文章目录
测试题:参考博文
作业1. 建立你的深度神经网络
1. 导入包
import numpy as np
import h5py
import matplotlib.pyplot as plt
from testCases_v2 import *
from dnn_utils_v2 import sigmoid, sigmoid_backward, relu, relu_backward
%matplotlib inline
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
np.random.seed(1)
2. 算法主要流程
3. 初始化
第4节笔记:01.神经网络和深度学习 W4.深层神经网络
3.1 两层神经网络
模型结构:LINEAR -> RELU -> LINEAR -> SIGMOID
权重:np.random.randn(shape)*0.01
偏置:np.zeros(shape)
# GRADED FUNCTION: initialize_parameters
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)
### START CODE HERE ### (≈ 4 lines of code)
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))
### END CODE HERE ###
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
3.2 多层神经网络
模型结构:[LINEAR -> RELU] × (L-1) -> LINEAR -> SIGMOID
# GRADED FUNCTION: initialize_parameters_deep
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(3)
parameters = {}
L = len(layer_dims) # number of layers in the network
for l in range(1, L):
### START CODE HERE ### (≈ 2 lines of code)
parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l-1])*0.01
parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))
### END CODE HERE ###
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
4. 前向传播
4.1 线性模块
向量化公式
其中
计算 ,缓存
# GRADED FUNCTION: linear_forward
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
"""
### START CODE HERE ### (≈ 1 line of code)
Z = np.dot(W, A) + b
### END CODE HERE ###
assert(Z.shape == (W.shape[0], A.shape[1]))
cache = (A, W, b)
return Z, cache
4.2 线性激活模块
计算激活输出
,以及缓存
(反向传播时要用到)(作业里的激活函数会返回这两项)
其中
是激活函数,可以是ReLu
,Sigmoid
等
# GRADED FUNCTION: linear_activation_forward
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".
### START CODE HERE ### (≈ 2 lines of code)
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = sigmoid(Z)
### END CODE HERE ###
elif activation == "relu":
# Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
### START CODE HERE ### (≈ 2 lines of code)
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = relu(Z)
### END CODE HERE ###
assert (A.shape == (W.shape[0], A_prev.shape[1]))
cache = (linear_cache, activation_cache)
return A, cache
4.3 多层模型
前面使用
层 ReLu
,最后使用 1 层 Sigmoid
# GRADED FUNCTION: L_model_forward
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
### START CODE HERE ### (≈ 2 lines of code)
A, cache = linear_activation_forward(A_prev, parameters['W'+str(l)], parameters['b'+str(l)], 'relu')
caches.append(cache) # 每一层的 (A,W,b, Z)
### END CODE HERE ###
# Implement LINEAR -> SIGMOID. Add "cache" to the "caches" list.
### START CODE HERE ### (≈ 2 lines of code)
AL, cache = linear_activation_forward(A, parameters['W'+str(L)], parameters['b'+str(L)], 'sigmoid')
caches.append(cache)
### END CODE HERE ###
assert(AL.shape == (1,X.shape[1]))
return AL, caches
现在得到了一个完整的前向传播,AL 包含预测值,可以计算损失函数
5. 损失函数
计算损失:
# GRADED FUNCTION: compute_cost
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.
### START CODE HERE ### (≈ 1 lines of code)
cost = np.sum(Y*np.log(AL)+(1-Y)*np.log(1-AL))/(-m)
### END CODE HERE ###
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
6. 反向传播
计算损失函数的梯度:
6.1 线性模块
# GRADED FUNCTION: linear_backward
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]
### START CODE HERE ### (≈ 3 lines of code)
dW = np.dot(dZ, A_prev.T)/m
db = 1/m*np.sum(dZ, axis=1, keepdims=True)
dA_prev = np.dot(W.T, dZ)
### END CODE HERE ###
assert (dA_prev.shape == A_prev.shape)
assert (dW.shape == W.shape)
assert (db.shape == b.shape)
return dA_prev, dW, db
6.2 线性激活模块
# GRADED FUNCTION: linear_activation_backward
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":
### START CODE HERE ### (≈ 2 lines of code)
dZ = relu_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
### END CODE HERE ###
elif activation == "sigmoid":
### START CODE HERE ### (≈ 2 lines of code)
dZ = sigmoid_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
### END CODE HERE ###
return dA_prev, dW, db
6.3 多层模型
# GRADED FUNCTION: L_model_backward
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"
(it's caches[l], for l in range(L-1) i.e l = 0...L-2)
the cache of linear_activation_forward() with "sigmoid"
(it's caches[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
### START CODE HERE ### (1 line of code)
dAL = -np.divide(Y, AL) + np.divide(1-Y, 1-AL)
