前言
作業(yè)一中一步步構(gòu)建了一個(gè)神經(jīng)網(wǎng)絡(luò)许布，本部分作業(yè)將會(huì)利用作業(yè)一中的知識(shí)構(gòu)建一個(gè)神經(jīng)網(wǎng)絡(luò)圖片分類器绢淀。這個(gè)圖片分類器通過訓(xùn)練可以識(shí)別出圖片中的具體內(nèi)容是否是貓蚁廓。
1. 導(dǎo)入相關(guān)包
首先陌选，還是導(dǎo)入搭建神經(jīng)網(wǎng)絡(luò)分類器所需要的python包睡汹，并對(duì)整個(gè)程序做一些基本的設(shè)置肴甸，具體代碼如下所示：
import time
import numpy as np
import h5py
import matplotlib.pyplot as plt
import scipy
from PIL import Image
%matplotlib inline
plt.rcParams['figure.figsize'] = (5.0, 4.0) # 設(shè)置圖片默認(rèn)顯示大小
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
%load_ext autoreload
%autoreload 2
# 設(shè)置隨機(jī)種子
np.random.seed(1)
2. 數(shù)據(jù)集
神經(jīng)網(wǎng)絡(luò)所用到的數(shù)據(jù)集主要分為訓(xùn)練集和測試集，都是以.h5文件存儲(chǔ)的囚巴，處理此類文件用到的python庫是h5py庫原在。對(duì)于訓(xùn)練集和測試集而言，輸出數(shù)據(jù)都有一個(gè)標(biāo)簽彤叉，要么是0(表示該圖片內(nèi)容不是貓)庶柿，要么是1（表示該圖片內(nèi)容內(nèi)容是貓），數(shù)據(jù)集的特征都是(num_px,num_px,3)形式的矩陣秽浇，其中浮庐，3代表的是RGB3通道。加載數(shù)據(jù)集的代碼如下所示：
def load_data():
train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r")
train_set_x_orig = np.array(train_dataset["train_set_x"][:]) #訓(xùn)練集的特征
train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # 訓(xùn)練集輸出的標(biāo)簽
test_dataset = h5py.File('datasets/test_catvnoncat.h5', "r")
test_set_x_orig = np.array(test_dataset["test_set_x"][:]) #測試集的輸入特征
test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # 測試集的輸出標(biāo)簽
classes = np.array(test_dataset["list_classes"][:]) # 類別列表
train_set_y_orig = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))
test_set_y_orig = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))
return train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes
train_x_orig, train_y, test_x_orig, test_y, classes = load_data()
隨便找一張數(shù)據(jù)集中的數(shù)據(jù)柬焕，顯示結(jié)果如下所示：
index = 7
plt.imshow(train_x_orig[index])
print ("y = " + str(train_y[0,index]) + ". It's a " + classes[train_y[0,index]].decode("utf-8") + " picture.")
為了確認(rèn)數(shù)據(jù)集的形狀并且為了方便神經(jīng)網(wǎng)絡(luò)的搭建和后續(xù)的運(yùn)算审残，需要對(duì)數(shù)據(jù)集的形狀和大小進(jìn)行顯示，具體代碼如下所示;
m_train = train_x_orig.shape[0] # 訓(xùn)練集的樣本大小
num_px = train_x_orig.shape[1] #樣本的像素
m_test = test_x_orig.shape[0] #測試集的樣本大小
print ("Number of training examples: " + str(m_train))
print ("Number of testing examples: " + str(m_test))
print ("Each image is of size: (" + str(num_px) + ", " + str(num_px) + ", 3)")
print ("train_x_orig shape: " + str(train_x_orig.shape))
print ("train_y shape: " + str(train_y.shape))
print ("test_x_orig shape: " + str(test_x_orig.shape))
print ("test_y shape: " + str(test_y.shape))
最后斑举，輸出結(jié)果如下所示：
單個(gè)樣本的數(shù)據(jù)集的形狀為(64,64,3)搅轿，表示一個(gè)寬和高都是64像素且為3通道的圖像，在神經(jīng)網(wǎng)絡(luò)訓(xùn)練之前富玷，需要對(duì)上述數(shù)據(jù)集做出一些改變璧坟，即單個(gè)樣本的矩陣轉(zhuǎn)化為一個(gè)列向量，具體過程可以由下圖表示：
除了將其轉(zhuǎn)化一個(gè)向量之外赎懦，還需要將其標(biāo)準(zhǔn)化雀鹃，確保每一個(gè)值都是在之間，標(biāo)準(zhǔn)化的過程可以通過將每一個(gè)像素除以255得到铲敛，具體的實(shí)現(xiàn)代碼如下所示:
# 重新改變訓(xùn)練集和測試集的大小
train_x_flatten = train_x_orig.reshape(train_x_orig.shape[0], -1).T # The "-1" makes reshape flatten the remaining dimensions
test_x_flatten = test_x_orig.reshape(test_x_orig.shape[0], -1).T
# 標(biāo)準(zhǔn)化數(shù)據(jù)集
train_x = train_x_flatten/255.
