之前的随笔卷积层和池化层中有一个凌乱的CNN实现，此处做一些修改。
主要改动：
1.将ConvLayer和PoolLayer合并。
在theano的例子（基于theano的深度卷积神经网络）中，这两层共用一套weight和biasis；在caffe中（Caffe学习 一 网络参数和自定义网络），没有设置PoolLayer相应的权重和偏置。
上面代码中，给PoolLayer添加权重时，只有在loc在1附近，scale较小时才能得到较好的结果。
我的理解是池化通过采样降低数据量、增加平移不变性的同时保留信息，添加权重后会丢失一部分如max pooling得到的信息。
2.将不同的层分开。
在前向和后向传播中，层与层之间方法未变，只是输入输出不一样。
分开之后，方便配置不同的网络结构。
根据公式，卷积核在前向和反向传播中需要旋转180度一次。此例中前向不旋转，反向旋转，相当于卷积核是旋转过的weight。（sg.convolve2d自带旋转）
下一篇中，将采用相反的方式。
存在的问题：
1.mini_batch实际上是单个更新的。
2.卷积速度太慢。
将在后续修改。
# coding:utf8 import cPickle import numpy as np from scipy.signal.signaltools import convolve2d class ConvPoolLayer(object): # layer init def __init__(self, image_shape,filter_shape,poolsize=(2,2)): self.filter_shape = filter_shape # 5, 5, 5, 卷积核5*5，5个 self.image_shape = image_shape # 28, 28 self.w = np.random.normal(loc=0, scale=np.sqrt(1.0/np.prod(filter_shape[1:])), size=filter_shape) # 2*2/5/5/5 self.b = np.random.normal(loc=0, scale=0.2, size=(filter_shape[0],)) self.samp_shape=(image_shape[0] - filter_shape[1] + 1,image_shape[1] - filter_shape[2] + 1) # 12*12 self.poolsize = poolsize # 2,2 self.out_shape=(self.samp_shape[0]/poolsize[0],self.samp_shape[1]/poolsize[1]) def conv(self,a, v, full=0): # valid:0 full:1 ah, aw = a.shape vh, vw = v.shape if full: temp = np.zeros((ah + 2 * vh - 2, aw + 2 * vw - 2)) temp[vh - 1:vh - 1 + ah, vw - 1:vw - 1 + aw] = a a = temp ah, aw = np.shape(a) k=np.ones((ah - vh + 1,aw - vw + 1)) # vt=np.mat(v.flatten()).T for i in range(ah - vh + 1): for j in range(aw - vw + 1): #k[i, j] = np.dot(a[i:i + vh, j:j + vw].flatten(), vt) k[i, j] = np.sum(np.multiply(a[i:i + vh, j:j + vw], v)) return k def feedforward(self, a): #28*28 #self.out = [self.relu(self.conv(a, self.rot180(w_))+b_) for b_,w_ in zip(self.b,self.w)] self.out = [self.relu(convolve2d(a, self.rot180(w_),mode='valid')+b_) for b_,w_ in zip(self.b,self.w)] return np.array([self.samp(a_) for a_ in self.out]) def backprop(self, x, dnext,eta=0.001): if dnext.ndim<3: dnext = np.reshape(dnext, (self.filter_shape[0], self.out_shape[0], self.out_shape[1])) # 5*12*12 u = self.relu_prime(self.out) #5*24*24 delta = [(np.multiply(u_,self.up(d_,2))) for u_,d_ in zip(u,dnext)] b = np.array([np.sum(d_) for d_ in delta]) w = [convolve2d(x, d_,mode='valid') for d_ in delta] w = np.array([np.rot90(i,2) for i in w]) self.w -= eta * w self.b -= eta * b return delta def samp(self,a): # 24*24->12*12 ah, aw = self.samp_shape # 24,24 vh, vw = self.poolsize # 2,2 k = [[np.max(a[i*vh:i*vh+vh,j*vw :j*vw+vw]) for j in range(aw / vw)] for i in range(ah / vh)] return np.array(k) 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) 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, (1, 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, (1, 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*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 = training_data[0][k:k + mini_batch_size] batch_y = training_data[1][k:k + mini_batch_size] self.update_mini_batch(batch_x,batch_y) if k%1000==0: print "Epoch {0}:{1} train: {2} cost={3}, test: {4}".format(j,k, self.evaluate([training_data[0][:500],training_data[1][:500]]) ,self.cost, self.evaluate([test_data[0],test_data[1]])) def update_mini_batch(self, batch_x,batch_y): for i in range(10): self.backprop(batch_x[i], batch_y[i]) 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 x=[self.feedforward(i)[0] for i in x] 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(500),yp]) return np.mean(yp == xp)*100 if __name__ == '__main__': def get_data(data): return [np.reshape(x, (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]) net = Network([ConvPoolLayer(image_shape=[28,28],filter_shape=[5,5,5],poolsize=(2,2)), FullLayer(in_num=720,out_num=100), SoftmaxLayer(in_num=100,out_num=10)]) net.SGD([training_inputs,training_label],[test_inputs[:500],test_data[1][:500]], epochs=10,mini_batch_size=10, eta=0.005) # Epoch 0:27000 train: 94.6 cost=0.235302322005, test: 94.2