卷积神经网络(CNN)详解与代码实现

目录

1.应用场景

2.卷积神经网络结构

 2.1 卷积（convelution）

 2.2 Relu激活函数

 2.3 池化（pool）

 2.4 全连接（full connection）

 2.5 损失函数（softmax_loss）

 2.6 前向传播（forward propagation）

 2.7 反向传播（backford propagation）

 2.8 随机梯度下降（sgd_momentum）

3.代码实现流程图以及介绍

4.代码实现（python3.6）

5.运行结果以及分析

6.参考文献

 

1.应用场景

卷积神经网络的应用不可谓不广泛，主要有两大类，数据预测和图片处理。数据预测自然不需要多说，图片处理主要包含有图像分类，检测，识别，以及分割方面的应用。

图像分类：场景分类，目标分类

图像检测：显著性检测，物体检测，语义检测等等

图像识别：人脸识别，字符识别，车牌识别，行为识别，步态识别等等

图像分割：前景分割，语义分割

2.卷积神经网络结构

卷积神经网络主要是由输入层、卷积层、激活函数、池化层、全连接层、损失函数组成，表面看比较复杂，其实质就是特征提取以及决策推断。

要使特征提取尽量准确，就需要将这些网络层结构进行组合，比如经典的卷积神经网络模型AlexNet:5个卷积层+3个池化层+3个连接层结构。

2.1 卷积（convolution）

卷积的作用就是提取特征，因为一次卷积可能提取的特征比较粗糙，所以多次卷积，以及层层纵深卷积，层层提取特征（千万要区别于多次卷积，因为每一层里含有多次卷积）。

这里可能就有小伙伴问：为什么要进行层层纵深卷积，而且还要每层多次？

你可以理解为物质A有自己的多个特征（高、矮、胖、瘦、、、），所以在物质A上需要多次提取，得到不同的特征，然后这些特征组合后发生化学反应生成物质B，

而物质B又有一些新的专属于自己的特征，所以需要进一步卷积。这是我个人的理解，不对的话或者有更形象的比喻还请不吝赐教啊。

 

在卷积层中，每一层的卷积核是不一样的。比如AlexNet

第一层：96*11*11（96表示卷积核个数，11表示卷积核矩阵宽*高） stride（步长） = 4  pad（边界补零） = 0

第二层：256*5*5 stride（步长） = 1  pad（边界补零） = 2

第三，四层：384*3*3 stride（步长） = 1  pad（边界补零） = 1

第五层：256*3*3 stride（步长） = 1  pad（边界补零） = 2

卷积的篇幅说了这么多，那么到底是如何进行运算的呢，虽说网络上关于卷积运算原理铺天盖地，但是个人总感觉讲得不够透彻，或者说本人智商有待提高，

希望通过如下这幅图（某位大神的杰作）来使各位看官们能够真正理解。

 

 

这里举的例子是一个输入图片（5*5*3），卷积核（3*3*3），有两个（Filter W0，W1），偏置b也有两个（Bios b0，b1），卷积结果Output Volumn（3*3*2），步长stride = 2。

输入：7*7*3 是因为 pad = 1 （在图片边界行和列都补零，补零的行和的数目是1），

（对于彩色图片，一般都是RGB3种颜色，号称3通道，7*7指图片高h * 宽w）

，补零的作用是能够提取图片边界的特征。

卷积核深度为什么要设置成3呢？这是因为输入是3通道，所以卷积核深度必须与输入的深度相同。至于卷积核宽w，高h则是可以变化的，但是宽高必须相等。

卷积核输出o[0,0,0] = 3 （Output Volumn下浅绿色框结果），这个结果是如何得到的呢？ 其实关键就是矩阵对应位置相乘再相加（千万不要跟矩阵乘法搞混淆啦）

=> w0[:,:,0] * x[:,:,0]蓝色区域矩阵(R通道) +  w0[:,:,1] * x[:,:,1]蓝色区域矩阵（G通道）+  w0[:,:,2] * x[:,:,2]蓝色区域矩阵（B通道） + b0（千万不能丢，因为 y = w * x + b）

第一项  => 0 * 1 + 0 * 1 + 0 * 1 + 0 * (-1) + 1 * (-1) + 1 * 0 + 0 * (-1) + 1 * 1 + 1 * 0  =  0

第二项 => 0 * (-1) + 0 * (-1) + 0 * 1 + 0 * (-1) + 0 * 1 + 1 * 0 + 0 * (-1) + 2 * 1 + 2 * 0 = 2

第三项 => 0 * 1 + 0 * 0 + 0 * (-1) + 0 * 0 + 2 * 0 + 2 * 0 + 0 * 1 + 0 * (-1) + 0 * (-1) = 0

卷积核输出o[0,0,0] = > 第一项 + 第二项 + 第三项 + b0 = 0 + 2 + 0 + 1 = 3

o[0,0,1] = -5 又是如何得到的呢？

因为这里的stride = 2 ，所以 输入的窗口就要滑动两个步长，也就是红色框的区域，而运算跟之前是一样的

第一项  => 0 * 1 + 0 * 1 + 0 * 1 + 1 * (-1) + 2 * (-1) + 2 * 0 + 1 * (-1) + 1 * 1 + 2 * 0 = -3

第二项 => 0 * (-1) + 0 * (-1) + 0 * 1 + 1 * (-1) + 2 * 1 + 0 * 0 + 2 * (-1) + 1 * 1 + 1 * 0 = 0

第三项 => 0 * 1 + 0 * 0 + 0 * (-1) + 2 * 0 + 0 * 0 + 1 * 0 + 0 * 1 + 2 * (-1) + 1 * (-1)  = - 3

卷积核输出o[0,0,1] = > 第一项 + 第二项 + 第三项 + b0 = (-3) + 0 + (-3) + 1 = -5

之后以此卷积核窗口大小在输入图片上滑动，卷积求出结果，因为有两个卷积核，所有就有两个输出结果。

这里小伙伴可能有个疑问，输出窗口是如何得到的呢？

这里有一个公式：输出窗口宽 w = (输入窗口宽 w - 卷积核宽 w + 2 * pad)/stride  + 1 ，输出高 h  = 输出窗口宽 w

以上面例子， 输出窗口宽 w = ( 5 - 3 + 2 * 1)/2 + 1 = 3 ，则输出窗口大小为 3 * 3，因为有2个输出，所以是 3*3*2。

2.2 Relu激活函数

相信看过卷积神经网络结构（CNN）的伙伴们都知道，激活函数无处不在，特别是CNN中，在卷积层后，全连接（FC）后都有激活函数Relu的身影，

那么这就自然不得不让我们产生疑问：

问题1、为什么要用激活函数？它的作用是什么？

问题2、在CNN中为什么要用Relu，相比于sigmoid，tanh，它的优势在什么地方？

对于第1个问题：由 y = w * x + b 可知，如果不用激活函数，每个网络层的输出都是一种线性输出，而我们所处的现实场景，其实更多的是各种非线性的分布。

这也说明了激活函数的作用是将线性分布转化为非线性分布，能更逼近我们的真实场景。

对于第2个问题： 先看sigmoid，tanh分布

他们在 x -> 时，输出就变成了恒定值，因为求梯度时需要对函数求一阶偏导数，而不论是sigmoid，还是tanhx，他们的偏导都为0，

也就是存在所谓的梯度消失问题，最终也就会导致权重参数w ， b 无法更新。相比之下，Relu就不存在这样的问题，另外在 x > 0 时，

Relu求导 = 1，这对于反向传播计算dw，db，是能够大大的简化运算的。

使用sigmoid还会存在梯度爆炸的问题，比如在进行前向传播和反向传播迭代次数非常多的情况下，sigmoid因为是指数函数，其结果中

某些值会在迭代中累积，并成指数级增长，最终会出现NaN而导致溢出。

2.3 池化

池化层一般在卷积层+ Relu之后，它的作用是：

1、减小输入矩阵的大小（只是宽和高，而不是深度），提取主要特征。（不可否认的是，在池化后，特征会有一定的损失，所以，有些经典模型就去掉了池化这一层）。

它的目的是显而易见的，就是在后续操作时能降低运算。

2、一般采用mean_pooling（均值池化）和max_pooling（最大值池化），对于输入矩阵有translation（平移），rotation（旋转），能够保证特征的不变性。

mean_pooling 就是输入矩阵池化区域求均值，这里要注意的是池化窗口在输入矩阵滑动的步长跟stride有关，一般stride = 2.（图片是直接盗过来，这里感谢原创）

