卷积神经网络CNN（LeNet）的Theano实现

一、LeNet 结构

二、卷积层

ConvOp是在Theano中实现卷积层的主要主力。 ConvOp由theano.tensor.signal.conv2d使用，它具有两个输入：
1. input：对应于小批量输入图像的4D tensor。 tensor的形状如下：[mini-batch大小，输入的feature maps数量，图像height，图像width]。
2. W: 对应于权重矩阵W的4D tensor。tensor的形状是：[层 m的feature map的数量，层m-1处的feature map的数量，filter height，filter width]

举个简单的栗子：
输入： 3个feature map（一个500*500大小的RGB图片）
卷积：2个9*9*3大小的卷积核
输出：2个feature map

代码如下：

import theanofrom theano import tensor as Tfrom theano.tensor.nnet import conv2dimport numpyimport pylabfrom PIL import Imagerng = numpy.random.RandomState(23455)# instantiate 4D tensor for inputinput = T.tensor4(name='input')# initialize shared variable for weights.w_shp = (2, 3, 9, 9)# [#f_map of the m layer,#f_map of the m-1 layer, n_filter,filter_height,filter_width]w_bound = numpy.sqrt(3 * 9 * 9)W = theano.shared(numpy.asarray(    rng.uniform(        low=-1.0 / w_bound,        high=1.0 / w_bound,        size=w_shp),    dtype=input.dtype), name='W')# initialize shared variable for bias (1D tensor) with random values# IMPORTANT: biases are usually initialized to zero. However in this# particular application, we simply apply the convolutional layer to# an image without learning the parameters. We therefore initialize# them to random values to "simulate" learning.b_shp = (2,)b = theano.shared(numpy.asarray(    rng.uniform(low=-.5, high=.5, size=b_shp),    dtype=input.dtype), name='b')# build symbolic expression that computes the convolution of input with# filters in wconv_out = conv2d(input, W)   #4d tensor dimension [batch_size, n_filter,f_map_height,f_map_width]  [1,2,112,112]# build symbolic expression to add bias and apply activation function, i.e. produce neural net layer outputoutput = T.nnet.sigmoid(conv_out + b.dimshuffle('x', 0, 'x', 'x'))# create theano function to compute filtered imagesf = theano.function([input], output,allow_input_downcast=True)# open random image of dimensions 639x516#path=r'E:\\py\\theano\\3wolfmoon.jpg'img = Image.open('cat.jpg')# dimensions are (height, width, channel)img = numpy.asarray(img, dtype='float64') / 256.# put image in 4D tensor of shape (1, 3, height, width)img_ = img.transpose(2, 0, 1).reshape(1, 3, 500, 500)filtered_img = f(img_)# plot original image and first and second components of outputpylab.subplot(1, 3, 1); pylab.axis('off'); pylab.imshow(img)pylab.gray();# recall that the convOp output (filtered image) is actually a "minibatch",# of size 1 here, so we take index 0 in the first dimension:pylab.subplot(1, 3, 2); pylab.axis('off'); pylab.imshow(filtered_img[0, 0, :, :])pylab.subplot(1, 3, 3); pylab.axis('off'); pylab.imshow(filtered_img[0, 1, :, :])pylab.show()

运行结果如下：

可以看到，随机生成的卷积核也能达到类似边缘滤波的效果！

三、MaxPooling

Maxpooling 实际上是下采样的过程，在每个n*n的子块中取最大的值输出。

主要作用有两点：
1. 去除最大值以外的值，使得后续计算量减少
2. 提供平移不变性，原因如下：

每张图的底层是卷积层的输出，上层是池化后的输出。上图是原本的，下图是向右平移一位后的。可以看到虽然底层的每个数值都变了，但是池化后的输出中只有一半数值变化了。因为maxpooling只对最大值敏感，只要左边新引入的数值不比原来的最大值大，右边移出池化区域的数值不是原本的最大值，那么maxpooling的结果就不会变。

Maxpooling通过theano.tensor.signal.pool.pool_2d完成

输入：
1. input . N维tensor
2. 下采样因子，比如[2,2]
3. ignore_border: 一般设为True

再举个栗子：

from theano.tensor.signal import poolinput = T.dtensor4('input')maxpool_shape = (2, 2)pool_out = pool.pool_2d(input, maxpool_shape, ignore_border=True)f = theano.function([input],pool_out)invals = numpy.random.RandomState(1).rand(3, 2, 5, 5)print 'With ignore_border set to True:'print 'invals[0, 0, :, :] =\n', invals[0, 0, :, :]print 'output[0, 0, :, :] =\n', f(invals)[0, 0, :, :]pool_out = pool.pool_2d(input, maxpool_shape, ignore_border=False)f = theano.function([input],pool_out)print 'With ignore_border set to False:'print 'invals[1, 0, :, :] =\n ', invals[1, 0, :, :]print 'output[1, 0, :, :] =\n ', f(invals)[1, 0, :, :]

