卷積神經網絡(CNN)詳解與代碼實現
本文系作者原創，轉載請註明出處:https://www.cnblogs.com/further-further-further/p/10430073.html
目錄
1.應用場景
2.卷積神經網絡結構
2.1 卷積（convelution）
2.2 Relu激活函數
2.3 池化（pool）
2.4 全連接（full connection）
2.5 損失函數（softmax_loss）
2.6 前向傳播（forward propagation）
2.7 反向傳播（backford propagation）
2.8 隨機梯度下降（sgd_momentum）
3.代碼實現流程圖以及介紹
4.代碼實現（python3.6）
5.運行結果以及分析
6.參考文獻
1.應用場景
卷積神經網絡的應用不可謂不廣泛，主要有兩大類，數據預測和圖片處理。數據預測自然不需要多說，圖片處理主要包含有圖像分類，檢測，識別，以及分割方面的應用。
圖像分類：場景分類，目標分類
圖像檢測：顯著性檢測，物體檢測，語義檢測等等
圖像識別：人臉識別，字符識別，車牌識別，行爲識別，步態識別等等
圖像分割：前景分割，語義分割
2.卷積神經網絡結構
卷積神經網絡主要是由輸入層、卷積層、激活函數、池化層、全連接層、損失函數組成，表面看比較複雜，其實質就是特徵提取以及決策推斷。
要使特徵提取儘量準確，就需要將這些網絡層結構進行組合，比如經典的卷積神經網絡模型AlexNet:5個卷積層+3個池化層+3個連接層結構。
2.1 卷積（convolution）
卷積的作用就是提取特徵，因爲一次卷積可能提取的特徵比較粗糙，所以多次卷積，以及層層縱深卷積，層層提取特徵（千萬要區別於多次卷積，因爲每一層裏含有多次卷積）。
這裏可能就有小夥伴問：爲什麼要進行層層縱深卷積，而且還要每層多次？
你可以理解爲物質A有自己的多個特徵（高、矮、胖、瘦、、、），所以在物質A上需要多次提取，得到不同的特徵，然後這些特徵組合後發生化學反應生成物質B，
而物質B又有一些新的專屬於自己的特徵，所以需要進一步卷積。這是我個人的理解，不對的話或者有更形象的比喻還請不吝賜教啊。
在卷積層中，每一層的卷積核是不一樣的。比如AlexNet
第一層：96*11*11（96表示卷積核個數，11表示卷積核矩陣寬*高） stride（步長） = 4 pad（邊界補零） = 0
第二層：256*5*5 stride（步長） = 1 pad（邊界補零） = 2
第三，四層：384*3*3 stride（步長） = 1 pad（邊界補零） = 1
第五層：256*3*3 stride（步長） = 1 pad（邊界補零） = 2
卷積的篇幅說了這麼多，那麼到底是如何進行運算的呢，雖說網絡上關於卷積運算原理鋪天蓋地，但是個人總感覺講得不夠透徹，或者說本人智商有待提高，
希望通過如下這幅圖（某位大神的傑作）來使各位看官們能夠真正理解。
這裏舉的例子是一個輸入圖片（5*5*3），卷積核（3*3*3），有兩個（Filter W0，W1），偏置b也有兩個（Bios b0，b1），卷積結果Output Volumn（3*3*2），步長stride = 2。
輸入：7*7*3 是因爲 pad = 1 （在圖片邊界行和列都補零，補零的行和的數目是1），
（對於彩色圖片，一般都是RGB3種顏色，號稱3通道，7*7指圖片高h * 寬w）
，補零的作用是能夠提取圖片邊界的特徵。
卷積核深度爲什麼要設置成3呢？這是因爲輸入是3通道，所以卷積核深度必須與輸入的深度相同。至於卷積核寬w，高h則是可以變化的，但是寬高必須相等。
卷積核輸出o[0,0,0] = 3 （Output Volumn下淺綠色框結果），這個結果是如何得到的呢？ 其實關鍵就是矩陣對應位置相乘再相加（千萬不要跟矩陣乘法搞混淆啦）
=> w0[:,:,0] * x[:,:,0]藍色區域矩陣(R通道) + w0[:,:,1] * x[:,:,1]藍色區域矩陣（G通道）+ w0[:,:,2] * x[:,:,2]藍色區域矩陣（B通道） + b0（千萬不能丟，因爲 y = w * x + b）
第一項 => 0 * 1 + 0 * 1 + 0 * 1 + 0 * (-1) + 1 * (-1) + 1 * 0 + 0 * (-1) + 1 * 1 + 1 * 0 = 0
第二項 => 0 * (-1) + 0 * (-1) + 0 * 1 + 0 * (-1) + 0 * 1 + 1 * 0 + 0 * (-1) + 2 * 1 + 2 * 0 = 2
第三項 => 0 * 1 + 0 * 0 + 0 * (-1) + 0 * 0 + 2 * 0 + 2 * 0 + 0 * 1 + 0 * (-1) + 0 * (-1) = 0
卷積核輸出o[0,0,0] = > 第一項 + 第二項 + 第三項 + b0 = 0 + 2 + 0 + 1 = 3
o[0,0,1] = -5 又是如何得到的呢？
因爲這裏的stride = 2 ，所以 輸入的窗口就要滑動兩個步長，也就是紅色框的區域，而運算跟之前是一樣的
