卷积神经网络CNN(Convolutional Neural Networks)没有原理只有实现

零.说明：

本文的所有代码均可在 DML 找到，欢迎点星星。

注.CNN的这份代码非常慢，基本上没有实际使用的可能，所以我只是发出来，代表我还是实践过而已

一.引入：

CNN这个模型实在是有些年份了，最近随着深度学习的兴起又开始焕发青春了，把imagenet测试的准确度提高了非常多，一个是Alex的工作，然后最近好像Zeiler又有突破性的成果，可惜这些我都没看过，主要是imagenet的数据太大了，我根本没有可能跑得动，所以学习的积极性有些打折扣。不说那么多，还是先实现一个最基础的CNN再说吧：

二.实现：

好吧，基本是根据DeepLearnToolbox的结构按照 Notes on Convolutional Neural Networks 来写的，大家可以先看这里的代码讲解：【面向代码】学习
Deep Learning（三）Convolution Neural Network(CNN)

本来是想根据Notes那篇文章来写的，只是最后发现如果给subsampling层加上sigmoid之后整个结构就不收敛了~~~，我用numeric_grad_check检测发现梯度计算也是对的，不明所以~~~这份代码我也上传了(old)，不过下面的代码最后就只能改成稍简化版的，貌似通常情况下CNN的pooling(subsampling)层也是没有sigmoid的，先这样吧，这个东西理解起来简单还是写了我两个下午……伤……

代码： DML/CNN/cnn.py

from __future__ import division
import numpy as np
import scipy as sp
from scipy.signal import convolve as conv
from dml.tool import sigmoid,expand,showimage
from numpy import rot90
'''
	this algorithm have refered to the DeepLearnToolBox(https://github.com/rasmusbergpalm/DeepLearnToolbox)
	also:[1]:"Notes on Convolutional Neural Networks" Jake Bouvrie 2006 - How to implement CNNs
	I want to implement as [1] described,where the subsampling layer have sigmoid function
	 but finally it does not converge,but I can pass the gradcheck!!
	 (this version is dml/CNN/cnn.py.old ,if you can figure out what is wrong in the code,PLEASE LET ME KNOW)
	at last I changed code back to simple version,delete the sigmoid in 's' layer
	ps:this code in python is too slow!don't use it do anything except reading.
'''
class LayerC:
	def __init__(self,types='i',out=0,scale=0,kernelsize=0):
		self.types=types
		self.a=None
		self.b=None
		self.d=None
		if (types=='i'):
			pass
		elif (types=='c'):
			self.out=out
			self.kernelsize=kernelsize
			self.k=None
		elif (types=='s'):
			self.scale=scale
			self.Beta={}
			self.dBeta={}

class CNNC:
	def __init__(self,X,y,layers,opts):
		self.X=np.array(X)
		self.y=np.array(y)
		self.layers=layers
		self.opts=opts
		inputmap = 1
		mapsize = np.array(self.X[0].shape)

		for i in range(len(self.layers)):
			if self.layers[i].types=='s':
				mapsize = mapsize / self.layers[i].scale
				assert np.sum(np.floor(mapsize)== mapsize)==mapsize.size
				self.layers[i].b={}
				self.layers[i].db={}
				for j in range(inputmap):
					self.layers[i].b.setdefault(j,0)
					self.layers[i].db.setdefault(j,0)
					self.layers[i].Beta.setdefault(j,1)
					self.layers[i].dBeta.setdefault(j,0.0)
				pass
			if self.layers[i].types=='c':
				mapsize = mapsize - self.layers[i].kernelsize + 1
				fan_out = self.layers[i].out*self.layers[i].kernelsize**2
				self.layers[i].k={}
				self.layers[i].dk={}
				self.layers[i].b={}
				self.layers[i].db={}
				for j in range(self.layers[i].out):