最右边7/4 => (1 + 1 + 2 + 3)/4

 

 

max_pooling 最大值池化，就是每个池化区域的最大值放在输出对应位置上。

2.4 全连接（full connection）

作用：分类器角色，将特征映射到样本标记空间，本质是矩阵变换（affine）。

至于变换的实现见后面的代码流程图，或者最好是跟一下代码，这样理解更透彻。

2.5 损失函数（softmax_loss）

作用：计算损失loss，从而求出梯度grad。

常用损失函数有:MSE均方误差，SVM（支持向量机）合页损失函数，Cross Entropy交叉熵损失函数。

这几种损失函数目前还看不出谁优谁劣，估计只有在具体的应用场景中去验证了。至于这几种损失函数的介绍，

大家可以去参考《常用损失函数小结》https://blog.csdn.net/zhangjunp3/article/details/80467350，这个哥们写得比较详细。

在后面的代码实例中，用到的是softmax_loss，它属于Cross Entropy交叉熵损失函数。

softmax计算公式：

其中， 是要计算的类别  的网络输出，分母是网络输出所有类别之和（共有  个类别）， 表示第  类的概率。

交叉熵损失：

 

其中， 是类别  的真实标签， 表示第  类的概率， 是样本总数， 是类别数。

梯度:

     =        当   != 

     =    - 1   当   = 

其中  表示真实标签对应索引下预测的目标值， 类别索引。

这个有点折磨人，原理讲解以及推导请大家可以参考这位大神的博客：http://www.cnblogs.com/zongfa/p/8971213.html。

2.6 前向传播（forward propagation）

前向传播包含之前的卷积，Relu激活函数，池化（pool），全连接(fc)，可以说，在损失函数之前操作都属于前向传播。

主要是权重参数w , b 初始化，迭代，以及更新w, b,生成分类器模型。

2.7 反向传播（back propagation）

反向传播包含损失函数，通过梯度计算dw，db，Relu激活函数逆变换，反池化，反全连接。

2.8 随机梯度下降（sgd_momentum）

作用：由梯度grad计算新的权重矩阵w

sgd公式：

其中，η为学习率，gt为x在t时刻的梯度。 

一般我们是将整个数据集分成n个epoch，每个epoch再分成m个batch，每次更新都利用一个batch的数据，而非整个训练集。

优点：batch的方法可以减少机器的压力，并且可以更快地收敛。

缺点：其更新方向完全依赖于当前的batch，因而其更新十分不稳定。

为了解决这个问题，momentum就横空出世了，具体原理详解见下路派出所（这名字霸气）的博客http://www.cnblogs.com/callyblog/p/8299074.html。

momentum即动量，它模拟的是物体运动时的惯性，即更新的时候在一定程度上保留之前更新的方向，同时利用当前batch的梯度微调最终的更新方向。

这样一来，可以在一定程度上增加稳定性，从而学习地更快，并且还有一定摆脱局部最优的能力：

其中，ρ 即momentum，表示要在多大程度上保留原来的更新方向，这个值在0-1之间，在训练开始时，由于梯度可能会很大，所以初始值一般选为0.5；

当梯度不那么大时，改为0.9。η 是学习率，即当前batch的梯度多大程度上影响最终更新方向，跟普通的SGD含义相同。ρ 与 η 之和不一定为1。

3.代码实现流程图以及介绍

代码流程图：费了老大劲，终于弄完了，希望对各位看官们有所帮助，建议对比流程图和跟踪代码，加深对原理的理解。

特别是前向传播和反向传播维度的变换，需要重点关注。

 

4.代码实现

当然，代码的整个实现是某位大神实现的，我只是在上面做了些小改动以及重点函数做了些注释，有不妥之处也希望大家不吝指教。

因为原始图片数据集太大，不好上传，大家可以直接在http://www.cs.toronto.edu/~kriz/cifar.html下载CIFAR-10 python version，

有163M，放在代码文件同路径下即可。

 start.py

 1 # -*- coding: utf-8 -*-
 2 import matplotlib.pyplot as plt
 3 '''同路径下py模块引用'''
 4 
 5 try:
 6     from . import data_utils
 7     from . import solver
 8     from . import cnn
 9 except Exception:
10     import data_utils
11     import solver
12     import cnn
13 
14 import numpy as np
15 # 获取样本数据
16 data = data_utils.get_CIFAR10_data()
17 # model初始化（权重因子以及对应偏置 w1,b1 ,w2,b2 ,w3,b3，数量取决于网络层数）
18 model = cnn.ThreeLayerConvNet(reg=0.9)
19 solver = solver.Solver(model, data,
20                 lr_decay=0.95,                
21                 print_every=10, num_epochs=5, batch_size=2, 
22                 update_rule='sgd_momentum',                
23                 optim_config={'learning_rate': 5e-4, 'momentum': 0.9})
24 # 训练，获取最佳model
25 solver.train()                 
26 
27 plt.subplot(2, 1, 1) 
28 plt.title('Training loss')
29 plt.plot(solver.loss_history, 'o')
30 plt.xlabel('Iteration')
31 
32 plt.subplot(2, 1, 2)
33 plt.title('Accuracy')
34 plt.plot(solver.train_acc_history, '-o', label='train')
35 plt.plot(solver.val_acc_history, '-o', label='val')
36 plt.plot([0.5] * len(solver.val_acc_history), 'k--')
37 plt.xlabel('Epoch')
38 plt.legend(loc='lower right')
39 plt.gcf().set_size_inches(15, 12)
40 plt.show()
41 
42 
43 best_model = model
44 y_test_pred = np.argmax(best_model.loss(data['X_test']), axis=1)
45 y_val_pred = np.argmax(best_model.loss(data['X_val']), axis=1)
46 print ('Validation set accuracy: ',(y_val_pred == data['y_val']).mean())
47 print ('Test set accuracy: ', (y_test_pred == data['y_test']).mean())
48 # Validation set accuracy:  about 52.9%
49 # Test set accuracy:  about 54.7%
50 
51 
52 # Visualize the weights of the best network
53 """
54 from vis_utils import visualize_grid
55 
56 def show_net_weights(net):    
57     W1 = net.params['W1']    
58     W1 = W1.reshape(3, 32, 32, -1).transpose(3, 1, 2, 0)    
59     plt.imshow(visualize_grid(W1, padding=3).astype('uint8'))   
60     plt.gca().axis('off')    
61 show_net_weights(best_model)
62 plt.show()
63 """

 

 

 cnn.py

 

 