test_x = test_x_flatten/255.
print ("train_x's shape: " + str(train_x.shape)) #輸出：(12288,209)
print ("test_x's shape: " + str(test_x.shape)) #輸出： （12288褐澎，50）
神經(jīng)網(wǎng)絡(luò)模型的結(jié)構(gòu)
數(shù)據(jù)預(yù)處理之后，就可以搭建神經(jīng)網(wǎng)絡(luò)的模型了伐蒋，對(duì)于神經(jīng)網(wǎng)絡(luò)模型的搭建工三，有以下的選擇：
- 搭建一個(gè)2層的神經(jīng)網(wǎng)絡(luò)模型
- 搭建一個(gè)
層的神經(jīng)網(wǎng)絡(luò)模型
可以通過搭建不同結(jié)構(gòu)的神經(jīng)網(wǎng)絡(luò)模型來比較哪種結(jié)構(gòu)的神經(jīng)網(wǎng)絡(luò)模型擁有更好的性能迁酸。
3.1 兩層的神經(jīng)網(wǎng)絡(luò)模型
對(duì)于兩層的神經(jīng)網(wǎng)絡(luò)模型的結(jié)構(gòu)可以由下圖所示：
整個(gè)神經(jīng)網(wǎng)絡(luò)的結(jié)構(gòu)可以總結(jié)為INPUT->LINEAR->RELU->LINEAR->SIGMOID->OUTPUT
輸入特征是(12288,1)的矩陣，對(duì)應(yīng)的權(quán)重參數(shù)是
(12288,12288)的矩陣俭正，而權(quán)重參數(shù)是
(1奸鬓，12288)的矩陣。
3.2 層的神經(jīng)網(wǎng)絡(luò)模型
層的神經(jīng)網(wǎng)絡(luò)模型的結(jié)構(gòu)可以由以下圖形表示：
層神經(jīng)網(wǎng)絡(luò)的結(jié)構(gòu)可以總結(jié)為
INPUT->[LINEAR->RELU]×(L-1)->LINEAE->SGMOID
層神經(jīng)網(wǎng)絡(luò)的更詳細(xì)的解釋可以參考一步步構(gòu)建了一個(gè)神經(jīng)網(wǎng)絡(luò).
3.3 總體實(shí)現(xiàn)方法
以上結(jié)構(gòu)的神經(jīng)網(wǎng)絡(luò)的總體實(shí)現(xiàn)方法可以總結(jié)為以下幾個(gè)步驟掸读，具體如下：
- 初始化權(quán)重參數(shù)/定義超參數(shù)
- 經(jīng)過多次迭代:
- 前向傳播
- 利用損失函數(shù)計(jì)算損失
- 反向傳播
- 利用反向傳播和梯度下降更新參數(shù)
- 用訓(xùn)練后得到的參數(shù)預(yù)測輸出
4. 兩層神經(jīng)網(wǎng)絡(luò)模型的實(shí)現(xiàn)
兩層神經(jīng)網(wǎng)絡(luò)的具體實(shí)現(xiàn)細(xì)節(jié)已經(jīng)有過介紹串远，故以下直接給出實(shí)現(xiàn)代碼。
4.1 定義神經(jīng)網(wǎng)絡(luò)的結(jié)構(gòu)
首先儿惫，定義神經(jīng)網(wǎng)絡(luò)模型的結(jié)構(gòu)澡罚，具體代碼如下所示：
n_x = 12288 # num_px * num_px * 3
n_h = 7
n_y = 1
layers_dims = (n_x, n_h, n_y)
4.2 兩層神經(jīng)網(wǎng)絡(luò)模型的參數(shù)初始化
#初始化權(quán)重參數(shù)
def initialize_parameters(n_x, n_h, n_y):
np.random.seed(1)
W1 = np.random.randn(n_h, n_x)*0.01
b1 = np.zeros((n_h, 1))
W2 = np.random.randn(n_y, n_h)*0.01
b2 = np.zeros((n_y, 1))
assert(W1.shape == (n_h, n_x))
assert(b1.shape == (n_h, 1))
assert(W2.shape == (n_y, n_h))
assert(b2.shape == (n_y, 1))
parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2}
return parameters
4.3 前向激活函數(shù)的計(jì)算
def linear_activation_forward(A_prev, W, b, activation):
if activation == "sigmoid":
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = sigmoid(Z)
elif activation == "relu":
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = relu(Z)
assert (A.shape == (W.shape[0], A_prev.shape[1]))
cache = (linear_cache, activation_cache)
return A, cache
4.4 損失函數(shù)的計(jì)算
def compute_cost(AL, Y):
m = Y.shape[1]
cost = (1./m) * (-np.dot(Y,np.log(AL).T) - np.dot(1-Y, np.log(1-AL).T))
cost = np.squeeze(cost)
assert(cost.shape == ())
return cost
4.5 反向傳播函數(shù)的計(jì)算
def linear_activation_backward(dA, cache, activation):
linear_cache, activation_cache = cache
if activation == "relu":
dZ = relu_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
elif activation == "sigmoid":
dZ = sigmoid_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
return dA_prev, dW, db
4.6 參數(shù)的更新
def update_parameters(parameters, grads, learning_rate):
L = len(parameters) // 2 # 神經(jīng)網(wǎng)絡(luò)的層數(shù)
for l in range(L):
