][k:k + mini_batch_size] self.backprop(batch_x,batch_y) if k%500==0: print "Epoch {0}:{1} cost={3}, test:{2}".format(j,k, self.evaluate([test_data[0],test_data[1]]),self.cost) def backprop(self, x_in, y): self.feedforward(x_in) for i in range(self.num_layers): delta=self.layers[-i-1].backprop(self.a[-i-2],y,eta=self.eta) y=delta def evaluate(self, test_data): x,y=test_data num=len(x) size=self.mini_batch_size x=[self.feedforward(np.array(x[size*i:size*i+size])) for i in range((num/size))] x=np.reshape(x,(num,np.shape(x)[-1])) xp = np.argmax(x, axis=1) yp= np.argmax(y, axis=1) if y[0].ndim else y self.cost = -np.mean(np.log(x)[np.arange(num),yp]) return np.mean(yp == xp)*100 if __name__ == '__main__': def get_data(data): return [np.reshape(x, (1,28,28)) for x in data[0]] def get_label(i): c = np.zeros((10)) c[i] = 1 return c f = open('data/mnist.pkl', 'rb') training_data, validation_data, test_data = cPickle.load(f) training_inputs = get_data(training_data) training_label=[get_label(y_) for y_ in training_data[1]] test_inputs = get_data(test_data) test = zip(test_inputs,test_data[1]) size=10 net = Network([ConvPoolLayer(image_shape=[size,1,28,28],filter_shape=[8,1,5,5],poolsize=(2,2)), ConvPoolLayer(image_shape=[size,8,12,12],filter_shape=[16,8,5,5], poolsize=(2,2)), FullLayer(in_num=16*4*4,out_num=100), SoftmaxLayer(in_num=100,out_num=10)]) net.SGD([training_inputs,training_label],[test_inputs[:500],test_data[1][:500]], epochs=3,mini_batch_size=size, eta=0.05) # Epoch 0:10000 cost=0.137396947661, test:95.6