### END CODE HERE ###
# Lth layer (SIGMOID -> LINEAR) gradients.
# Inputs: "AL, Y, caches".
# Outputs: "grads["dAL"], grads["dWL"], grads["dbL"]
### START CODE HERE ### (approx. 2 lines)
current_cache = caches[L-1]
grads["dA" + str(L)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, 'sigmoid')
### END CODE HERE ###
for l in reversed(range(L-1)):
# lth layer: (RELU -> LINEAR) gradients.
# Inputs: "grads["dA" + str(l + 2)], caches".
# Outputs: "grads["dA" + str(l + 1)] , grads["dW" + str(l + 1)] , grads["db" + str(l + 1)]
### START CODE HERE ### (approx. 5 lines)
current_cache = caches[l]
dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads['dA'+str(l+2)], current_cache, 'relu')
grads["dA" + str(l + 1)] = dA_prev_temp
grads["dW" + str(l + 1)] = dW_temp
grads["db" + str(l + 1)] = db_temp
### END CODE HERE ###
return grads
6.4 梯度下降、更新参数
# GRADED FUNCTION: update_parameters
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.
### START CODE HERE ### (≈ 3 lines of code)
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)]
### END CODE HERE ###
return parameters
作业2. 深度神经网络应用:图像分类
使用上面的函数,建立深度神经网络,并对图片是不是猫进行预测。
1. 导入包
import time
import numpy as np
import h5py
import matplotlib.pyplot as plt
import scipy
from PIL import Image
from scipy import ndimage
from dnn_app_utils_v2 import *
%matplotlib inline
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
np.random.seed(1)
2. 数据集
01.神经网络和深度学习 W2.神经网络基础(作业:逻辑回归 图片识别)
使用 01W2 作业里面的数据集,逻辑回归的准确率只有 70%
- 加载数据
train_x_orig, train_y, test_x_orig, test_y, classes = load_data()
- 查看数据
# Example of a picture
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.")
- 查看数据大小
# Explore your dataset
m_train = train_x_orig.shape[0]
num_px = train_x_orig.shape[1]
m_test = test_x_orig.shape[0]
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))
Number of training examples: 209
Number of testing examples: 50
Each image is of size: (64, 64, 3)
train_x_orig shape: (209, 64, 64, 3)
train_y shape: (1, 209)
test_x_orig shape: (50, 64, 64, 3)
test_y shape: (1, 50)