第一項 => 0 * 1 + 0 * 1 + 0 * 1 + 1 * (-1) + 2 * (-1) + 2 * 0 + 1 * (-1) + 1 * 1 + 2 * 0 = -3
第二項 => 0 * (-1) + 0 * (-1) + 0 * 1 + 1 * (-1) + 2 * 1 + 0 * 0 + 2 * (-1) + 1 * 1 + 1 * 0 = 0
第三項 => 0 * 1 + 0 * 0 + 0 * (-1) + 2 * 0 + 0 * 0 + 1 * 0 + 0 * 1 + 2 * (-1) + 1 * (-1) = - 3
卷積核輸出o[0,0,1] = > 第一項 + 第二項 + 第三項 + b0 = (-3) + 0 + (-3) + 1 = -5
之後以此卷積核窗口大小在輸入圖片上滑動，卷積求出結果，因爲有兩個卷積核，所有就有兩個輸出結果。
這裏小夥伴可能有個疑問，輸出窗口是如何得到的呢？
這裏有一個公式：輸出窗口寬 w = (輸入窗口寬 w - 卷積核寬 w + 2 * pad)/stride + 1 ，輸出高 h = 輸出窗口寬 w
以上面例子， 輸出窗口寬 w = ( 5 - 3 + 2 * 1)/2 + 1 = 3 ，則輸出窗口大小爲 3 * 3，因爲有2個輸出，所以是 3*3*2。
2.2 Relu激活函數
相信看過卷積神經網絡結構（CNN）的夥伴們都知道，激活函數無處不在，特別是CNN中，在卷積層後，全連接（FC）後都有激活函數Relu的身影，
那麼這就自然不得不讓我們產生疑問：
問題1、爲什麼要用激活函數？它的作用是什麼？
問題2、在CNN中爲什麼要用Relu，相比於sigmoid，tanh，它的優勢在什麼地方？
對於第1個問題：由 y = w * x + b 可知，如果不用激活函數，每個網絡層的輸出都是一種線性輸出，而我們所處的現實場景，其實更多的是各種非線性的分佈。
這也說明了激活函數的作用是將線性分佈轉化爲非線性分佈，能更逼近我們的真實場景。
對於第2個問題： 先看sigmoid，tanh分佈
他們在 x ->
時，輸出就變成了恆定值，因爲求梯度時需要對函數求一階偏導數，而不論是sigmoid，還是tanhx，他們的偏導都爲0，
也就是存在所謂的梯度消失問題，最終也就會導致權重參數w ， b 無法更新。相比之下，Relu就不存在這樣的問題，另外在 x > 0 時，
Relu求導 = 1，這對於反向傳播計算dw，db，是能夠大大的簡化運算的。
使用sigmoid還會存在梯度爆炸的問題，比如在進行前向傳播和反向傳播迭代次數非常多的情況下，sigmoid因爲是指數函數，其結果中
某些值會在迭代中累積，併成指數級增長，最終會出現NaN而導致溢出。
2.3 池化
池化層一般在卷積層+ Relu之後，它的作用是：
1、減小輸入矩陣的大小（只是寬和高，而不是深度），提取主要特徵。（不可否認的是，在池化後，特徵會有一定的損失，所以，有些經典模型就去掉了池化這一層）。
它的目的是顯而易見的，就是在後續操作時能降低運算。
2、一般採用mean_pooling（均值池化）和max_pooling（最大值池化），對於輸入矩陣有translation（平移），rotation（旋轉），能夠保證特徵的不變性。
mean_pooling 就是輸入矩陣池化區域求均值，這裏要注意的是池化窗口在輸入矩陣滑動的步長跟stride有關，一般stride = 2.（圖片是直接盜過來，這裏感謝原創）
最右邊7/4 => (1 + 1 + 2 + 3)/4
max_pooling 最大值池化，就是每個池化區域的最大值放在輸出對應位置上。
2.4 全連接（full connection）
作用：分類器角色，將特徵映射到樣本標記空間，本質是矩陣變換（affine）。
至於變換的實現見後面的代碼流程圖，或者最好是跟一下代碼，這樣理解更透徹。
2.5 損失函數（softmax_loss）
作用：計算損失loss，從而求出梯度grad。
常用損失函數有:MSE均方誤差，SVM（支持向量機）合頁損失函數，Cross Entropy交叉熵損失函數。
這幾種損失函數目前還看不出誰優誰劣，估計只有在具體的應用場景中去驗證了。至於這幾種損失函數的介紹，
大家可以去參考《常用損失函數小結》https://blog.csdn.net/zhangjunp3/article/details/80467350，這個哥們寫得比較詳細。
在後面的代碼實例中，用到的是softmax_loss，它屬於Cross Entropy交叉熵損失函數。
softmax計算公式：
其中，
交叉熵損失：
其中，
梯度:
其中
這個有點折磨人，原理講解以及推導請大家可以參考這位大神的博客：http://www.cnblogs.com/zongfa/p/8971213.html。
2.6 前向傳播（forward propagation）
前向傳播包含之前的卷積，Relu激活函數，池化（pool），全連接(fc)，可以說，在損失函數之前操作都屬於前向傳播。
主要是權重參數w , b 初始化，迭代，以及更新w, b,生成分類器模型。