parameters["W" + str(l+1)] = parameters["W" + str(l+1)] - learning_rate * grads["dW" + str(l+1)]
parameters["b" + str(l+1)] = parameters["b" + str(l+1)] - learning_rate * grads["db" + str(l+1)]
return parameters
4.7 兩層神經(jīng)網(wǎng)絡(luò)模型的總體實(shí)現(xiàn)
根據(jù)以上代碼，神經(jīng)網(wǎng)絡(luò)模型的總體實(shí)現(xiàn)代碼肾请，如下所示;
def two_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):
np.random.seed(1)
grads = {}
costs = []
m = X.shape[1]
(n_x, n_h, n_y) = layers_dims
# 初始化權(quán)重參數(shù)
parameters = initialize_parameters(n_x,n_h,n_y)
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
多次迭代
for i in range(0, num_iterations):
前向傳播的實(shí)現(xiàn)
A1, cache1 = linear_activation_forward(X,W1,b1,'relu')
A2, cache2 = linear_activation_forward(A1,W2,b2,'sigmoid')
# 損失函數(shù)計(jì)算
cost = compute_cost(A2,Y)
# 反向傳播的第一步計(jì)算公式
dA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))
#反向傳播的計(jì)算
dA1, dW2, db2 = linear_activation_backward(dA2,cache2,'sigmoid')
dA0, dW1, db1 = linear_activation_backward(dA1,cache1,'relu')
grads['dW1'] = dW1
grads['db1'] = db1
grads['dW2'] = dW2
grads['db2'] = db2
#參數(shù)更新
parameters = update_parameters(parameters,grads,learning_rate)
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
if print_cost and i % 100 == 0:
print("Cost after iteration {}: {}".format(i, np.squeeze(cost)))
if print_cost and i % 100 == 0:
costs.append(cost)
# 繪制損失函數(shù)圖形
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per tens)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
return parameters
經(jīng)過多次迭代之后留搔，可以看到損失已經(jīng)下降到一個(gè)非常小的值。
4.8 做出預(yù)測
有了以上實(shí)現(xiàn)铛铁，得到了能夠使損失函數(shù)最小化的參數(shù)隔显，利用此參數(shù)和神經(jīng)網(wǎng)絡(luò)的前向傳播函數(shù)做出預(yù)測如下所示;
def predict(X, y, parameters):
m = X.shape[1]
n = len(parameters) // 2 # number of layers in the neural network
p = np.zeros((1,m))
probas, caches = L_model_forward(X, parameters)
for i in range(0, probas.shape[1]):
if probas[0,i] > 0.5:
p[0,i] = 1
else:
p[0,i] = 0
print("Accuracy: " + str(np.sum((p == y)/m)))
return p
分別對(duì)訓(xùn)練集和測試集做出預(yù)測，精確度結(jié)果如下所示:
訓(xùn)練集預(yù)測精度
測試集預(yù)測精度
5 L層神經(jīng)網(wǎng)絡(luò)模型的實(shí)現(xiàn)
層神經(jīng)網(wǎng)絡(luò)模型的實(shí)現(xiàn)已經(jīng)在一步步實(shí)現(xiàn)一個(gè)神經(jīng)網(wǎng)絡(luò)中有過詳細(xì)介紹了饵逐，一些多層神經(jīng)網(wǎng)絡(luò)分類器的主要的代碼實(shí)現(xiàn)如下所示：
5.1 多層神經(jīng)網(wǎng)絡(luò)模型的參數(shù)初始化
def initialize_parameters_deep(layer_dims):
np.random.seed(1)
parameters = {}
L = len(layer_dims) #網(wǎng)絡(luò)的層數(shù)
for l in range(1, L):
parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l-1]) / np.sqrt(layer_dims[l-1]) *0.01
parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))
assert(parameters['W' + str(l)].shape == (layer_dims[l], layer_dims[l-1]))
assert(parameters['b' + str(l)].shape == (layer_dims[l], 1))
return parameters
5.2 多層神經(jīng)網(wǎng)絡(luò)前向傳播函數(shù)的實(shí)現(xiàn)
def L_model_forward(X, parameters):
caches = []
A = X
L = len(parameters) // 2
for l in range(1, L):
A_prev = A
A, cache = linear_activation_forward(A_prev, parameters['W' + str(l)], parameters['b' + str(l)], activation = "relu")
caches.append(cache)