运行结果：

With ignore_border set to True:    invals[0, 0, :, :] =    [[  4.17022005e-01   7.20324493e-01   1.14374817e-04   3.02332573e-01 1.46755891e-01]     [  9.23385948e-02   1.86260211e-01   3.45560727e-01   3.96767474e-01 5.38816734e-01]     [  4.19194514e-01   6.85219500e-01   2.04452250e-01   8.78117436e-01 2.73875932e-02]     [  6.70467510e-01   4.17304802e-01   5.58689828e-01   1.40386939e-01 1.98101489e-01]     [  8.00744569e-01   9.68261576e-01   3.13424178e-01   6.92322616e-01 8.76389152e-01]]    output[0, 0, :, :] =    [[ 0.72032449  0.39676747]     [ 0.6852195   0.87811744]]With ignore_border set to False:    invals[1, 0, :, :] =    [[ 0.01936696  0.67883553  0.21162812  0.26554666  0.49157316]     [ 0.05336255  0.57411761  0.14672857  0.58930554  0.69975836]     [ 0.10233443  0.41405599  0.69440016  0.41417927  0.04995346]     [ 0.53589641  0.66379465  0.51488911  0.94459476  0.58655504]     [ 0.90340192  0.1374747   0.13927635  0.80739129  0.39767684]]    output[1, 0, :, :] =    [[ 0.67883553  0.58930554  0.69975836]     [ 0.66379465  0.94459476  0.58655504]     [ 0.90340192  0.80739129  0.39767684]]

四、CNN结构

具体采取的cnn结构如下图：

layer0： conv+pool
layer1： conv+pool
layer3： tanh
layer4： softmax

全部代码下载：csdn下载链接

这里贴一下build model的代码：

def evaluate_lenet(learning_rate=0.1, n_epochs=200,                   dataset='mnist.pkl.gz',                   nkerns=[20, 50], batch_size=500):    rng = numpy.random.RandomState(23455)    # load data    datasets = load_data(dataset)    train_setx, train_sety = datasets[0]    valid_setx, valid_sety = datasets[1]    test_setx, test_sety = datasets[2]    # compute number of minibatches for train/valid/test    n_train_batches = train_setx.get_value(borrow=True).shape[0] // batch_size    n_valid_batches = valid_setx.get_value(borrow=True).shape[0] // batch_size    n_test_batches = test_setx.get_value(borrow=True).shape[0] // batch_size    # declare variables of the data    index = T.lscalar()  # index to a minibatch    x = T.matrix('x')  # data representing  images    y = T.ivector('y')  # data representing tags(classes)    ###############    # build model #    ###############    print('... building the model')    # reshape the image data into 4D tensor of the shape(batch_size,number of    # feature map, image height,image width) in order to be compatible with    # our LeNetConvPoolLayer.    # (28,28) is the size of MNIST images    layer0_input = x.reshape((batch_size, 1, 28, 28))    layer0 = LeNetConvPoolLayer(        rng,        input=layer0_input,        filter_shape=(nkerns[0], 1, 5, 5),        image_shape=(batch_size, 1, 28, 28),    )    layer1 = LeNetConvPoolLayer(        rng,        input=layer0.output,        filter_shape=(nkerns[1], nkerns[0], 5, 5),        image_shape=(batch_size, nkerns[0], 12, 12)    )    layer2_input = layer1.output.flatten(2)    layer2 = HiddenLayer(        rng,        input=layer2_input,        n_in=nkerns[1] * 4 * 4,        n_out=500,        activation=T.tanh    )    layer3 = LogisticRegression(input=layer2.output, n_in=500, n_out=10)    cost = layer3.negative_log_likelihood(y)    params = layer3.params + layer2.params + layer1.params + layer0.params    grads = T.grad(cost, params)    updates = [        (param_i, param_i - learning_rate * grad_i)        # param and its corresponding grad in pairs        for param_i, grad_i in zip(params, grads)    ]    train_model = theano.function(        [index],        cost,        updates=updates,        givens={            x: train_setx[index * batch_size:(index + 1) * batch_size],            y: train_sety[index * batch_size:(index + 1) * batch_size]        }    )

五、 结果