 1 # -*- coding: utf-8 -*-
 2 try:
 3     from . import layer_utils
 4     from . import layers
 5 except Exception:
 6     import layer_utils
 7     import layers
 8 import numpy as np
 9 
10 class  ThreeLayerConvNet(object):
11     """    
12     A three-layer convolutional network with the following architecture:       
13        conv - relu - 2x2 max pool - affine - relu - affine - softmax
14     """
15 
16     def __init__(self, input_dim=(3, 32, 32), num_filters=32, filter_size=7,             
17                  hidden_dim=100, num_classes=10, weight_scale=1e-3, reg=0.0,
18                  dtype=np.float32):
19         self.params = {}
20         self.reg = reg
21         self.dtype = dtype
22 
23         # Initialize weights and biases
24         C, H, W = input_dim
25         self.params['W1'] = weight_scale * np.random.randn(num_filters, C, filter_size, filter_size)
26         self.params['b1'] = np.zeros(num_filters)
27         self.params['W2'] = weight_scale * np.random.randn(num_filters*H*W//4, hidden_dim)
28         self.params['b2'] = np.zeros(hidden_dim)
29         self.params['W3'] = weight_scale * np.random.randn(hidden_dim, num_classes)
30         self.params['b3'] = np.zeros(num_classes)
31 
32         for k, v in self.params.items():    
33             self.params[k] = v.astype(dtype)
34 
35 
36     def loss(self, X, y=None):
37         W1, b1 = self.params['W1'], self.params['b1']
38         W2, b2 = self.params['W2'], self.params['b2']
39         W3, b3 = self.params['W3'], self.params['b3']
40 
41         # pass conv_param to the forward pass for the convolutional layer
42         filter_size = W1.shape[2]
43         conv_param = {'stride': 1, 'pad': (filter_size - 1) // 2}
44 
45         # pass pool_param to the forward pass for the max-pooling layer
46         pool_param = {'pool_height': 2, 'pool_width': 2, 'stride': 2}
47 
48         # compute the forward pass
49         a1, cache1 = layer_utils.conv_relu_pool_forward(X, W1, b1, conv_param, pool_param)
50         a2, cache2 = layer_utils.affine_relu_forward(a1, W2, b2)
51         scores, cache3 = layers.affine_forward(a2, W3, b3)
52 
53         if y is None:    
54             return scores
55 
56         # compute the backward pass
57         data_loss, dscores = layers.softmax_loss(scores, y)
58         da2, dW3, db3 = layers.affine_backward(dscores, cache3)
59         da1, dW2, db2 = layer_utils.affine_relu_backward(da2, cache2)
60         dX, dW1, db1 = layer_utils.conv_relu_pool_backward(da1, cache1)
61 
62         # Add regularization 引入修正因子，重新计算损失，梯度
63         dW1 += self.reg * W1
64         dW2 += self.reg * W2
65         dW3 += self.reg * W3
66         reg_loss = 0.5 * self.reg * sum(np.sum(W * W) for W in [W1, W2, W3])
67 
68         loss = data_loss + reg_loss
69         grads = {'W1': dW1, 'b1': db1, 'W2': dW2, 'b2': db2, 'W3': dW3, 'b3': db3}
70 
71         return loss, grads

 

 

data.utils.py

 

 

  1 # -*- coding: utf-8 -*-
  2 import pickle 
  3 import numpy as np
  4 import os
  5 
  6 #from scipy.misc import imread
  7 
  8 def load_CIFAR_batch(filename):
  9   """ load single batch of cifar """
 10   with open(filename, 'rb') as f:
 11     datadict = pickle.load(f, encoding='bytes')
 12     X = datadict[b'data']
 13     Y = datadict[b'labels']
 14     X = X.reshape(10000, 3, 32, 32).transpose(0,2,3,1).astype("float")
 15     Y = np.array(Y)
 16     return X, Y
 17 
 18 def load_CIFAR10(ROOT):
 19   """ load all of cifar """
 20   xs = []
 21   ys = []
 22   for b in range(1,2):
 23     f = os.path.join(ROOT, 'data_batch_%d' % (b, ))
 24     X, Y = load_CIFAR_batch(f)
 25     xs.append(X)
 26     ys.append(Y)    
 27   Xtr = np.concatenate(xs)
 28   Ytr = np.concatenate(ys)
 29   del X, Y
 30   Xte, Yte = load_CIFAR_batch(os.path.join(ROOT, 'test_batch'))
 31   return Xtr, Ytr, Xte, Yte
 32 
 33 
 34 def get_CIFAR10_data(num_training=500, num_validation=50, num_test=50):
 35 
 36     """
 37     Load the CIFAR-10 dataset from disk and perform preprocessing to prepare
 38     it for classifiers. These are the same steps as we used for the SVM, but
 39     condensed to a single function.
 40     """
 41     # Load the raw CIFAR-10 data
 42 
 43     #cifar10_dir = 'C://download//cifar-10-python//cifar-10-batches-py//'
 44     cifar10_dir = '.\\cifar-10-batches-py\\'
 45     X_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)
 46     print (X_train.shape)
 47     # Subsample the data
 48     mask = range(num_training, num_training + num_validation)
 49     X_val = X_train[mask]
 50     y_val = y_train[mask]
 51     mask = range(num_training)
 52     X_train = X_train[mask]
 53     y_train = y_train[mask]
 54     mask = range(num_test)
 55     X_test = X_test[mask]
 56     y_test = y_test[mask]
 57 
 58     # 标准化数据，求样本均值，然后 样本 - 样本均值，作用：使样本数据更收敛一些，便于后续处理
 59     # Normalize the data: subtract the mean image
 60     # 如果2维空间 m*n np.mean()后 => 1*n
 61     # 对于4维空间 m*n*k*j np.mean()后 => 1*n*k*j
 62     mean_image = np.mean(X_train, axis=0)
 63     X_train -= mean_image
 64     X_val -= mean_image
 65     X_test -= mean_image
 66 
 67     # 把通道channel 提前
 68     # Transpose so that channels come first
 69     X_train = X_train.transpose(0, 3, 1, 2).copy()
 70     X_val = X_val.transpose(0, 3, 1, 2).copy()
 71     X_test = X_test.transpose(0, 3, 1, 2).copy()
 72 
 73     # Package data into a dictionary
 74     return {
 75       'X_train': X_train, 'y_train': y_train,
 76       'X_val': X_val, 'y_val': y_val,
 77       'X_test': X_test, 'y_test': y_test,
 78     }
 79     
 80 """
 81 def load_tiny_imagenet(path, dtype=np.float32):
 82   
 83   Load TinyImageNet. Each of TinyImageNet-100-A, TinyImageNet-100-B, and
 84   TinyImageNet-200 have the same directory structure, so this can be used
 85   to load any of them.
 86 
 87   Inputs:
 88   - path: String giving path to the directory to load.
 89   - dtype: numpy datatype used to load the data.
 90 
 91   Returns: A tuple of
 92   - class_names: A list where class_names[i] is a list of strings giving the
 93     WordNet names for class i in the loaded dataset.
 94   - X_train: (N_tr, 3, 64, 64) array of training images
 95   - y_train: (N_tr,) array of training labels
 96   - X_val: (N_val, 3, 64, 64) array of validation images
 97   - y_val: (N_val,) array of validation labels
 98   - X_test: (N_test, 3, 64, 64) array of testing images.
 99   - y_test: (N_test,) array of test labels; if test labels are not available
100     (such as in student code) then y_test will be None.
101   
102   # First load wnids
103   with open(os.path.join(path, 'wnids.txt'), 'r') as f:
104     wnids = [x.strip() for x in f]
105 
106   # Map wnids to integer labels
107   wnid_to_label = {wnid: i for i, wnid in enumerate(wnids)}
108 
109   # Use words.txt to get names for each class
110   with open(os.path.join(path, 'words.txt'), 'r') as f:
111     wnid_to_words = dict(line.split('\t') for line in f)
112     for wnid, words in wnid_to_words.iteritems():
113       wnid_to_words[wnid] = [w.strip() for w in words.split(',')]
114   class_names = [wnid_to_words[wnid] for wnid in wnids]
115 
116   # Next load training data.
117   X_train = []
118   y_train = []
119   for i, wnid in enumerate(wnids):
120     if (i + 1) % 20 == 0:
121       print 'loading training data for synset %d / %d' % (i + 1, len(wnids))
122     # To figure out the filenames we need to open the boxes file
123     boxes_file = os.path.join(path, 'train', wnid, '%s_boxes.txt' % wnid)
124     with open(boxes_file, 'r') as f:
125       filenames = [x.split('\t')[0] for x in f]
126     num_images = len(filenames)
127     
128     X_train_block = np.zeros((num_images, 3, 64, 64), dtype=dtype)
129     y_train_block = wnid_to_label[wnid] * np.ones(num_images, dtype=np.int64)
130     for j, img_file in enumerate(filenames):
131       img_file = os.path.join(path, 'train', wnid, 'images', img_file)
132       img = imread(img_file)
133       if img.ndim == 2:
134         ## grayscale file
135         img.shape = (64, 64, 1)
136       X_train_block[j] = img.transpose(2, 0, 1)
137     X_train.append(X_train_block)
138     y_train.append(y_train_block)
139       
140   # We need to concatenate all training data
141   X_train = np.concatenate(X_train, axis=0)
142   y_train = np.concatenate(y_train, axis=0)
143   
144   # Next load validation data
145   with open(os.path.join(path, 'val', 'val_annotations.txt'), 'r') as f:
146     img_files = []
147     val_wnids = []
148     for line in f:
149       img_file, wnid = line.split('\t')[:2]
150       img_files.append(img_file)
151       val_wnids.append(wnid)
152     num_val = len(img_files)
153     y_val = np.array([wnid_to_label[wnid] for wnid in val_wnids])
154     X_val = np.zeros((num_val, 3, 64, 64), dtype=dtype)
155     for i, img_file in enumerate(img_files):
156       img_file = os.path.join(path, 'val', 'images', img_file)
157       img = imread(img_file)
158       if img.ndim == 2:
159         img.shape = (64, 64, 1)
160       X_val[i] = img.transpose(2, 0, 1)
161 
162   # Next load test images
163   # Students won't have test labels, so we need to iterate over files in the
164   # images directory.
165   img_files = os.listdir(os.path.join(path, 'test', 'images'))
166   X_test = np.zeros((len(img_files), 3, 64, 64), dtype=dtype)
167   for i, img_file in enumerate(img_files):
168     img_file = os.path.join(path, 'test', 'images', img_file)
169     img = imread(img_file)
170     if img.ndim == 2:
171       img.shape = (64, 64, 1)
172     X_test[i] = img.transpose(2, 0, 1)
173 
174   y_test = None
175   y_test_file = os.path.join(path, 'test', 'test_annotations.txt')
176   if os.path.isfile(y_test_file):
177     with open(y_test_file, 'r') as f:
178       img_file_to_wnid = {}
179       for line in f:
180         line = line.split('\t')
181         img_file_to_wnid[line[0]] = line[1]
182     y_test = [wnid_to_label[img_file_to_wnid[img_file]] for img_file in img_files]
183     y_test = np.array(y_test)
184   
185   return class_names, X_train, y_train, X_val, y_val, X_test, y_test
186 
187 """
188 def load_models(models_dir):
189   """
190   Load saved models from disk. This will attempt to unpickle all files in a
191   directory; any files that give errors on unpickling (such as README.txt) will
192   be skipped.
193 
194   Inputs:
195   - models_dir: String giving the path to a directory containing model files.
196     Each model file is a pickled dictionary with a 'model' field.
197 
198   Returns:
199   A dictionary mapping model file names to models.
200   """
201   models = {}
202   for model_file in os.listdir(models_dir):
203     with open(os.path.join(models_dir, model_file), 'rb') as f:
204       try:
205         models[model_file] = pickle.load(f)['model']
206       except pickle.UnpicklingError:
207         continue
208   return models