					fan_in = inputmap*self.layers[i].kernelsize**2
					for t in range(inputmap):
						self.layers[i].k.setdefault(t,{})
						self.layers[i].k[t].setdefault(j)
						self.layers[i].k[t][j]=(np.random.rand(self.layers[i].kernelsize,self.layers[i].kernelsize)-
												0.5)*2*np.sqrt(6/(fan_out+fan_in))
						self.layers[i].dk.setdefault(t,{})
						self.layers[i].dk[t].setdefault(j)
						self.layers[i].dk[t][j]=np.zeros(self.layers[i].k[t][j].shape)
					self.layers[i].b.setdefault(j,0)
					self.layers[i].db.setdefault(j,0)
				inputmap=self.layers[i].out
			if self.layers[i].types=='i':
				pass
		fvnum = np.prod(mapsize)*inputmap;
		onum = self.y.shape[0];
		self.ffb=np.zeros((onum,1))
		self.ffW=(np.random.rand(onum, fvnum)-0.5)*2*np.sqrt(6/(onum+fvnum))
	def cnnff(self,x):
		#print x
		self.layers[0].a={}
		self.layers[0].a.setdefault(0)
		self.layers[0].a[0]=x.copy()
		inputmap=1
		n=len(self.layers)

		for l in range(1,n):
			if self.layers[l].types=='s':
				for j in range(inputmap):

					temp=np.ones((self.layers[l].scale,self.layers[l].scale))/(self.layers[l].scale**2)
					z=conv(self.layers[l-1].a[j],np.array([temp]), 'valid')
					z=np.array(z)[:,::self.layers[l].scale,::self.layers[l].scale]

					if self.layers[l].a==None:
						self.layers[l].a={}
					self.layers[l].a.setdefault(j)
					self.layers[l].a[j] =z

			if self.layers[l].types=='c':
				if self.layers[l].a==None:
					self.layers[l].a={}
				for j in range(self.layers[l].out): #for each outmaps
					z = np.zeros(self.layers[l-1].a[0].shape - np.array([0,self.layers[l].kernelsize-1,self.layers[l].kernelsize-1]))
					for i in range(inputmap):       #cumulate from inputmaps
						z+=conv(self.layers[l-1].a[i],np.array([self.layers[l].k[i][j]]),'valid')
					self.layers[l].a.setdefault(j)
					self.layers[l].a[j]=sigmoid(z+self.layers[l].b[j])
				inputmap = self.layers[l].out

		self.fv=None
		for j in range(len(self.layers[n-1].a)):
			sa=self.layers[n-1].a[j].shape
			p=self.layers[n-1].a[j].reshape(sa[0],sa[1]*sa[2]).copy()
			if (self.fv==None):
				self.fv=p
			else:
				self.fv=np.concatenate((self.fv,p),axis=1)
		self.fv=self.fv.transpose()
		self.o=sigmoid(np.dot(self.ffW,self.fv) + self.ffb)

	def cnnbp(self,y):
		n=len(self.layers)
		self.e=self.o-y
		self.L=0.5*np.sum(self.e**2)/self.e.shape[1]
		self.od=self.e*(self.o*(1-self.o))

		self.fvd=np.dot(self.ffW.transpose(),self.od)
		if self.layers[n-1].types=='c':
			self.fvd=self.fvd*(self.fv*(1-self.fv))
		sa=self.layers[n-1].a[0].shape
		fvnum=sa[1]*sa[2]
		for j in range(len(self.layers[n-1].a)):
			if self.layers[n-1].d==None:
				self.layers[n-1].d={}
			self.layers[n-1].d.setdefault(j)
			self.layers[n-1].d[j]=self.fvd[(j*fvnum):((j+1)*fvnum),:].transpose().reshape(sa[0],sa[1],sa[2])

		for l in range(n-2,-1,-1):
			if self.layers[l].types=='c':
				for j in range(len(self.layers[l].a)):
					if self.layers[l].d==None:
						self.layers[l].d={}
					self.layers[l].d.setdefault(j)
					self.layers[l].d[j]=self.layers[l].a[j]*(1-self.layers[l].a[j])*
										np.kron(self.layers[l+1].d[j],np.ones((	self.layers[l+1].scale,self.layers[l+1].scale))/(self.layers[l+1].scale**2))

			elif self.layers[l].types=='s':
				for j in range(len(self.layers[l].a)):
					if self.layers[l].d==None:
						self.layers[l].d={}
					self.layers[l].d.setdefault(j)
					z=np.zeros(self.layers[l].a[0].shape)
					for i in range(len(self.layers[l+1].a)):
						rotated=np.array([rot90(self.layers[l+1].k[j][i],2)])
						z=z+conv(self.layers[l+1].d[i],rotated,'full')
					self.layers[l].d[j]=z

