Deep Neural Network for Image Classification（吴恩达老师课后作业）
Deep Neural Network for Image Classification
1.前言
这里吴恩达老师大课第一部分第四周的实验作业，上一次的实验作业（logistics回归模型实现二分类算法）是相关联的，类似一个渐变的过程。本次实现先讲述搭建二层神经网络在到多层神经网络的构建，类似一个由浅入深的过程。老师给出的jupyter文件中详细的将每一个过程写了出来，对于新手的学习十分友好。我将实验过程记录了下来，在部分地方添加了个人的一些理解（如有错误还请指正），并且记录了实现过程中遇到的一些问题和个人的感悟，希望能给其他一些学习的朋友带来一些帮助
2.代码实现
2.1两层神经网络的实现
搭建两层神经网络实现二分类算法，比之前的单层神经网络要多一个隐藏层，网络的结构图如下所示：
导入实验需要的依赖包
# 导入实验所需要的依赖
import time
import datetime
import numpy as np
import h5py
import matplotlib.pyplot as plt
from PIL import Image
from scipy import ndimage
from dnn_app_utils_v2 import *
%matplotlib inline
# rc:run configuration 设置图像显示的一些参数
plt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
%load_ext autoreload
%autoreload 2
# 设置一个随机数种子
np.random.seed(1)
这里使用的工具类dnn_app_utils_v2是老师提前准备好的
import numpy as np
import matplotlib.pyplot as plt
import h5py
def sigmoid(Z):
"""
Implements the sigmoid activation in numpy
Arguments:
Z -- numpy array of any shape
Returns:
A -- output of sigmoid(z), same shape as Z
cache -- returns Z as well, useful during backpropagation
"""
A = 1/(1+np.exp(-Z))
cache = Z
return A, cache
def relu(Z):
"""
Implement the RELU function.
Arguments:
Z -- Output of the linear layer, of any shape
Returns:
A -- Post-activation parameter, of the same shape as Z
cache -- a python dictionary containing "A" ; stored for computing the backward pass efficiently
"""
A = np.maximum(0,Z)
assert(A.shape == Z.shape)
cache = Z
return A, cache
def relu_backward(dA, cache):
"""
Implement the backward propagation for a single RELU unit.
Arguments:
dA -- post-activation gradient, of any shape
cache -- 'Z' where we store for computing backward propagation efficiently
Returns:
dZ -- Gradient of the cost with respect to Z
"""
Z = cache
dZ = np.array(dA, copy=True) # just converting dz to a correct object.
# When z <= 0, you should set dz to 0 as well.
dZ[Z <= 0] = 0
assert (dZ.shape == Z.shape)
return dZ
def sigmoid_backward(dA, cache):
"""
Implement the backward propagation for a single SIGMOID unit.
Arguments:
dA -- post-activation gradient, of any shape
cache -- 'Z' where we store for computing backward propagation efficiently
Returns:
dZ -- Gradient of the cost with respect to Z
"""
Z = cache
s = 1/(1+np.exp(-Z))
dZ = dA * s * (1-s)
assert (dZ.shape == Z.shape)
return dZ
def load_data():
train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r")
train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set features
train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labels
test_dataset = h5py.File('datasets/test_catvnoncat.h5', "r")
test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set features
test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labels
classes = np.array(test_dataset["list_classes"][:]) # the list of classes
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
def initialize_parameters(n_x, n_h, n_y):
"""
Argument:
n_x -- size of the input layer
n_h -- size of the hidden layer
n_y -- size of the output layer
Returns:
parameters -- python dictionary containing your parameters:
W1 -- weight matrix of shape (n_h, n_x)
b1 -- bias vector of shape (n_h, 1)
W2 -- weight matrix of shape (n_y, n_h)
b2 -- bias vector of shape (n_y, 1)
"""
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
def initialize_parameters_deep(layer_dims):
"""
Arguments:
layer_dims -- python array (list) containing the dimensions of each layer in our network
Returns:
parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
Wl -- weight matrix of shape (layer_dims[l], layer_dims[l-1])
bl -- bias vector of shape (layer_dims[l], 1)
"""
np.random.seed(1)
parameters = {}
L = len(layer_dims) # number of layers in the network
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
def linear_forward(A, W, b):
"""
Implement the linear part of a layer's forward propagation.