 

layer.utils.py

 

 

 1 # -*- coding: utf-8 -*-
 2 try:
 3   from . import layers
 4 except Exception:
 5   import layers
 6 
 7 
 8 
 9 
10 def affine_relu_forward(x, w, b):
11   """
12   Convenience layer that perorms an affine transform followed by a ReLU
13 
14   Inputs:
15   - x: Input to the affine layer
16   - w, b: Weights for the affine layer
17 
18   Returns a tuple of:
19   - out: Output from the ReLU
20   - cache: Object to give to the backward pass
21   """
22   a, fc_cache = layers.affine_forward(x, w, b)
23   out, relu_cache = layers.relu_forward(a)
24   cache = (fc_cache, relu_cache)
25   return out, cache
26 
27 
28 def affine_relu_backward(dout, cache):
29   """
30   Backward pass for the affine-relu convenience layer
31   """
32   fc_cache, relu_cache = cache
33   da = layers.relu_backward(dout, relu_cache)
34   dx, dw, db = layers.affine_backward(da, fc_cache)
35   return dx, dw, db
36 
37 
38 pass
39 
40 
41 def conv_relu_forward(x, w, b, conv_param):
42   """
43   A convenience layer that performs a convolution followed by a ReLU.
44 
45   Inputs:
46   - x: Input to the convolutional layer
47   - w, b, conv_param: Weights and parameters for the convolutional layer
48   
49   Returns a tuple of:
50   - out: Output from the ReLU
51   - cache: Object to give to the backward pass
52   """
53   a, conv_cache = layers.conv_forward_fast(x, w, b, conv_param)
54   out, relu_cache = layers.relu_forward(a)
55   cache = (conv_cache, relu_cache)
56   return out, cache
57 
58 
59 def conv_relu_backward(dout, cache):
60   """
61   Backward pass for the conv-relu convenience layer.
62   """
63   conv_cache, relu_cache = cache
64   da = layers.relu_backward(dout, relu_cache)
65   dx, dw, db = layers.conv_backward_fast(da, conv_cache)
66   return dx, dw, db
67 
68 
69 def conv_relu_pool_forward(x, w, b, conv_param, pool_param):
70   """
71   Convenience layer that performs a convolution, a ReLU, and a pool.
72 
73   Inputs:
74   - x: Input to the convolutional layer
75   - w, b, conv_param: Weights and parameters for the convolutional layer
76   - pool_param: Parameters for the pooling layer
77 
78   Returns a tuple of:
79   - out: Output from the pooling layer
80   - cache: Object to give to the backward pass
81   """
82   a, conv_cache = layers.conv_forward_naive(x, w, b, conv_param)
83   s, relu_cache = layers.relu_forward(a)
84   out, pool_cache = layers.max_pool_forward_naive(s, pool_param)
85   cache = (conv_cache, relu_cache, pool_cache)
86   return out, cache
87 
88 
89 def conv_relu_pool_backward(dout, cache):
90   """
91   Backward pass for the conv-relu-pool convenience layer
92   """
93   conv_cache, relu_cache, pool_cache = cache
94   ds = layers.max_pool_backward_naive(dout, pool_cache)
95   da = layers.relu_backward(ds, relu_cache)
96   dx, dw, db = layers.conv_backward_naive(da, conv_cache)
97   return dx, dw, db

 

layers.py

 

 

