01神經網路和深度學習-Logistic-Regression-with-a-Neural-Network-mindset-第二週程式設計作業2
演算法大概流程:
1、輸入w,b並初始化;
2、反向傳播,遞迴下降,計算dw,db;,
3、利用超引數學習率,迭代計算w,b的值;
4、預測。
import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
from scipy import ndimage
from lr_utils import load_dataset
# Loading the data (cat/non-cat)
train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()
# Example of a picture
index = 25
plt.imshow(train_set_x_orig[index])
print ("y = " + str(train_set_y[:, index]) + ", it's a '" + classes[np.squeeze(train_set_y[:, index])].decode("utf-8") + "' picture.")
### START CODE HERE ### (≈ 3 lines of code)
m_train = train_set_x_orig.shape[0]
m_test = test_set_x_orig.shape[0]
num_px = train_set_x_orig.shape[1]
### END CODE HERE ###
print ("Number of training examples: m_train = " + str(m_train))
print ("Number of testing examples: m_test = " + str(m_test))
print ("Height/Width of each image: num_px = " + str(num_px))
print ("Each image is of size: (" + str(num_px) + ", " + str(num_px) + ", 3)")
print ("train_set_x shape: " + str(train_set_x_orig.shape))
print ("train_set_y shape: " + str(train_set_y.shape))
print ("test_set_x shape: " + str(test_set_x_orig.shape))
print ("test_set_y shape: " + str(test_set_y.shape))
# Reshape the training and test examples
### START CODE HERE ### (≈ 2 lines of code)
train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0],-1).T
test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0],-1).T
### END CODE HERE ###
print ("train_set_x_flatten shape: " + str(train_set_x_flatten.shape))
print ("train_set_y shape: " + str(train_set_y.shape))
print ("test_set_x_flatten shape: " + str(test_set_x_flatten.shape))
print ("test_set_y shape: " + str(test_set_y.shape))
print ("sanity check after reshaping: " + str(train_set_x_flatten[0:5,0]))
train_set_x = train_set_x_flatten/255.
test_set_x = test_set_x_flatten/255.
# GRADED FUNCTION: sigmoid
def sigmoid(z):#啟用函式
"""
Compute the sigmoid of z
Arguments:
z -- A scalar or numpy array of any size.
Return:
s -- sigmoid(z)
"""
### START CODE HERE ### (≈ 1 line of code)
s = 1 / (1+np.exp(-z))
### END CODE HERE ###
return s
# GRADED FUNCTION: initialize_with_zeros
def initialize_with_zeros(dim):#初始化全為0
"""
This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.
Argument:
dim -- size of the w vector we want (or number of parameters in this case)
Returns:
w -- initialized vector of shape (dim, 1)
b -- initialized scalar (corresponds to the bias)
"""
### START CODE HERE ### (≈ 1 line of code)
w = np.zeros(dim).reshape(dim, 1)
b = 0
### END CODE HERE ###
assert(w.shape == (dim, 1))
assert(isinstance(b, float) or isinstance(b, int))
return w, b
# GRADED FUNCTION: propagate
def propagate(w, b, X, Y):#傳播
"""
Implement the cost function and its gradient for the propagation explained above
Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of size (num_px * num_px * 3, number of examples)
Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)
Return:
cost -- negative log-likelihood cost for logistic regression
dw -- gradient of the loss with respect to w, thus same shape as w
db -- gradient of the loss with respect to b, thus same shape as b
Tips:
- Write your code step by step for the propagation. np.log(), np.dot()
"""
m = X.shape[1]
# FORWARD PROPAGATION (FROM X TO COST)
### START CODE HERE ### (≈ 2 lines of code)
A = sigmoid((w.T).dot(X)+b) # compute activation
cost = (-1.0/m) * np.sum(Y*np.log(A) + (1-Y)*np.log(1-A)) # compute cost
### END CODE HERE ###
# BACKWARD PROPAGATION (TO FIND GRAD)
### START CODE HERE ### (≈ 2 lines of code)
dw = (1.0/m) * X.dot(((A-Y).T))
db = (1.0/m) * np.sum(A-Y)
### END CODE HERE ###
assert(dw.shape == w.shape)#2,1
assert(db.dtype == float)
cost = np.squeeze(cost)
assert(cost.shape == ())
grads = {"dw": dw,
"db": db}
return grads, cost
# GRADED FUNCTION: optimize
def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):#優化
"""
This function optimizes w and b by running a gradient descent algorithm
Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of shape (num_px * num_px * 3, number of examples)
Y -- true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)
num_iterations -- number of iterations of the optimization loop
learning_rate -- learning rate of the gradient descent update rule
print_cost -- True to print the loss every 100 steps
Returns:
params -- dictionary containing the weights w and bias b
grads -- dictionary containing the gradients of the weights and bias with respect to the cost function
costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.