Arguments:
A -- activations from previous layer (or input data): (size of previous layer, number of examples)
W -- weights matrix: numpy array of shape (size of current layer, size of previous layer)
b -- bias vector, numpy array of shape (size of the current layer, 1)
Returns:
Z -- the input of the activation function, also called pre-activation parameter
cache -- a python dictionary containing "A", "W" and "b" ; stored for computing the backward pass efficiently
"""
Z = W.dot(A) + b
assert(Z.shape == (W.shape[0], A.shape[1]))
cache = (A, W, b)
return Z, cache
def linear_activation_forward(A_prev, W, b, activation):
"""
Implement the forward propagation for the LINEAR->ACTIVATION layer
Arguments:
A_prev -- activations from previous layer (or input data): (size of previous layer, number of examples)
W -- weights matrix: numpy array of shape (size of current layer, size of previous layer)
b -- bias vector, numpy array of shape (size of the current layer, 1)
activation -- the activation to be used in this layer, stored as a text string: "sigmoid" or "relu"
Returns:
A -- the output of the activation function, also called the post-activation value
cache -- a python dictionary containing "linear_cache" and "activation_cache";
stored for computing the backward pass efficiently
"""
if activation == "sigmoid":
# Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = sigmoid(Z)
elif activation == "relu":
# Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
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
def L_model_forward(X, parameters):
"""
Implement forward propagation for the [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID computation
Arguments:
X -- data, numpy array of shape (input size, number of examples)
parameters -- output of initialize_parameters_deep()
Returns:
AL -- last post-activation value
caches -- list of caches containing:
every cache of linear_relu_forward() (there are L-1 of them, indexed from 0 to L-2)
the cache of linear_sigmoid_forward() (there is one, indexed L-1)
"""
caches = []
A = X
L = len(parameters) // 2 # number of layers in the neural network
# Implement [LINEAR -> RELU]*(L-1). Add "cache" to the "caches" list.
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)
# Implement LINEAR -> SIGMOID. Add "cache" to the "caches" list.
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
def compute_cost(AL, Y):
"""
Implement the cost function defined by equation (7).
Arguments:
AL -- probability vector corresponding to your label predictions, shape (1, number of examples)
Y -- true "label" vector (for example: containing 0 if non-cat, 1 if cat), shape (1, number of examples)
Returns:
cost -- cross-entropy cost
"""
m = Y.shape[1]
# Compute loss from aL and y.
cost = (1./m) * (-np.dot(Y,np.log(AL).T) - np.dot(1-Y, np.log(1-AL).T))
cost = np.squeeze(cost) # To make sure your cost's shape is what we expect (e.g. this turns [[17]] into 17).
assert(cost.shape == ())
return cost
def linear_backward(dZ, cache):
"""
Implement the linear portion of backward propagation for a single layer (layer l)
Arguments:
dZ -- Gradient of the cost with respect to the linear output (of current layer l)
cache -- tuple of values (A_prev, W, b) coming from the forward propagation in the current layer
Returns:
dA_prev -- Gradient of the cost with respect to the activation (of the previous layer l-1), same shape as A_prev
dW -- Gradient of the cost with respect to W (current layer l), same shape as W
db -- Gradient of the cost with respect to b (current layer l), same shape as b
"""
A_prev, W, b = cache
m = A_prev.shape[1]
dW = 1./m * np.dot(dZ,A_prev.T)
db = 1./m * np.sum(dZ, axis = 1, keepdims = True)
dA_prev = np.dot(W.T,dZ)
assert (dA_prev.shape == A_prev.shape)
assert (dW.shape == W.shape)
assert (db.shape == b.shape)
return dA_prev, dW, db
def linear_activation_backward(dA, cache, activation):
"""
Implement the backward propagation for the LINEAR->ACTIVATION layer.
Arguments:
dA -- post-activation gradient for current layer l
cache -- tuple of values (linear_cache, activation_cache) we store for computing backward propagation efficiently
activation -- the activation to be used in this layer, stored as a text string: "sigmoid" or "relu"
Returns:
dA_prev -- Gradient of the cost with respect to the activation (of the previous layer l-1), same shape as A_prev
dW -- Gradient of the cost with respect to W (current layer l), same shape as W
db -- Gradient of the cost with respect to b (current layer l), same shape as b
"""
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
def L_model_backward(AL, Y, caches):
"""
Implement the backward propagation for the [LINEAR->RELU] * (L-1) -> LINEAR -> SIGMOID group
Arguments:
AL -- probability vector, output of the forward propagation (L_model_forward())
Y -- true "label" vector (containing 0 if non-cat, 1 if cat)
caches -- list of caches containing:
every cache of linear_activation_forward() with "relu" (there are (L-1) or them, indexes from 0 to L-2)
the cache of linear_activation_forward() with "sigmoid" (there is one, index L-1)
Returns:
grads -- A dictionary with the gradients
grads["dA" + str(l)] = ...
grads["dW" + str(l)] = ...
grads["db" + str(l)] = ...