  1 import numpy as np
  2 
  3 '''
  4 全连接层：矩阵变换，获取对应目标相同的行与列
  5 输入x: 2*32*16*16 
  6 输入x_row: 2*8192
  7 超参w：8192*100
  8 输出：矩阵乘法 2*8192 ->8192*100 =>2*100
  9 '''
 10 def affine_forward(x, w, b):   
 11     """    
 12     Computes the forward pass for an affine (fully-connected) layer. 
 13     The input x has shape (N, d_1, ..., d_k) and contains a minibatch of N   
 14     examples, where each example x[i] has shape (d_1, ..., d_k). We will    
 15     reshape each input into a vector of dimension D = d_1 * ... * d_k, and    
 16     then transform it to an output vector of dimension M.    
 17     Inputs:    
 18     - x: A numpy array containing input data, of shape (N, d_1, ..., d_k)    
 19     - w: A numpy array of weights, of shape (D, M)    
 20     - b: A numpy array of biases, of shape (M,)   
 21     Returns a tuple of:    
 22     - out: output, of shape (N, M)    
 23     - cache: (x, w, b)   
 24     """
 25     out = None
 26     # Reshape x into rows
 27     N = x.shape[0]
 28     x_row = x.reshape(N, -1)         # (N,D) -1表示不知道多少列，指定行，就能算出列 = 2 * 32 * 16 * 16/2 = 8192
 29     out = np.dot(x_row, w) + b       # (N,M) 2*8192 8192*100 =>2 * 100
 30     cache = (x, w, b)
 31 
 32     return out, cache
 33 '''
 34 反向传播之affine矩阵变换
 35 根据dout求出dx,dw,db
 36 由 out = w * x =>
 37 dx = dout * w
 38 dw = dout * x
 39 db = dout * 1
 40 因为dx 与 x，dw 与 w，db 与 b 大小（维度）必须相同
 41 dx = dout * wT  矩阵乘法
 42 dw = dxT * dout 矩阵乘法
 43 db = dout 按列求和
 44 '''
 45 def affine_backward(dout, cache):   
 46     """    
 47     Computes the backward pass for an affine layer.    
 48     Inputs:    
 49     - dout: Upstream derivative, of shape (N, M)    
 50     - cache: Tuple of: 
 51     - x: Input data, of shape (N, d_1, ... d_k)    
 52     - w: Weights, of shape (D, M)    
 53     Returns a tuple of:   
 54     - dx: Gradient with respect to x, of shape (N, d1, ..., d_k)
 55       dx = dout * w
 56     - dw: Gradient with respect to w, of shape (D, M)
 57       dw = dout * x
 58     - db: Gradient with respect to b, of shape (M,)
 59       db = dout * 1
 60     """
 61 
 62     x, w, b = cache    
 63     dx, dw, db = None, None, None
 64     dx = np.dot(dout, w.T)                       # (N,D)
 65     # dx维度必须跟x维度相同
 66     dx = np.reshape(dx, x.shape)                 # (N,d1,...,d_k)
 67     # 转换成二维矩阵
 68     x_row = x.reshape(x.shape[0], -1)            # (N,D)
 69     dw = np.dot(x_row.T, dout)                   # (D,M)
 70 
 71     db = np.sum(dout, axis=0, keepdims=True)     # (1,M)    
 72 
 73     return dx, dw, db
 74 
 75 def relu_forward(x):   
 76     """ 激活函数，解决sigmoid梯度消失问题，网络性能比sigmoid更好
 77     Computes the forward pass for a layer of rectified linear units (ReLUs).    
 78     Input:    
 79     - x: Inputs, of any shape    
 80     Returns a tuple of:    
 81     - out: Output, of the same shape as x    
 82     - cache: x    
 83     """   
 84     out = None    
 85     out = ReLU(x)    
 86     cache = x    
 87 
 88     return out, cache
 89 
 90 def relu_backward(dout, cache):   
 91     """  
 92     Computes the backward pass for a layer of rectified linear units (ReLUs).   
 93     Input:    
 94     - dout: Upstream derivatives, of any shape    
 95     - cache: Input x, of same shape as dout    
 96     Returns:    
 97     - dx: Gradient with respect to x    
 98     """    
 99     dx, x = None, cache    
100     dx = dout    
101     dx[x <= 0] = 0    
102 
103     return dx
104 
105 def svm_loss(x, y):   
106     """    
107     Computes the loss and gradient using for multiclass SVM classification.    
108     Inputs:    
109     - x: Input data, of shape (N, C) where x[i, j] is the score for the jth class         
110          for the ith input.    
111     - y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and         
112          0 <= y[i] < C   
113     Returns a tuple of:    
114     - loss: Scalar giving the loss   
115     - dx: Gradient of the loss with respect to x    
116     """    
117     N = x.shape[0]   
118     correct_class_scores = x[np.arange(N), y]    
119     margins = np.maximum(0, x - correct_class_scores[:, np.newaxis] + 1.0)    
120     margins[np.arange(N), y] = 0   
121     loss = np.sum(margins) / N   
122     num_pos = np.sum(margins > 0, axis=1)    
123     dx = np.zeros_like(x)   
124     dx[margins > 0] = 1    
125     dx[np.arange(N), y] -= num_pos    
126     dx /= N    
127 
128     return loss, dx
129 '''
130 softmax_loss 求梯度优点: 求梯度运算简单，方便 
131 softmax: softmax用于多分类过程中，它将多个神经元的输出，映射到（0,1）区间内，
132 可以看成概率来理解，从而来进行多分类。
133 Si = exp(i)/[exp(j)求和]
134 softmax_loss：损失函数，求梯度dx必须用到损失函数，通过梯度下降更新超参
135 Loss = -[Ypred*ln(Sj真实类别位置的概率值)]求和
136 梯度dx : 对损失函数求一阶偏导
137 如果 j = i =>dx = Sj - 1
138 如果 j != i => dx = Sj
139 '''
140 def softmax_loss(x, y):    
141     """    
142     Computes the loss and gradient for softmax classification.    Inputs:    
143     - x: Input data, of shape (N, C) where x[i, j] is the score for the jth class         
144     for the ith input.    
145     - y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and         
146          0 <= y[i] < C   
147     Returns a tuple of:    
148     - loss: Scalar giving the loss    
149     - dx: Gradient of the loss with respect to x   
150     """
151     '''
152      x - np.max(x, axis=1, keepdims=True) 对数据进行预处理，
153      防止np.exp(x - np.max(x, axis=1, keepdims=True))得到结果太分散；
154      np.max(x, axis=1, keepdims=True)保证所得结果维度不变；
155     '''