Tips:
You basically need to write down two steps and iterate through them:
1) Calculate the cost and the gradient for the current parameters. Use propagate().
2) Update the parameters using gradient descent rule for w and b.
"""
costs = []
for i in range(num_iterations):
# Cost and gradient calculation (≈ 1-4 lines of code)
### START CODE HERE ###
grads, cost = propagate(w, b, X, Y)
### END CODE HERE ###
# Retrieve derivatives from grads
dw = grads["dw"]
db = grads["db"]
# update rule (≈ 2 lines of code)
### START CODE HERE ###
w = w-learning_rate*dw
b = b-learning_rate*db
### END CODE HERE ###
# Record the costs
if i % 100 == 0:
costs.append(cost)
# Print the cost every 100 training examples
if print_cost and i % 100 == 0:
print ("Cost after iteration %i: %f" %(i, cost))
params = {"w": w,
"b": b}
grads = {"dw": dw,
"db": db}
return params, grads, costs
# GRADED FUNCTION: predict
def predict(w, b, X):#預測
'''
Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)
Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of size (num_px * num_px * 3, number of examples)
Returns:
Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X
'''
m = X.shape[1]
Y_prediction = np.zeros((1,m))
w = w.reshape(X.shape[0], 1)
# Compute vector "A" predicting the probabilities of a cat being present in the picture
### START CODE HERE ### (≈ 1 line of code)
A = sigmoid((w.T).dot(X)+b)
### END CODE HERE ###
for i in range(A.shape[1]):
# Convert probabilities A[0,i] to actual predictions p[0,i]
### START CODE HERE ### (≈ 4 lines of code)
if A[0,i] <= 0.5:
Y_prediction[0,i]=0
elif A[0,i] > 0.5:
Y_prediction[0,i]=1
### END CODE HERE ###
assert(Y_prediction.shape == (1, m))
return Y_prediction
# GRADED FUNCTION: model
def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):
"""
Builds the logistic regression model by calling the function you've implemented previously
Arguments:
X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train)
Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train)
X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test)
Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test)
num_iterations -- hyperparameter representing the number of iterations to optimize the parameters
learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize()
print_cost -- Set to true to print the cost every 100 iterations
Returns:
d -- dictionary containing information about the model.
"""
### START CODE HERE ###
# initialize parameters with zeros (≈ 1 line of code)
w, b = initialize_with_zeros(X_train.shape[0])
# Gradient descent (≈ 1 line of code)
parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost = False)
# Retrieve parameters w and b from dictionary "parameters"
w = parameters["w"]
b = parameters["b"]
# Predict test/train set examples (≈ 2 lines of code)
Y_prediction_test = predict(w, b, X_test)
Y_prediction_train = predict(w, b, X_train)
### END CODE HERE ###
# Print train/test Errors
print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))
print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))
d = {"costs": costs,
"Y_prediction_test": Y_prediction_test,
"Y_prediction_train" : Y_prediction_train,
"w" : w,
"b" : b,
"learning_rate" : learning_rate,
"num_iterations": num_iterations}
return d
if __name__=='__main__':
print ("sigmoid([0, 2]) = " + str(sigmoid(np.array([0,2]))))
dim = 2
w, b = initialize_with_zeros(dim)
print ("w = " + str(w))
print ("b = " + str(b))
w, b, X, Y = np.array([[1],[2]]), 2, np.array([[1,2],[3,4]]), np.array([[1,0]])
grads, cost = propagate(w, b, X, Y)
print ("dw = " + str(grads["dw"]))
print ("db = " + str(grads["db"]))
print ("cost = " + str(cost))
params, grads, costs = optimize(w, b, X, Y, num_iterations= 100, learning_rate = 0.009, print_cost = False)
print ("w = " + str(params["w"]))
print ("b = " + str(params["b"]))
print ("dw = " + str(grads["dw"]))
print ("db = " + str(grads["db"]))
print ("predictions = " + str(predict(w, b, X)))
d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)