"""
grads = {}
L = len(caches) # the number of layers
m = AL.shape[1]
Y = Y.reshape(AL.shape) # after this line, Y is the same shape as AL
# Initializing the backpropagation
dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
# Lth layer (SIGMOID -> LINEAR) gradients. Inputs: "AL, Y, caches". Outputs: "grads["dAL"], grads["dWL"], grads["dbL"]
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)):
# lth layer: (RELU -> LINEAR) gradients.
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
def update_parameters(parameters, grads, learning_rate):
"""
Update parameters using gradient descent
Arguments:
parameters -- python dictionary containing your parameters
grads -- python dictionary containing your gradients, output of L_model_backward
Returns:
parameters -- python dictionary containing your updated parameters
parameters["W" + str(l)] = ...
parameters["b" + str(l)] = ...
"""
L = len(parameters) // 2 # number of layers in the neural network
# Update rule for each parameter. Use a for loop.
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
def predict(X, y, parameters):
"""
This function is used to predict the results of a L-layer neural network.
Arguments:
X -- data set of examples you would like to label
parameters -- parameters of the trained model
Returns:
p -- predictions for the given dataset X
"""
m = X.shape[1]
n = len(parameters) // 2 # number of layers in the neural network
p = np.zeros((1,m))
# Forward propagation
probas, caches = L_model_forward(X, parameters)
# convert probas to 0/1 predictions
for i in range(0, probas.shape[1]):
if probas[0,i] > 0.5:
p[0,i] = 1
else:
p[0,i] = 0
#print results
#print ("predictions: " + str(p))
#print ("true labels: " + str(y))
print("Accuracy: " + str(np.sum((p == y)/m)))
return p
def print_mislabeled_images(classes, X, y, p):
"""
Plots images where predictions and truth were different.
X -- dataset
y -- true labels
p -- predictions
"""
a = p + y
mislabeled_indices = np.asarray(np.where(a == 1))
plt.rcParams['figure.figsize'] = (40.0, 40.0) # set default size of plots
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"))
导入实验所需要的数据集和测试集
# 导入实验需要的数据集和训练集；我们在工具类中已经定义好了导入数据的函数
train_x_orig, train_y, test_x_orig, test_y, classes = load_data()
# 我们可以随机抽取一张图片看看
index = 1
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.")
我们要经常检查一下我们的数据维度是否正确，避免出现不必要的错误
# Explore your dataset
m_train = train_x_orig.shape[0]
num_px = train_x_orig.shape[1]
m_test = test_x_orig.shape[0]
# 将维度打印出来查看一下
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))
将训练集和测试集维度修改成为我们实验需要的维度
# 将训练集和测试集的数据改成我们实现需要的数据维度（所有的输入特征要编程一个列向量）
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
# 将所有的特征进行标准化
train_x = train_x_flatten/255.
test_x = test_x_flatten/255.