2.7 反向傳播（back propagation）
反向傳播包含損失函數，通過梯度計算dw，db，Relu激活函數逆變換，反池化，反全連接。
2.8 隨機梯度下降（sgd_momentum）
作用：由梯度grad計算新的權重矩陣w
sgd公式：
其中，η爲學習率，gt爲x在t時刻的梯度。
一般我們是將整個數據集分成n個epoch，每個epoch再分成m個batch，每次更新都利用一個batch的數據，而非整個訓練集。
優點：batch的方法可以減少機器的壓力，並且可以更快地收斂。
缺點：其更新方向完全依賴於當前的batch，因而其更新十分不穩定。
爲了解決這個問題，momentum就橫空出世了，具體原理詳解見下路派出所（這名字霸氣）的博客http://www.cnblogs.com/callyblog/p/8299074.html。
momentum即動量，它模擬的是物體運動時的慣性，即更新的時候在一定程度上保留之前更新的方向，同時利用當前batch的梯度微調最終的更新方向。
這樣一來，可以在一定程度上增加穩定性，從而學習地更快，並且還有一定擺脫局部最優的能力：
其中，ρ 即momentum，表示要在多大程度上保留原來的更新方向，這個值在0-1之間，在訓練開始時，由於梯度可能會很大，所以初始值一般選爲0.5；
當梯度不那麼大時，改爲0.9。η 是學習率，即當前batch的梯度多大程度上影響最終更新方向，跟普通的SGD含義相同。ρ 與 η 之和不一定爲1。
3.代碼實現流程圖以及介紹
代碼流程圖：費了老大勁，終於弄完了，希望對各位看官們有所幫助，建議對比流程圖和跟蹤代碼，加深對原理的理解。
特別是前向傳播和反向傳播維度的變換，需要重點關注。
4.代碼實現
當然，代碼的整個實現是某位大神實現的，我只是在上面做了些小改動以及重點函數做了些註釋，有不妥之處也希望大家不吝指教。
因爲原始圖片數據集太大，不好上傳，大家可以直接在http://www.cs.toronto.edu/~kriz/cifar.html下載CIFAR-10 python version，
有163M，放在代碼文件同路徑下即可。
start.py
1 # -*- coding: utf-8 -*- 2 import matplotlib.pyplot as plt 3 '''同路徑下py模塊引用''' 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 # 獲取樣本數據 16 data = data_utils.get_CIFAR10_data() 17 # model初始化（權重因子以及對應偏置 w1,b1 ,w2,b2 ,w3,b3，數量取決於網絡層數） 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 # 訓練，獲取最佳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，重新計算損失，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 # 標準化數據，求樣本均值，然後 樣本 - 樣本均值，作用：使樣本數據更收斂一些，便於後續處理 59 # Normalize the data: subtract the mean image 60 # 如果2維空間 m*n np.mean()後 => 1*n 61 # 對於4維空間 m*n*k*j np.mean()後 => 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 全連接層：矩陣變換，獲取對應目標相同的行與列 5 輸入x: 2*32*16*16 6 輸入x_row: 2*8192 7 超參w：8192*100 8 輸出：矩陣乘法 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 反向傳播之affine矩陣變換 35 根據dout求出dx,dw,db 36 由 out = w * x => 37 dx = dout * w 38 dw = dout * x 39 db = dout * 1 40 因爲dx 與 x，dw 與 w，db 與 b 大小（維度）必須相同 41 dx = dout * wT 矩陣乘法 42 dw = dxT * dout 矩陣乘法 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維度必須跟x維度相同 66 dx = np.reshape(dx, x.shape) # (N,d1,...,d_k) 67 # 轉換成二維矩陣 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 """ 激活函數，解決sigmoid梯度消失問題，網絡性能比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 求梯度優點: 求梯度運算簡單，方便 131 softmax: softmax用於多分類過程中，它將多個神經元的輸出，映射到（0,1）區間內， 132 可以看成概率來理解，從而來進行多分類。 