AL, cache = linear_activation_forward(A, parameters['W' + str(L)], parameters['b' + str(L)], activation = "sigmoid")
caches.append(cache)
assert(AL.shape == (1,X.shape[1]))
return AL, caches
5.3 多層神經(jīng)網(wǎng)絡(luò)模型的反向傳播實(shí)現(xiàn)
def L_model_backward(AL, Y, caches):
grads = {}
m = AL.shape[1]
Y = Y.reshape(AL.shape)
dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
current_cache = caches[L-1]
grads["dA" + str(L)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, activation = "sigmoid")
for l in reversed(range(L-1)):
current_cache = caches[l]
dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l + 2)], current_cache, activation = "relu")
grads["dA" + str(l + 1)] = dA_prev_temp
grads["dW" + str(l + 1)] = dW_temp
grads["db" + str(l + 1)] = db_temp
return grads
5.4 參數(shù)更新
def update_parameters(parameters, grads, learning_rate):
L = len(parameters) // 2 # number of layers in the neural network
for l in range(L):
parameters["W" + str(l+1)] = parameters["W" + str(l+1)] - learning_rate * grads["dW" + str(l+1)]
parameters["b" + str(l+1)] = parameters["b" + str(l+1)] - learning_rate * grads["db" + str(l+1)]
return parameters
5.5 多層神經(jīng)網(wǎng)絡(luò)的整體實(shí)現(xiàn)代碼
將以上所有的代碼按照神經(jīng)網(wǎng)絡(luò)的計(jì)算方式組合在一起括眠，如下所示：
def L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):#lr was 0.009
np.random.seed(1)
costs = [] # keep track of cost
parameters = initialize_parameters_deep(layers_dims)
for i in range(0, num_iterations):
AL, caches = L_model_forward(X,parameters)
cost = compute_cost(AL, Y)
grads = L_model_backward(AL,Y,caches)
parameters = update_parameters(parameters,grads,learning_rate)
if print_cost and i % 100 == 0:
print ("Cost after iteration %i: %f" %(i, cost))
if print_cost and i % 100 == 0:
costs.append(cost)
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per tens)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
在運(yùn)行以上代碼之前，需要定義一個(gè)網(wǎng)絡(luò)的結(jié)構(gòu)倍权，包括輸入層掷豺，隱藏層和輸出層的基本信息，具體實(shí)現(xiàn)代碼如下所示：
layers_dims = [12288, 20, 7, 5, 1] # 5-層的神經(jīng)網(wǎng)絡(luò)
最后薄声，以上代碼運(yùn)行結(jié)果和損失的下降過程如下所示：
5.6 做出預(yù)測
根據(jù)4.7的預(yù)測代碼萌业，分別對(duì)訓(xùn)練集和測試集做出預(yù)測，其結(jié)果分別如下所示：
可以看出奸柬，與淺層神經(jīng)網(wǎng)絡(luò)相比生年，多層神經(jīng)網(wǎng)絡(luò)的性能有所上升。
6 分類結(jié)果分析
利用以下代碼對(duì)神經(jīng)網(wǎng)絡(luò)分類不正確的圖像進(jìn)行輸出
def print_mislabeled_images(classes, X, y, p):
"""
X -- 數(shù)據(jù)集
y --真實(shí)標(biāo)簽
p -- 預(yù)測標(biāo)簽
"""
a = p + y # 相加同為2或者同為0表示預(yù)測結(jié)果正確
mislabeled_indices = np.asarray(np.where(a == 1))
plt.rcParams['figure.figsize'] = (40.0, 40.0)
num_images = len(mislabeled_indices[0])
for i in range(num_images):
index = mislabeled_indices[1][i]
plt.subplot(2, num_images, i + 1)
plt.imshow(X[:,index].reshape(64,64,3), interpolation='nearest')
plt.axis('off')
plt.title("Prediction: " + classes[int(p[0,index])].decode("utf-8") + " \n Class: " + classes[y[0,index]].decode("utf-8"))
print_mislabeled_images(classes, test_x, test_y, pred_test)
最后廓奕，造成這種異常結(jié)果的原因可能如下：
- 貓的身體處在照片中不合適的位置
- 貓的顏色與圖片背景色太過接近
- 貓的顏色較為罕見
- 拍照角度
- 圖片的亮度
- 貓的身體在圖片中過大或者過小