print ("train_x's shape: " + str(train_x.shape))
print ("test_x's shape: " + str(test_x.shape))
核心步骤，实现神经网络前向传播和反向传播的过程
# 接下来我们构建一个两层的神经网络
'''
#定义一个初始化两层网络维度的函数
# n_x就是0层输入的特征值的个数
# n_h就是1层神经元的个数
# n_y就是2层神经元的个数(我们实现的是二分类的算法，所以则一层是只有一个输出神经元的)
'''
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))
# 这是使用了assert，可以确保我们的维度上是正确的
assert((n_h, n_x) == W1.shape)
assert((n_h, 1) == b1.shape)
assert((n_y, n_h) == W2.shape)
assert((n_y, 1) == b2.shape)
parameters = {
"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2
}
return parameters
# 激活函数的前向传播过程
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]))
# 这里记录好cache是方便方向传播的时候使用（避免重复计算）
cache = (linear_cache, activation_cache)
return A, cache
# 定义计算损失值的函数
def compute_cost(AL, Y):
m = Y.shape[1]
cost = -(np.dot(np.log(AL), Y.T) + np.dot(np.log(1 - AL), (1 - Y).T)) / (1.0 * m)
#print(cost.shape)
cost = np.squeeze(cost)
#print(cost.shape)
#print(cost)
assert(cost.shape == ( ))
return cost
# 激活函数的方向传播过程
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
# 参数更新函数
def update_parameters(parameters, grads, learning_rate):
# //2表示向下取整的除法
L = len(parameters) // 2
for i in range(1, L + 1):
parameters["W" + str(i)] -= learning_rate * grads["dW" + str(i)]
parameters["b" + str(i)] -= learning_rate * grads["db" + str(i)]
return parameters
实现两层神经网络模型
# GRADED FUNCTION: two_layer_model
def two_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):
"""
Implements a two-layer neural network: LINEAR->RELU->LINEAR->SIGMOID.
Arguments:
X -- input data, of shape (n_x, number of examples)
Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples)
layers_dims -- dimensions of the layers (n_x, n_h, n_y)
num_iterations -- number of iterations of the optimization loop
learning_rate -- learning rate of the gradient descent update rule
print_cost -- If set to True, this will print the cost every 100 iterations
Returns:
parameters -- a dictionary containing W1, W2, b1, and b2
"""
np.random.seed(1)
grads = {}
costs = [] # to keep track of the cost
m = X.shape[1] # number of examples
(n_x, n_h, n_y) = layers_dims
# Initialize parameters dictionary, by calling one of the functions you'd previously implemented
### START CODE HERE ### (≈ 1 line of code)
parameters = initialize_parameters(n_x, n_h, n_y)
### END CODE HERE ###
# Get W1, b1, W2 and b2 from the dictionary parameters.
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Loop (gradient descent)
for i in range(0, num_iterations):
# Forward propagation: LINEAR -> RELU -> LINEAR -> SIGMOID. Inputs: "X, W1, b1". Output: "A1, cache1, A2, cache2".
### START CODE HERE ### (≈ 2 lines of code)
A1, cache1 = linear_activation_forward(X, parameters["W1"], parameters["b1"], activation="relu")
A2, cache2 = linear_activation_forward(A1, parameters["W2"], parameters["b2"], activation="sigmoid")
### END CODE HERE ###
# Compute cost
### START CODE HERE ### (≈ 1 line of code)
cost = compute_cost(A2, Y)
### END CODE HERE ###
# Initializing backward propagation
dA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))
# Backward propagation. Inputs: "dA2, cache2, cache1". Outputs: "dA1, dW2, db2; also dA0 (not used), dW1, db1".
### START CODE HERE ### (≈ 2 lines of code)
dA1, dW2, db2 = linear_activation_backward(dA2, cache2, activation="sigmoid")
dA0, dW1, db1 = linear_activation_backward(dA1, cache1, activation="relu")