156     probs = np.exp(x - np.max(x, axis=1, keepdims=True))
157     # 计算softmax，准确的说应该是soft，因为还没有选取概率最大值的操作
158     probs /= np.sum(probs, axis=1, keepdims=True)
159     # 样本图片个数
160     N = x.shape[0]
161     # 计算图片损失
162     loss = -np.sum(np.log(probs[np.arange(N), y])) / N
163     # 复制概率
164     dx = probs.copy()
165     # 针对 i = j 求梯度
166     dx[np.arange(N), y] -= 1
167     # 计算每张样本图片梯度
168     dx /= N    
169 
170     return loss, dx
171 
172 def ReLU(x):    
173     """ReLU non-linearity."""    
174     return np.maximum(0, x)
175 '''
176 功能：获取图片特征
177 前向卷积：每次用一个3维的卷积核与图片RGB各个通道分别卷积（卷积核1与R进行点积，卷积核2与G点积，卷积核3与B点积）,
178 然后将3个结果求和（也就是 w*x ）,再加上 b，就是新结果某一位置输出，这是卷积核在图片某一固定小范围内（卷积核大小）的卷积，
179 要想获得整个图片的卷积结果，需要在图片上滑动卷积核（先右后下），直至遍历整个图片。
180 x: 2*3*32*32  每次选取2张图片，图片大小32*32，彩色(3通道)
181 w: 32*3*7*7   卷积核每个大小是7*7；对应输入x的3通道，所以是3维，有32个卷积核
182 pad = 3(图片边缘行列补0)，stride = 1(卷积核移动步长)
183 输出宽*高结果：(32-7+2*3)/1 + 1 = 32
184 输出大小：2*32*32*32
185 '''
186 def conv_forward_naive(x, w, b, conv_param):
187     stride, pad = conv_param['stride'], conv_param['pad']
188     N, C, H, W = x.shape
189     F, C, HH, WW = w.shape
190     x_padded = np.pad(x, ((0, 0), (0, 0), (pad, pad), (pad, pad)), mode='constant')
191     '''// : 求整型'''
192     H_new = 1 + (H + 2 * pad - HH) // stride
193     W_new = 1 + (W + 2 * pad - WW) // stride
194     s = stride
195     out = np.zeros((N, F, H_new, W_new))
196 
197     for i in range(N):       # ith image    
198         for f in range(F):   # fth filter        
199             for j in range(H_new):            
200                 for k in range(W_new):   
201                     #print x_padded[i, :, j*s:HH+j*s, k*s:WW+k*s].shape
202                     #print w[f].shape  
203                     #print b.shape  
204                     #print np.sum((x_padded[i, :, j*s:HH+j*s, k*s:WW+k*s] * w[f]))         
205                     out[i, f, j, k] = np.sum(x_padded[i, :, j*s:HH+j*s, k*s:WW+k*s] * w[f]) + b[f]
206 
207     cache = (x, w, b, conv_param)
208 
209     return out, cache
210 
211 '''
212 反向传播之卷积：卷积核3*7*7
213 输入dout:2*32*32*32
214 输出dx:2*3*32*32
215 '''
216 def conv_backward_naive(dout, cache):
217 
218     x, w, b, conv_param = cache
219     # 边界补0
220     pad = conv_param['pad']
221     # 步长
222     stride = conv_param['stride']
223     F, C, HH, WW = w.shape
224     N, C, H, W = x.shape
225     H_new = 1 + (H + 2 * pad - HH) // stride
226     W_new = 1 + (W + 2 * pad - WW) // stride
227 
228     dx = np.zeros_like(x)
229     dw = np.zeros_like(w)
230     db = np.zeros_like(b)
231 
232     s = stride
233     x_padded = np.pad(x, ((0, 0), (0, 0), (pad, pad), (pad, pad)), 'constant')
234     dx_padded = np.pad(dx, ((0, 0), (0, 0), (pad, pad), (pad, pad)), 'constant')
235     # 图片个数
236     for i in range(N):       # ith image
237         # 卷积核滤波个数
238         for f in range(F):   # fth filter        
239             for j in range(H_new):            
240                 for k in range(W_new):
241                     # 3*7*7
242                     window = x_padded[i, :, j*s:HH+j*s, k*s:WW+k*s]
243                     db[f] += dout[i, f, j, k]
244                     # 3*7*7
245                     dw[f] += window * dout[i, f, j, k]
246                     # 3*7*7 => 2*3*38*38
247                     dx_padded[i, :, j*s:HH+j*s, k*s:WW+k*s] += w[f] * dout[i, f, j, k]
248 
249     # Unpad
250     dx = dx_padded[:, :, pad:pad+H, pad:pad+W]
251 
252     return dx, dw, db
253 '''
254 功能：减少特征尺寸大小
255 前向最大池化：在特征矩阵中选取指定大小窗口，获取窗口内元素最大值作为输出窗口映射值，
256 先有后下遍历，直至获取整个特征矩阵对应的新映射特征矩阵。
257 输入x：2*32*32*32
258 池化参数：窗口：2*2，步长：2
259 输出窗口宽，高：(32-2)/2 + 1 = 16
260 输出大小：2*32*16*16
261 '''
262 def max_pool_forward_naive(x, pool_param):
263     HH, WW = pool_param['pool_height'], pool_param['pool_width']
264     s = pool_param['stride']
265     N, C, H, W = x.shape
266     H_new = 1 + (H - HH) // s
267     W_new = 1 + (W - WW) // s
268     out = np.zeros((N, C, H_new, W_new))
269     for i in range(N):    
270         for j in range(C):        
271             for k in range(H_new):            
272                 for l in range(W_new):                
273                     window = x[i, j, k*s:HH+k*s, l*s:WW+l*s] 
274                     out[i, j, k, l] = np.max(window)
275 
276     cache = (x, pool_param)
277 
278     return out, cache
279 
280 '''
281 反向传播之池化：增大特征尺寸大小
282 在缓存中取出前向池化时输入特征，选取某一范围矩阵窗口，
283 找出最大值所在的位置，根据这个位置将dout值映射到新的矩阵对应位置上，
284 而新矩阵其他位置都初始化为0.
285 输入dout:2*32*16*16
286 输出dx:2*32*32*32
287 '''
288 def max_pool_backward_naive(dout, cache):
289     x, pool_param = cache
290     HH, WW = pool_param['pool_height'], pool_param['pool_width']
291     s = pool_param['stride']
292     N, C, H, W = x.shape
293     H_new = 1 + (H - HH) // s
294     W_new = 1 + (W - WW) // s
295     dx = np.zeros_like(x)
296     for i in range(N):    
297         for j in range(C):        
298             for k in range(H_new):            
299                 for l in range(W_new):
300                     # 取前向传播时输入的某一池化窗口
301                     window = x[i, j, k*s:HH+k*s, l*s:WW+l*s]
302                     # 计算窗口最大值
303                     m = np.max(window)
304                     # 根据最大值所在位置以及dout对应值=>新矩阵窗口数值
305                     # [false,false
306                     #  true, false]  * 1 => [0,0
307                     #                        1,0]
308                     dx[i, j, k*s:HH+k*s, l*s:WW+l*s] = (window == m) * dout[i, j, k, l]
309 
310     return dx