133 Si = exp(i)/[exp(j)求和] 134 softmax_loss：損失函數，求梯度dx必須用到損失函數，通過梯度下降更新超參 135 Loss = -[Ypred*ln(Sj真實類別位置的概率值)]求和 136 梯度dx : 對損失函數求一階偏導 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) 對數據進行預處理， 153 防止np.exp(x - np.max(x, axis=1, keepdims=True))得到結果太分散； 154 np.max(x, axis=1, keepdims=True)保證所得結果維度不變； 155 ''' 156 probs = np.exp(x - np.max(x, axis=1, keepdims=True)) 157 # 計算softmax，準確的說應該是soft，因爲還沒有選取概率最大值的操作 158 probs /= np.sum(probs, axis=1, keepdims=True) 159 # 樣本圖片個數 160 N = x.shape[0] 161 # 計算圖片損失 162 loss = -np.sum(np.log(probs[np.arange(N), y])) / N 163 # 複製概率 164 dx = probs.copy() 165 # 針對 i = j 求梯度 166 dx[np.arange(N), y] -= 1 167 # 計算每張樣本圖片梯度 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：獲取圖片特徵 177 前向卷積：每次用一個3維的卷積核與圖片RGB各個通道分別卷積（卷積核1與R進行點積，卷積核2與G點積，卷積核3與B點積）, 178 然後將3個結果求和（也就是 w*x ）,再加上 b，就是新結果某一位置輸出，這是卷積核在圖片某一固定小範圍內（卷積核大小）的卷積， 179 要想獲得整個圖片的卷積結果，需要在圖片上滑動卷積核（先右後下），直至遍歷整個圖片。 180 x: 2*3*32*32 每次選取2張圖片，圖片大小32*32，彩色(3通道) 181 w: 32*3*7*7 卷積核每個大小是7*7；對應輸入x的3通道，所以是3維，有32個卷積核 182 pad = 3(圖片邊緣行列補0)，stride = 1(卷積核移動步長) 183 輸出寬*高結果：(32-7+2*3)/1 + 1 = 32 184 輸出大小：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 反向傳播之卷積：卷積核3*7*7 213 輸入dout:2*32*32*32 214 輸出dx:2*3*32*32 215 ''' 216 def conv_backward_naive(dout, cache): 217 218 x, w, b, conv_param = cache 219 # 邊界補0 220 pad = conv_param['pad'] 221 # 步長 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 # 圖片個數 236 for i in range(N): # ith image 237 # 卷積核濾波個數 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：減少特徵尺寸大小 255 前向最大池化：在特徵矩陣中選取指定大小窗口，獲取窗口內元素最大值作爲輸出窗口映射值， 256 先有後下遍歷，直至獲取整個特徵矩陣對應的新映射特徵矩陣。 257 輸入x：2*32*32*32 258 池化參數：窗口：2*2，步長：2 259 輸出窗口寬，高：(32-2)/2 + 1 = 16 260 輸出大小：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 反向傳播之池化：增大特徵尺寸大小 282 在緩存中取出前向池化時輸入特徵，選取某一範圍矩陣窗口， 283 找出最大值所在的位置，根據這個位置將dout值映射到新的矩陣對應位置上， 284 而新矩陣其他位置都初始化爲0. 285 輸入dout:2*32*16*16 286 輸出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 # 取前向傳播時輸入的某一池化窗口 301 window = x[i, j, k*s:HH+k*s, l*s:WW+l*s] 302 # 計算窗口最大值 303 m = np.max(window) 304 # 根據最大值所在位置以及dout對應值=>新矩陣窗口數值 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:隨機梯度下降：由梯度計算新的權重矩陣w 16 sgd_momentum 是sgd的改進版，解決sgd更新不穩定，陷入局部最優的問題。 