### END CODE HERE ###
# Set grads['dWl'] to dW1, grads['db1'] to db1, grads['dW2'] to dW2, grads['db2'] to db2
grads['dW1'] = dW1
grads['db1'] = db1
grads['dW2'] = dW2
grads['db2'] = db2
# Update parameters.
### START CODE HERE ### (approx. 1 line of code)
parameters = update_parameters(parameters, grads, learning_rate)
### END CODE HERE ###
# Retrieve W1, b1, W2, b2 from parameters
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Print the cost every 100 training example
if print_cost and i % 100 == 0:
print("Cost after iteration {}: {}".format(i, np.squeeze(cost)))
if i % 100 == 0:
costs.append(cost)
if not(print_cost):
print("The final cost = %f" %(cost))
# plot the cost
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per hundreds)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
return parameters
对模型进行测试
# 接下来对二层神经网络的各层维度进行赋值
n_x = 12288 # num_px * num_px * 3
n_h = 7
n_y = 1
layers_dims = (n_x, n_h, n_y)
# 调用模型
parameters = two_layer_model(train_x, train_y, layers_dims = (n_x, n_h, n_y), num_iterations = 2500, print_cost=True)
定义预测函数，用来输出模型预测的正确率
# 自定义预测函数，用来得到预测的正确率
def predict(X, y, parameters):
m = X.shape[1]
n = len(parameters) // 2
p = np.zeros((1, m))
probas, caches = L_model_forward(X, parameters)
for i in range(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) / (1.0 * m)*100) + "%")
return p
# 用训练集得到的参数，再来对训练集中的数据进行预测，得到正确率
predictions_train = predict(train_x, train_y, parameters)
# 用训练集得到的参数，再来对测试集中的数据进行预测，得到正确率
predictions_test = predict(test_x, test_y, parameters)
2.2 L层神经网络的实现
由上面的两层神经网络的实现，我们可以将两层模型推广至L层，需要对之前的部分函数进行调整
核心部分：前向传播、反向传播和参数调整
# 实现一个L层的神经网络；需要将前面的代码进行修改
def initialize_parameters_deep(layer_dims):
np.random.seed(1)
parameters = {}
L = len(layer_dims)
for i in range(1, L):
#Be careful, the scaler is np.sqrt(layers_dims[i - 1]), not constant 0.01
parameters['W' + str(i)] = np.random.randn(layer_dims[i], layer_dims[i - 1]) / np.sqrt(layers_dims[i - 1])
parameters["b" + str(i)] = np.zeros((layer_dims[i], 1))
assert((layer_dims[i], layer_dims[i - 1]) == parameters["W" + str(i)].shape)
assert((layer_dims[i], 1) == parameters["b" + str(i)].shape)
return parameters
def L_model_forward(X, parameters):
caches = []
A = X
L = len(parameters) // 2
for i in range(1, L):
A_prev = A
A, cache = linear_activation_forward(A_prev, parameters["W" + str(i)], parameters["b" + str(i)], "relu")
caches.append(cache)
AL, cache = linear_activation_forward(A, parameters["W" + str(L)], parameters["b" + str(L)], "sigmoid")
caches.append(cache)
assert(AL.shape == (1, X.shape[1]))
return AL, caches
def compute_cost(AL, Y):
m = Y.shape[1]
cost = -(np.dot(np.log(AL), Y.T) + np.dot(np.log(1 - AL), (1 - Y).T)) / (m * 1.0)
#print(cost.shape)
cost = np.squeeze(cost)
#print(cost.shape)
#print(cost)
assert(cost.shape == ( ))
return cost
def L_model_backward(AL, Y, caches):
grads = {}
L = len(caches)
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 i in reversed(range(L - 1)):
current_cache = caches[i]
dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(i + 2)], current_cache, activation="relu")
grads["dA" + str(i + 1)] = dA_prev_temp
grads["dW" + str(i + 1)] = dW_temp
grads["db" + str(i + 1)] = db_temp
return grads
def update_parameters(parameters, grads, learning_rate):
L = len(parameters) // 2
for i in range(1, L + 1):
parameters["W" + str(i)] -= learning_rate * grads["dW" + str(i)]
parameters["b" + str(i)] -= learning_rate * grads["db" + str(i)]
return parameters
实现L层神经网络模型
# GRADED FUNCTION: L_layer_model
def L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):#lr was 0.009
"""
Implements a L-layer neural network: [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID.
Arguments:
X -- data, numpy array of shape (number of examples, num_px * num_px * 3)
Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples)
layers_dims -- list containing the input size and each layer size, of length (number of layers + 1).
learning_rate -- learning rate of the gradient descent update rule
num_iterations -- number of iterations of the optimization loop
print_cost -- if True, it prints the cost every 100 steps
Returns:
parameters -- parameters learnt by the model. They can then be used to predict.
"""
np.random.seed(1)
costs = [] # keep track of cost
# Parameters initialization.
### START CODE HERE ###
parameters = initialize_parameters_deep(layers_dims)
### END CODE HERE ###
# Loop (gradient descent)
for i in range(0, num_iterations):
# Forward propagation: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID.
### START CODE HERE ### (≈ 1 line of code)
AL, caches = L_model_forward(X, parameters)
### END CODE HERE ###
# Compute cost.
### START CODE HERE ### (≈ 1 line of code)
cost = compute_cost(AL, Y)
### END CODE HERE ###
# Backward propagation.
### START CODE HERE ### (≈ 1 line of code)
grads = L_model_backward(AL, Y, caches)