 

optim.py

 

  1 import numpy as np
  2 
  3 def sgd(w, dw, config=None):    
  4     """    
  5     Performs vanilla stochastic gradient descent.    
  6     config format:    
  7     - learning_rate: Scalar learning rate.    
  8     """    
  9     if config is None: config = {}    
 10     config.setdefault('learning_rate', 1e-2)    
 11     w -= config['learning_rate'] * dw    
 12 
 13     return w, config
 14 '''
 15 SGD:随机梯度下降：由梯度计算新的权重矩阵w
 16 sgd_momentum 是sgd的改进版，解决sgd更新不稳定，陷入局部最优的问题。
 17 增加一个动量因子momentum，可以在一定程度上增加稳定性，
 18 从而学习地更快，并且还有一定摆脱局部最优的能力。
 19 
 20 '''
 21 def sgd_momentum(w, dw, config=None):    
 22     """    
 23     Performs stochastic gradient descent with momentum.    
 24     config format:    
 25     - learning_rate: Scalar learning rate.    
 26     - momentum: Scalar between 0 and 1 giving the momentum value.                
 27     Setting momentum = 0 reduces to sgd.    
 28     - velocity（速度）: A numpy array of the same shape as w and dw used to store a moving
 29     average of the gradients.   
 30     """   
 31     if config is None: config = {}    
 32     config.setdefault('learning_rate', 1e-2)   
 33     config.setdefault('momentum', 0.9)
 34     # config 如果存在属性velocity，则获取config['velocity']，否则获取np.zeros_like(w)
 35     v = config.get('velocity', np.zeros_like(w))    
 36     next_w = None    
 37     v = config['momentum'] * v - config['learning_rate'] * dw    
 38     next_w = w + v    
 39     config['velocity'] = v    
 40 
 41     return next_w, config
 42 
 43 def rmsprop(x, dx, config=None):    
 44     """    
 45     Uses the RMSProp update rule, which uses a moving average of squared gradient    
 46     values to set adaptive per-parameter learning rates.    
 47     config format:    
 48     - learning_rate: Scalar learning rate.    
 49     - decay_rate: Scalar between 0 and 1 giving the decay rate for the squared                  
 50     gradient cache.    
 51     - epsilon: Small scalar used for smoothing to avoid dividing by zero.    
 52     - cache: Moving average of second moments of gradients.   
 53     """    
 54     if config is None: config = {}    
 55     config.setdefault('learning_rate', 1e-2)  
 56     config.setdefault('decay_rate', 0.99)    
 57     config.setdefault('epsilon', 1e-8)    
 58     config.setdefault('cache', np.zeros_like(x))    
 59     next_x = None    
 60     cache = config['cache']    
 61     decay_rate = config['decay_rate']    
 62     learning_rate = config['learning_rate']    
 63     epsilon = config['epsilon']    
 64     cache = decay_rate * cache + (1 - decay_rate) * (dx**2)    
 65     x += - learning_rate * dx / (np.sqrt(cache) + epsilon)  
 66     config['cache'] = cache    
 67     next_x = x    
 68 
 69     return next_x, config
 70 
 71 def adam(x, dx, config=None):    
 72     """    
 73     Uses the Adam update rule, which incorporates moving averages of both the  
 74     gradient and its square and a bias correction term.    
 75     config format:    
 76     - learning_rate: Scalar learning rate.    
 77     - beta1: Decay rate for moving average of first moment of gradient.    
 78     - beta2: Decay rate for moving average of second moment of gradient.   
 79     - epsilon: Small scalar used for smoothing to avoid dividing by zero.    
 80     - m: Moving average of gradient.    
 81     - v: Moving average of squared gradient.    
 82     - t: Iteration number.   
 83     """    
 84     if config is None: config = {}    
 85     config.setdefault('learning_rate', 1e-3)    
 86     config.setdefault('beta1', 0.9)    
 87     config.setdefault('beta2', 0.999)    
 88     config.setdefault('epsilon', 1e-8)    
 89     config.setdefault('m', np.zeros_like(x))    
 90     config.setdefault('v', np.zeros_like(x))    
 91     config.setdefault('t', 0)   
 92     next_x = None    
 93     m = config['m']    
 94     v = config['v']    
 95     beta1 = config['beta1']    
 96     beta2 = config['beta2']    
 97     learning_rate = config['learning_rate']    
 98     epsilon = config['epsilon']   
 99     t = config['t']    
100     t += 1    
101     m = beta1 * m + (1 - beta1) * dx    
102     v = beta2 * v + (1 - beta2) * (dx**2)    
103     m_bias = m / (1 - beta1**t)    
104     v_bias = v / (1 - beta2**t)    
105     x += - learning_rate * m_bias / (np.sqrt(v_bias) + epsilon)    
106     next_x = x    
107     config['m'] = m    
108     config['v'] = v    
109     config['t'] = t    
110 
111     return next_x, config

