02改善深層神經網路-Initialization-第一週程式設計作業1

分別使用

全零：parameters['W' + str(l)] = np.zeros((layers_dims[l], layers_dims[l-1]))

隨機：parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l-1]) * 10

“he”：parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l-1]) * (math.sqrt(2./layers_dims[l-1])) 

三種初始化方法對引數W進行初始化，其中引數b始終parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))，初始化為0。

#coding=utf-8
import math
import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
from init_utils import sigmoid, relu, compute_loss, forward_propagation, backward_propagation
from init_utils import update_parameters, predict, load_dataset, plot_decision_boundary, predict_dec

plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'

# load image dataset: blue/red dots in circles
train_X, train_Y, test_X, test_Y = load_dataset()
 
def model(X, Y, learning_rate = 0.01, num_iterations = 15000, print_cost = True, initialization = "he"):
    """
    Implements a three-layer neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SIGMOID.
    
    Arguments:
    X -- input data, of shape (2, number of examples)
    Y -- true "label" vector (containing 0 for red dots; 1 for blue dots), of shape (1, number of examples)
    learning_rate -- learning rate for gradient descent 
    num_iterations -- number of iterations to run gradient descent
    print_cost -- if True, print the cost every 1000 iterations
    initialization -- flag to choose which initialization to use ("zeros","random" or "he")
    
    Returns:
    parameters -- parameters learnt by the model
    """
        
    grads = {}
    costs = [] # to keep track of the loss
    m = X.shape[1] # number of examples
    layers_dims = [X.shape[0], 10, 5, 1]
    
    # Initialize parameters dictionary.
    if initialization == "zeros":
        parameters = initialize_parameters_zeros(layers_dims)
    elif initialization == "random":
        parameters = initialize_parameters_random(layers_dims)
    elif initialization == "he":
        parameters = initialize_parameters_he(layers_dims)

    # Loop (gradient descent)

    for i in range(0, num_iterations):

        # Forward propagation: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.
        a3, cache = forward_propagation(X, parameters)
        
        # Loss
        cost = compute_loss(a3, Y)

        # Backward propagation.
        grads = backward_propagation(X, Y, cache)
        
        # Update parameters.
        parameters = update_parameters(parameters, grads, learning_rate)
        
        # Print the loss every 1000 iterations
        if print_cost and i % 1000 == 0:
            print("Cost after iteration {}: {}".format(i, cost))
            costs.append(cost)
            
    # plot the loss
    plt.plot(costs)
    plt.ylabel('cost')
    plt.xlabel('iterations (per hundreds)')
    plt.title("Learning rate =" + str(learning_rate))
    plt.show()
    
    return parameters

    # GRADED FUNCTION: initialize_parameters_zeros 

def initialize_parameters_zeros(layers_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the size of each layer.
    
    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])
                    b1 -- bias vector of shape (layers_dims[1], 1)
                    ...
                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])
                    bL -- bias vector of shape (layers_dims[L], 1)
    """
    
    parameters = {}
    L = len(layers_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.zeros((layers_dims[l], layers_dims[l-1]))
        parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))
        ### END CODE HERE ###
    return parameters  
 
# GRADED FUNCTION: initialize_parameters_random

def initialize_parameters_random(layers_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the size of each layer.
    
    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])
                    b1 -- bias vector of shape (layers_dims[1], 1)
                    ...
                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])
                    bL -- bias vector of shape (layers_dims[L], 1)
    """
    
    np.random.seed(3)               # This seed makes sure your "random" numbers will be the as ours
    parameters = {}
    L = len(layers_dims)            # integer representing the number of layers
    
    for l in range(1, L):
        ### START CODE HERE ### (≈ 2 lines of code)
        parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l-1]) * 10
        parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))
        ### END CODE HERE ###

    return parameters
 
    # GRADED FUNCTION: initialize_parameters_he

def initialize_parameters_he(layers_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the size of each layer.
    
    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])
                    b1 -- bias vector of shape (layers_dims[1], 1)
                    ...
                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])
                    bL -- bias vector of shape (layers_dims[L], 1)
    """
    
    np.random.seed(3)
    parameters = {}
    L = len(layers_dims) - 1 # integer representing the number of layers
     
    for l in range(1, L + 1):
        ### START CODE HERE ### (≈ 2 lines of code)
        parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l-1]) * (math.sqrt(2./layers_dims[l-1])) 
        parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))
        ### END CODE HERE ###
        
    return parameters
     
if __name__=='__main__':  
    parameters = initialize_parameters_zeros([3,2,1])
    print("W1 = " + str(parameters["W1"]))
    print("b1 = " + str(parameters["b1"]))
    print("W2 = " + str(parameters["W2"]))
    print("b2 = " + str(parameters["b2"]))
   
    parameters = model(train_X, train_Y, initialization = "zeros")
    print ("On the train set:")
    predictions_train = predict(train_X, train_Y, parameters)
    print ("On the test set:")
    predictions_test = predict(test_X, test_Y, parameters)
    
    print ("predictions_train = " + str(predictions_train))
    print ("predictions_test = " + str(predictions_test)) 

    plt.title("Model with Zeros initialization")
    axes = plt.gca()
    axes.set_xlim([-1.5,1.5])
    axes.set_ylim([-1.5,1.5])
    plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)
    
    parameters = initialize_parameters_random([3, 2, 1])
    print("W1 = " + str(parameters["W1"]))
    print("b1 = " + str(parameters["b1"]))
    print("W2 = " + str(parameters["W2"]))
    print("b2 = " + str(parameters["b2"]))

    parameters = model(train_X, train_Y, initialization = "random")
    print ("On the train set:")
    predictions_train = predict(train_X, train_Y, parameters)
    print ("On the test set:")
    predictions_test = predict(test_X, test_Y, parameters)

    print (predictions_train)
    print (predictions_test)
    
    plt.title("Model with large random initialization")
    axes = plt.gca()
    axes.set_xlim([-1.5,1.5])
    axes.set_ylim([-1.5,1.5])
    plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)
    
    parameters = initialize_parameters_he([2, 4, 1])
    print("W1 = " + str(parameters["W1"]))
    print("b1 = " + str(parameters["b1"]))
    print("W2 = " + str(parameters["W2"]))
    print("b2 = " + str(parameters["b2"]))
    
    parameters = model(train_X, train_Y, initialization = "he")
    print ("On the train set:")
    predictions_train = predict(train_X, train_Y, parameters)
    print ("On the test set:")
    predictions_test = predict(test_X, test_Y, parameters)
    
    plt.title("Model with He initialization")
    axes = plt.gca()
    axes.set_xlim([-1.5,1.5])
    axes.set_ylim([-1.5,1.5])
    plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)

 

執行結果：

（1）全零

（2）隨機

（3）He

 

Note：

我發現如果隨機初始化W：parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l-1])

即不“/10”的話，效果比he還好……準確率達到0.997，而he是0.993……