### END CODE HERE ###
# Update parameters.
### START CODE HERE ### (≈ 1 line of code)
parameters = update_parameters(parameters, grads, learning_rate)
### END CODE HERE ###
# Print the cost every 100 training example
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)
# plot the cost
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per tens)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
return parameters
这里我们以L=5为例子，将L层模型跑起来，看看实验的效果
### CONSTANTS ###
layers_dims = [12288, 20, 7, 5, 1] # 5-layer model
parameters = L_layer_model(train_x, train_y, layers_dims, num_iterations = 2500, print_cost = True)
# 输出模型对训练集进行预测的正确率
pred_train = predict(train_x, train_y, parameters)
# 输出模型对测试集进行预测的正确率
pred_test = predict(test_x, test_y, parameters)
# 输出所有预测错误的图片
print_mislabeled_images(classes, test_x, test_y, pred_test)
3.实验总结
- 实现多层神经网络模型进行二分类，实现效果上比上一次实验中的单神经网络模型的表现要好，对于测试集的预测正确率由68%（单神经网络）—>72%(两层神经网络）---->80%（5层神经网络），这里只是一粗略的对比，因为对于学习率等其他因素没有控制相同变量
- 对于多层神经网络模型而言，比如上面实验中，两层和五层的神经网络，在相同学习率的条件下，五层神经网络模型的的实现效果较两层模型实现的效果好，但是这是否意味着模型的层数越多模型表现的效果就越好呢？（答案是否定的）
- 在实验中，对两层模型进行了学习率的实验的，发现学习率的选取对于模型的效果表现是十分重要的（高了或者太低都会适得其反）
- 在上次的单层神经网络模型中，我用自己的图片进行了测试，上次模型认为我的本地图片不是一只，这次我用五层神经网络模型进行测试，模型认为我的图片是一只猫。哈哈哈，虽然这个图片不正经，不过这个结果对比还是很有意思的。
# 用自己电脑本地图片输入到模型中进行预测
local_file_path = 'C:\\Users\\佳雨初林\\Desktop\\猫头.jpg'
local_image = plt.imread(local_file_path )
# 打印本地图片的尺寸：(200,197,3)
local_image.shape
# 我们需要将图片尺寸改成我们模型中数据集的尺寸：(200,197,3)->(64,64,3)
from skimage import transform
local_image_tran = transform.resize(local_image,(64, 64, 3))
# 将改变尺寸后的图片打印出来看看
plt.imshow(local_image_tran)
# 最后将改变好尺寸之后的图像数据转化为模型需要的向量数据（12288，1）
local_test = local_image_tran.reshape(64*64*3,1)
my_predicted_image = predict(local_test, [1], parameters)
print ("y = " + str(np.squeeze(my_predicted_image)) + ", your L-layer model predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") + "\" picture.")
4.问题记录
4.1 资源导入问题
当我重新实现一次代码时，数据集和实验所需要的工具类都不在我jupyter的文件目录下，当时想着如何导入不同文件下的包，可以使用sys改变导入包的路径(亲测有效），append中不仅可以添加绝对路径，也可以是相对路径。
import sys
sys.path.append('C://Users//Desktop//研究生学习//deeplearning.ai-andrewNG-master//COURSE 1 Neural Networks and Deep Learning//Week 4//Deep Neural Network Application_ Image Classification')
from dnn_app_utils_v2 import *
这样确实能够将工具类dnn_app_utils_v2导入，但是工具类的中导入数据的load_data()方法中的数据路径又得修改，我怕麻烦，直接把数据集和工具类复制一份放到我的jupyter文件目录下面。
4.2 部分代码解释
下面这两条语句是自动加载你导入的python模块，保证你每次在ipynb里使用的模块是最新版本，所以在你修改了模块代码之后，不需要重新刷新你的kenel。（这些命令是在jupyter中才有的，在pycharm中会报错）
%load_ext autoreload
%autoreload 2
assert语法的使用，在实验的过程中总是遇到assert，这是一个有用的减少错误办法，可以有效排除coding时出现的一些错误。
5.总结
自己对于python相关库函数的使用上面还是存在极大缺陷，这里需要自己好好补补相关知识点。如果要我自己根据吴老师上课时的数学推导再到模型建立，完全个人实现模型的代码的话，那一定会非常吃力，但是老师的实验作业中，我只需要补齐极少数代码，然后根据jupyter笔记上面的引导，从而实现整个模型，将上课的内容融入到代码中，加深理论知识的理解，这是非常好的。前路漫漫，还得继续努力。