solver.py

  1 import numpy as np
  2 try:
  3   from . import optim
  4 except Exception:
  5   import optim
  6 
  7 class Solver(object):
  8   """
  9   A Solver encapsulates all the logic necessary for training classification
 10   models. The Solver performs stochastic gradient descent using different
 11   update rules defined in optim.py.
 12 
 13   The solver accepts both training and validataion data and labels so it can
 14   periodically check classification accuracy on both training and validation
 15   data to watch out for overfitting.
 16 
 17   To train a model, you will first construct a Solver instance, passing the
 18   model, dataset, and various optoins (learning rate, batch size, etc) to the
 19   constructor. You will then call the train() method to run the optimization
 20   procedure and train the model.
 21   
 22   After the train() method returns, model.params will contain the parameters
 23   that performed best on the validation set over the course of training.
 24   In addition, the instance variable solver.loss_history will contain a list
 25   of all losses encountered during training and the instance variables
 26   solver.train_acc_history and solver.val_acc_history will be lists containing
 27   the accuracies of the model on the training and validation set at each epoch.
 28   
 29   Example usage might look something like this:
 30   
 31   data = {
 32     'X_train': # training data
 33     'y_train': # training labels
 34     'X_val': # validation data
 35     'X_train': # validation labels
 36   }
 37   model = MyAwesomeModel(hidden_size=100, reg=10)
 38   solver = Solver(model, data,
 39                   update_rule='sgd',
 40                   optim_config={
 41                     'learning_rate': 1e-3,
 42                   },
 43                   lr_decay=0.95,
 44                   num_epochs=10, batch_size=100,
 45                   print_every=100)
 46   solver.train()
 47 
 48 
 49   A Solver works on a model object that must conform to the following API:
 50 
 51   - model.params must be a dictionary mapping string parameter names to numpy
 52     arrays containing parameter values.
 53 
 54   - model.loss(X, y) must be a function that computes training-time loss and
 55     gradients, and test-time classification scores, with the following inputs
 56     and outputs:
 57 
 58     Inputs:
 59     - X: Array giving a minibatch of input data of shape (N, d_1, ..., d_k)
 60     - y: Array of labels, of shape (N,) giving labels for X where y[i] is the
 61       label for X[i].
 62 
 63     Returns:
 64     If y is None, run a test-time forward pass and return:
 65     - scores: Array of shape (N, C) giving classification scores for X where
 66       scores[i, c] gives the score of class c for X[i].
 67 
 68     If y is not None, run a training time forward and backward pass and return
 69     a tuple of:
 70     - loss: Scalar giving the loss
 71     - grads: Dictionary with the same keys as self.params mapping parameter
 72       names to gradients of the loss with respect to those parameters.
 73   """
 74 
 75   def __init__(self, model, data, **kwargs):
 76     """
 77     Construct a new Solver instance.
 78     
 79     Required arguments:
 80     - model: A model object conforming to the API described above
 81     - data: A dictionary of training and validation data with the following:
 82       'X_train': Array of shape (N_train, d_1, ..., d_k) giving training images
 83       'X_val': Array of shape (N_val, d_1, ..., d_k) giving validation images
 84       'y_train': Array of shape (N_train,) giving labels for training images
 85       'y_val': Array of shape (N_val,) giving labels for validation images
 86       
 87     Optional arguments:
 88     - update_rule: A string giving the name of an update rule in optim.py.
 89       Default is 'sgd'.
 90     - optim_config: A dictionary containing hyperparameters that will be
 91       passed to the chosen update rule. Each update rule requires different
 92       hyperparameters (see optim.py) but all update rules require a
 93       'learning_rate' parameter so that should always be present.
 94     - lr_decay: A scalar for learning rate decay; after each epoch the learning
 95       rate is multiplied by this value.
 96     - batch_size: Size of minibatches used to compute loss and gradient during
 97       training.
 98     - num_epochs: The number of epochs to run for during training.
 99     - print_every: Integer; training losses will be printed every print_every
100       iterations.
101     - verbose: Boolean; if set to false then no output will be printed during
102       training.
103     """
104     self.model = model
105     self.X_train = data['X_train']
106     self.y_train = data['y_train']
107     self.X_val = data['X_val']
108     self.y_val = data['y_val']
109     
110     # Unpack keyword arguments
111     # pop(key, default):删除kwargs对象中key，如果存在该key，返回该key对应的value，否则，返回default值。
112     self.update_rule = kwargs.pop('update_rule', 'sgd')
113     self.optim_config = kwargs.pop('optim_config', {})
114     self.lr_decay = kwargs.pop('lr_decay', 1.0)
115     self.batch_size = kwargs.pop('batch_size', 2)
116     self.num_epochs = kwargs.pop('num_epochs', 10)
117 
118     self.print_every = kwargs.pop('print_every', 10)
119     self.verbose = kwargs.pop('verbose', True)
120 
121     # Throw an error if there are extra keyword arguments
122     # 删除kwargs中参数后，校验是否还有多余参数
123     if len(kwargs) > 0:
124       extra = ', '.join('"%s"' % k for k in kwargs.keys())
125       raise ValueError('Unrecognized arguments %s' % extra)
126 
127     # Make sure the update rule exists, then replace the string
128     # name with the actual function
129     # 检查optim对象中是否有属性或方法名为self.update_rule
130     if not hasattr(optim, self.update_rule):
131       raise ValueError('Invalid update_rule "%s"' % self.update_rule)
132     self.update_rule = getattr(optim, self.update_rule)
133 
134     self._reset()
135 
136 
137   def _reset(self):
138     """
139     Set up some book-keeping variables for optimization. Don't call this
140     manually.
141     """
142     # Set up some variables for book-keeping
143     self.epoch = 0
144     self.best_val_acc = 0
145     self.best_params = {}
146     self.loss_history = []
147     self.train_acc_history = []
148     self.val_acc_history = []
149 
150     # Make a deep copy of the optim_config for each parameter
151     self.optim_configs = {}
152     for p in self.model.params:
153       d = {k: v for k, v in self.optim_config.items()}
154       self.optim_configs[p] = d
155 
156 
157   def _step(self):
158     """
159     Make a single gradient update. This is called by train() and should not
160     be called manually.
161     """
162     # Make a minibatch of training data
163     # 500 张图片
164     num_train = self.X_train.shape[0]
165     # 随机选出batch_size：2 张
166     batch_mask = np.random.choice(num_train, self.batch_size)
167 
168    # batch_mask = [t%(num_train//2), num_train//2 + t%(num_train//2)]
169 
170 
171 
172     # 训练样本矩阵[2,3,32,32]
173     X_batch = self.X_train[batch_mask]
174     # 标签矩阵[2,] 图片类型
175     y_batch = self.y_train[batch_mask]
176 
177     # Compute loss and gradient
178     loss, grads = self.model.loss(X_batch, y_batch)
179     self.loss_history.append(loss)
180 
181     # 更新模型超参(w1,b1),(w2,b2),(w3,b3)，以及保存更新超参时对应参数因子
182     # Perform a parameter update
183     for p, w in self.model.params.items():
184       dw = grads[p]
185       config = self.optim_configs[p]
186       next_w, next_config = self.update_rule(w, dw, config)
187       self.model.params[p] = next_w
188       # 保存参数因子，learning_rate(学习率)，velocity(速度)
189       self.optim_configs[p] = next_config
190 
191 
192   def check_accuracy(self, X, y, num_samples=None, batch_size=2):
193     """
194     Check accuracy of the model on the provided data.
195     
196     Inputs:
197     - X: Array of data, of shape (N, d_1, ..., d_k)
198     - y: Array of labels, of shape (N,)
199     - num_samples: If not None, subsample the data and only test the model
200       on num_samples datapoints.
201     - batch_size: Split X and y into batches of this size to avoid using too
202       much memory.
203       
204     Returns:
205     - acc: Scalar giving the fraction of instances that were correctly
206       classified by the model.
207     """
208     
209     # Maybe subsample the data
210     N = X.shape[0]
211     if num_samples is not None and N > num_samples:
212       # 随机选取num_samples张图片，返回选取图片索引
213       mask = np.random.choice(N, num_samples)
214       N = num_samples
215       X = X[mask]
216       y = y[mask]
217 
218     # Compute predictions in batches
219     num_batches = N // batch_size
220     if N % batch_size != 0:
221       num_batches += 1
222     y_pred = []
223     for i in range(num_batches):
224       start = i * batch_size
225       end = (i + 1) * batch_size
226       scores = self.model.loss(X[start:end])
227       y_pred.append(np.argmax(scores, axis=1))
228     y_pred = np.hstack(y_pred)
229     acc = np.mean(y_pred == y)
230 
231     return acc
232 
233   '''
234    训练模型：核心方法
235    epoch > batch_size > iteration >= 1
236    训练总的次数 = num_epochs * iterations_per_epoch
237   '''
238   def train(self):
239     """
240     Run optimization to train the model.
241     """
242     num_train = self.X_train.shape[0]
243     iterations_per_epoch = max(num_train // self.batch_size, 1)
244     num_iterations = self.num_epochs * iterations_per_epoch
245     # 迭代总的次数
246     for t in range(num_iterations):
247       # 某次iteration训练
248       self._step()
249 
250       # Maybe print training loss
251       # verbose：是否显示详细信息
252       if self.verbose and t % self.print_every == 0:
253         print ('(Iteration %d / %d) loss: %f' % (
254                t + 1, num_iterations, self.loss_history[-1]))
255 
256       # At the end of every epoch, increment the epoch counter and decay the
257       # learning rate.
258       # 每迭代完一次epoch后，更新学习率learning_rate，加快运算效率。
259       epoch_end = (t + 1) % iterations_per_epoch == 0
260       if epoch_end:
261         self.epoch += 1
262         for k in self.optim_configs:
263           self.optim_configs[k]['learning_rate'] *= self.lr_decay
264 
265       # Check train and val accuracy on the first iteration, the last
266       # iteration, and at the end of each epoch.
267       # 在第1次迭代，最后1次迭代，或者运行完一个epoch后，校验训练结果。
268       first_it = (t == 0)
269       last_it = (t == num_iterations + 1)
270       if first_it or last_it or epoch_end:
271         train_acc = self.check_accuracy(self.X_train, self.y_train,
272                                         num_samples=4)
273         val_acc = self.check_accuracy(self.X_val, self.y_val,num_samples=4)
274         self.train_acc_history.append(train_acc)
275         self.val_acc_history.append(val_acc)
276 
277         if self.verbose:
278           print ('(Epoch %d / %d) train acc: %f; val_acc: %f' % (
279                  self.epoch, self.num_epochs, train_acc, val_acc))
280 
281         # Keep track of the best model
282         if val_acc > self.best_val_acc:
283           self.best_val_acc = val_acc
284           self.best_params = {}
285           for k, v in self.model.params.items():
286             self.best_params[k] = v.copy()
287 
288     # At the end of training swap the best params into the model
289     self.model.params = self.best_params

 

 

5.运行结果以及分析

这里选取500张图片作为训练样本，epoch = 5，batch = 2，每次随机选取2张图片，迭代 5 * 500/2 = 1250次，测试样本选取50张。

由运行结果可以看出，损失loss是逐步下降的。

 

 

 

测试结果只有12%左右，原因有以下几点：

1. 模型比较简单，特征提取不能反映真实特征（一次卷积）；

2. 会出现过拟合问题；

3. 原始训练数据分类图片纹理复杂，这些图片可变性大，从而导致分类结果准确度低；

(airplane, automobile, bird, cat, deer, dog, frog, horse, ship, truck)

 

后续会通过tensorflow来实现CNN，测试准确率可以达到71.95%。

 

6. 参考文献

视觉一只白的博客《常用损失函数小结》https://blog.csdn.net/zhangjunp3/article/details/80467350

理想万岁的博客《Softmax函数详解与推导》：http://www.cnblogs.com/zongfa/p/8971213.html

下路派出所的博客《深度学习（九） 深度学习最全优化方法总结比较（SGD，Momentum，Nesterov Momentum，Adagrad，Adadelta，RMSprop，Adam）》

 http://www.cnblogs.com/callyblog/p/8299074.html

 

 

 

不要让懒惰占据你的大脑，不要让妥协拖垮了你的人生。青春就是一张票，能不能赶上时代的快车，你的步伐就掌握在你的脚下。