		for l in range(1,n):
			m=self.layers[l].d[0].shape[0]
			if self.layers[l].types=='c':
				for j in range(len(self.layers[l].a)):
					for i in range(len(self.layers[l-1].a)):
						#self.layers[l].dk[i][j]=rot90(conv(self.layers[l-1].a[i],rot90(self.layers[l].d[j],2),'valid'),2)
						self.layers[l].dk[i][j]=self.layers[l].dk[i][j]*0
						for t in range(self.layers[l].d[0].shape[0]):
							self.layers[l].dk[i][j]+=rot90(conv(self.layers[l-1].a[i][t],rot90(self.layers[l].d[j][t],2),'valid'),2)

						self.layers[l].dk[i][j]=self.layers[l].dk[i][j]/m
					self.layers[l].db[j]=np.sum(self.layers[l].d[j])/m
		self.dffW=np.dot(self.od,self.fv.transpose())/self.od.shape[1]
		self.dffb = np.mean(self.od,1).reshape(self.ffb.shape);

	def cnnapplygrads(self,alpha=0.1):
		n=len(self.layers)
		for l in range(1,n):
			if self.layers[l].types=='c':
				for j in range(len(self.layers[l].a)):
					for i in range(len(self.layers[l-1].a)):
						self.layers[l].k[i][j]-=alpha*self.layers[l].dk[i][j]
					self.layers[l].b[j]-=alpha*self.layers[l].db[j]
				pass

		self.ffW-=alpha*self.dffW
		self.ffb-=alpha*self.dffb

	def train(self):
		m=self.X.shape[0]
		batchsize=self.opts['batchsize']
		numbatches = m/batchsize
		print numbatches
		self.rL = []
		for i in range(self.opts['numepochs']):
			print 'the %d -th epoch is running'% (i+1)
			kk=np.random.permutation(m)
			for j in range(numbatches):
				print 'the %d -th batch is running , totally  %d batchs'% ((j+1),numbatches)
				batch_x=self.X[kk[(j)*batchsize:(j+1)*batchsize],:,:].copy()
				batch_y=self.y[:,kk[(j)*batchsize:(j+1)*batchsize]].copy()
				self.cnnff(batch_x)
				self.cnnbp(batch_y)
				self.cnnapplygrads(alpha=self.opts['alpha'])

				if len(self.rL)==0:
					self.rL.append(self.L)
				else:
					p=self.rL[len(self.rL)-1]
					self.rL.append(p*0.99+0.1*self.L)
				print self.L
	def gradcheck(self,test_x,test_y):
		#github上有这部分代码

	def test(self,test_x,test_y):
		self.cnnff(np.array(test_x))
		p=self.o.argmax(axis=0)
		bad= np.sum(p!=np.array(test_y).argmax(axis=0))
		print p,np.array(test_y).argmax(axis=0)
		print bad
		print np.array(test_y).shape[1]
		er=bad/np.array(test_y).shape[1]
		print er
	def pred(self,test_x):
		self.cnnff(np.array(test_x))
		p=self.o.argmax(axis=0)
		return p

三.测试

因为python跑这个实在是太慢了，主要原因我觉得是convolution函数(我用的scipy.signal.convolve)比matlab里慢太多了，所以跑MNIST以50为一个patch跑SGD一轮要二三十分钟，所以建议不要使用这份代码，你可以去用DeepLearnToolbox比这都快……

使用代码来测试：test/CNN_test/test_cnn.py

layers=[LayerC('i'),
		LayerC('c',out=6,kernelsize=5),
		LayerC('s',scale=2),
		LayerC('c',out=12,kernelsize=5),
		LayerC('s',scale=2)]
opts={}
opts['batchsize']=40
opts['numepochs']=1
opts['alpha']=1

a=CNNC(X,groundTruth,layers,opts)
#a.gradcheck(test_x[1:3,:,:],test_groundTruth[:,1:3])
a.train()
a.test(test_x,test_groundTruth)

这是一轮的结果，89.99%的准确度，应该还是正常的：