# Example of a picture that was wrongly classified.
index = 1
plt.imshow(test_set_x[:,index].reshape((num_px, num_px, 3)))
print ("y = " + str(test_set_y[0,index]) + ", you predicted that it is a \"" + classes[int(d["Y_prediction_test"][0,index])].decode("utf-8") + "\" picture.")
# Plot learning curve (with costs)
costs = np.squeeze(d['costs'])
plt.plot(costs)
plt.ylabel('cost')
plt.xlabel('iterations (per hundreds)')
plt.title("Learning rate =" + str(d["learning_rate"]))
plt.show()
相關文章
- 01神經網路和深度學習-Python-Basics-With-Numpy-第二週程式設計作業1神經網路深度學習Python程式設計
- 01神經網路和深度學習-Planar data classification with one hidden layer v3-第三週程式設計作業神經網路深度學習程式設計
- 01神經網路和深度學習-Deep Neural Network for Image Classification: Application-第四周程式設計作業2神經網路深度學習APP程式設計
- 神經網路和深度學習神經網路深度學習
- 深度學習系列(2)——神經網路與深度學習深度學習神經網路
- 02改善深層神經網路-Optimization+methods-第二週程式設計作業1神經網路程式設計
- 02改善深層神經網路-Regularization-第一週程式設計作業2神經網路程式設計
- 神經網路和深度學習(1):前言神經網路深度學習
- 01神經網路和深度學習-Building your Deep Neural Network: Step by Step-第四周程式設計作業1神經網路深度學習UI程式設計
- 《深度學習——Andrew Ng》第四課第四周程式設計作業_2_神經網路風格遷移深度學習程式設計神經網路
- 神經網路和深度學習簡史(全)神經網路深度學習
- 深入研究神經網路和深度學習神經網路深度學習
- 神經網路和深度學習簡史(一)神經網路深度學習
- 【deeplearning.ai-神經網路和深度學習】第一週答案AI神經網路深度學習
- 【深度學習】神經網路入門深度學習神經網路
- 再聊神經網路與深度學習神經網路深度學習
- 深度學習與圖神經網路深度學習神經網路
- AI之(神經網路+深度學習)AI神經網路深度學習
- 【深度學習篇】--神經網路中的卷積神經網路深度學習神經網路卷積
- 02改善深層神經網路-Initialization-第一週程式設計作業1神經網路程式設計
- 【深度學習】1.4深層神經網路深度學習神經網路
- 深度學習教程 | 深層神經網路深度學習神經網路
- 深度學習三:卷積神經網路深度學習卷積神經網路
- 《神經網路和深度學習》系列文章三十八:深度神經網路為何很難訓練?神經網路深度學習
- 深度學習與神經網路學習筆記一深度學習神經網路筆記
- 深度學習筆記------卷積神經網路深度學習筆記卷積神經網路
- 深度學習之上,圖神經網路(GNN )崛起深度學習神經網路GNN
- 深度學習卷積神經網路筆記深度學習卷積神經網路筆記
- 深度學習之step by step搭建神經網路深度學習神經網路
- 深度學習迴圈神經網路詳解深度學習神經網路
- 深度學習之RNN(迴圈神經網路)深度學習RNN神經網路
- nndl-復旦-神經網路與深度學習筆記第二章習題神經網路深度學習筆記
- 《神經網路和深度學習》系列文章三十:如何選擇神經網路的超引數神經網路深度學習
- 02改善深層神經網路-Gradient+Checking-第一週程式設計作業3神經網路程式設計
- 深度學習與圖神經網路學習分享:CNN 經典網路之-ResNet深度學習神經網路CNN
- 寫給人類的機器學習四、神經網路和深度學習機器學習神經網路深度學習
- NLP與深度學習(二)迴圈神經網路深度學習神經網路
- 【機器學習基礎】神經網路/深度學習基礎機器學習神經網路深度學習