- 图片数据
向量化
# Reshape the training and test examples
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
# Standardize data to have feature values between 0 and 1.
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))
train_x's shape: (12288, 209) # 12288 = 64 * 64 * 3
test_x's shape: (12288, 50)
3. 建立模型
3.1 两层神经网络
3.2 多层神经网络
3.3 一般步骤
- 初始化参数 / 定义超参数
n_iters
次 迭代循环:
– a. 正向传播
– b. 计算成本函数
– c. 反向传播
– d. 更新参数(使用参数、梯度)- 使用训练好的参数 预测
4. 两层神经网络
- 定义参数
### CONSTANTS DEFINING THE MODEL ####
n_x = 12288 # num_px * num_px * 3
n_h = 7 # 隐藏层单元个数
n_y = 1
layers_dims = (n_x, n_h, n_y)
- 组件模型
# 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, W1, b1, 'relu')
A2, cache2 = linear_activation_forward(A1, W2, b2, '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, 'sigmoid')
dA0, dW1, db1 = linear_activation_backward(dA1, cache1, '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 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
- 训练
parameters = two_layer_model(train_x, train_y, layers_dims = (n_x, n_h, n_y), num_iterations = 2500, print_cost=True)
Cost after iteration 0: 0.693049735659989
Cost after iteration 100: 0.6464320953428849
Cost after iteration 200: 0.6325140647912678
Cost after iteration 300: 0.6015024920354665
Cost after iteration 400: 0.5601966311605747
Cost after iteration 500: 0.5158304772764729
Cost after iteration 600: 0.4754901313943325
Cost after iteration 700: 0.43391631512257495
Cost after iteration 800: 0.4007977536203887
Cost after iteration 900: 0.35807050113237976
Cost after iteration 1000: 0.33942815383664127
Cost after iteration 1100: 0.30527536361962654
Cost after iteration 1200: 0.2749137728213016
Cost after iteration 1300: 0.24681768210614846
Cost after iteration 1400: 0.19850735037466097
Cost after iteration 1500: 0.17448318112556657
Cost after iteration 1600: 0.1708076297809689
Cost after iteration 1700: 0.11306524562164715
Cost after iteration 1800: 0.09629426845937145
Cost after iteration 1900: 0.08342617959726863
Cost after iteration 2000: 0.07439078704319078
Cost after iteration 2100: 0.06630748132267933
Cost after iteration 2200: 0.0591932950103817
Cost after iteration 2300: 0.05336140348560554
Cost after iteration 2400: 0.04855478562877016
- 预测
训练集:Accuracy: 0.9999999999999998
predictions_train = predict(train_x, train_y, parameters)
# Accuracy: 0.9999999999999998
测试集:Accuracy: 0.72,比之前的逻辑回归 0.70 好一些
predictions_test = predict(test_x, test_y, parameters)
# Accuracy: 0.72
5. 多层神经网络
- 定义参数,5层 NN
### CONSTANTS ###
layers_dims = [12288, 20, 7, 5, 1] # 5-layer model
- 组件模型
# 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
- 训练
parameters = L_layer_model(train_x, train_y, layers_dims, num_iterations = 2500, print_cost = True)
Cost after iteration 0: 0.771749
Cost after iteration 100: 0.672053
Cost after iteration 200: 0.648263
Cost after iteration 300: 0.611507
Cost after iteration 400: 0.567047
Cost after iteration 500: 0.540138
Cost after iteration 600: 0.527930
Cost after iteration 700: 0.465477
Cost after iteration 800: 0.369126
Cost after iteration 900: 0.391747
Cost after iteration 1000: 0.315187
Cost after iteration 1100: 0.272700
Cost after iteration 1200: 0.237419
Cost after iteration 1300: 0.199601
Cost after iteration 1400: 0.189263
Cost after iteration 1500: 0.161189
Cost after iteration 1600: 0.148214
Cost after iteration 1700: 0.137775
Cost after iteration 1800: 0.129740
Cost after iteration 1900: 0.121225
Cost after iteration 2000: 0.113821
Cost after iteration 2100: 0.107839
Cost after iteration 2200: 0.102855
Cost after iteration 2300: 0.100897
Cost after iteration 2400: 0.092878
- 预测
训练集:Accuracy: 0.9856459330143539
pred_train = predict(train_x, train_y, parameters)
# Accuracy: 0.9856459330143539
测试集:Accuracy: 0.8,比逻辑回归 0.70,两层NN 0.72 都要好
pred_test = predict(test_x, test_y, parameters)
# Accuracy: 0.8
下一门课将会系统的学习如何调参,使得模型的效果更好
6. 结果分析
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)) # 0+1, 1+0, wrong case
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"))
print_mislabeled_images(classes, test_x, test_y, pred_test)
错误特点:
- 猫的身体在一个不寻常的位置
- 猫出现在一个相似颜色的背景下
- 不常见的猫颜色和种类
- 照相机角度
- 图片的亮度
- 大小程度(猫在图像中非常大或很小)
7. 用自己的图片测试
## START CODE HERE ##
my_image = "my_image.jpg" # change this to the name of your image file
my_label_y = [1] # the true class of your image (1 -> cat, 0 -> non-cat)
## END CODE HERE ##
fname = "images/" + my_image
image = Image.open(fname)
my_image = np.array(image.resize((num_px,num_px))).reshape((num_px*num_px*3,1))
my_predicted_image = predict(my_image, my_label_y, parameters)
plt.imshow(image)
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.")
Accuracy: 1.0
y = 1.0, your L-layer model predicts a "cat" picture.
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