17 增加一個動量因子momentum，可以在一定程度上增加穩定性， 18 從而學習地更快，並且還有一定擺脫局部最優的能力。 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 如果存在屬性velocity，則獲取config['velocity']，否則獲取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):刪除kwargs對象中key，如果存在該key，返回該key對應的value，否則，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 # 刪除kwargs中參數後，校驗是否還有多餘參數 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 # 檢查optim對象中是否有屬性或方法名爲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 張圖片 164 num_train = self.X_train.shape[0] 165 # 隨機選出batch_size：2 張 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 # 訓練樣本矩陣[2,3,32,32] 173 X_batch = self.X_train[batch_mask] 174 # 標籤矩陣[2,] 圖片類型 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 # 更新模型超參(w1,b1),(w2,b2),(w3,b3)，以及保存更新超參時對應參數因子 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 # 保存參數因子，learning_rate(學習率)，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 # 隨機選取num_samples張圖片，返回選取圖片索引 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 訓練模型：核心方法 235 epoch > batch_size > iteration >= 1 236 訓練總的次數 = 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 # 迭代總的次數 246 for t in range(num_iterations): 247 # 某次iteration訓練 248 self._step() 249 250 # Maybe print training loss 251 # verbose：是否顯示詳細信息 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後，更新學習率learning_rate，加快運算效率。 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，最後1次迭代，或者運行完一個epoch後，校驗訓練結果。 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.運行結果以及分析
這裏選取500張圖片作爲訓練樣本，epoch = 5，batch = 2，每次隨機選取2張圖片，迭代 5 * 500/2 = 1250次，測試樣本選取50張。
由運行結果可以看出，損失loss是逐步下降的。
測試結果只有12%左右，原因有以下幾點：
1. 模型比較簡單，特徵提取不能反映真實特徵（一次卷積）；
2. 會出現過擬合問題；
3. 原始訓練數據分類圖片紋理複雜，這些圖片可變性大，從而導致分類結果準確度低；
(airplane, automobile, bird, cat, deer, dog, frog, horse, ship, truck)
後續會通過tensorflow來實現CNN，測試準確率可以達到71.95%。
6. 參考文獻
視覺一隻白的博客《常用損失函數小結》https://blog.csdn.net/zhangjunp3/article/details/80467350
理想萬歲的博客《Softmax函數詳解與推導》：http://www.cnblogs.com/zongfa/p/8971213.html
下路派出所的博客《深度學習（九） 深度學習最全優化方法總結比較（SGD，Momentum，Nesterov Momentum，Adagrad，Adadelta，RMSprop，Adam）》
http://www.cnblogs.com/callyblog/p/8299074.html
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