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

分別使用邏輯迴歸和加了隱藏層的神經網路對花的顏色進行預測。

一、邏輯迴歸

#coding=utf-8
# Package imports
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from testCases import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets

np.random.seed(1) # set a seed so that the results are consistent

if __name__=='__main__':  

    X, Y = load_planar_dataset()
    # Visualize the data:
    plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral)
    ### START CODE HERE ### (≈ 3 lines of code)
    shape_X = X.shape
    shape_Y = Y.shape

    m = shape_X[1] # training set size
    ### END CODE HERE ###
    
    print ('The shape of X is: ' + str(shape_X))
    print ('The shape of Y is: ' + str(shape_Y))
    print ('I have m = %d training examples!' % (m))   
    
    # Train the logistic regression classifier
    clf = sklearn.linear_model.LogisticRegressionCV();
    clf.fit(X.T, Y.T);
    
    # Plot the decision boundary for logistic regression
    plot_decision_boundary(lambda x: clf.predict(x), X, Y)
    plt.title("Logistic Regression")
    plt.show()
    
    # Print accuracy
    LR_predictions = clf.predict(X.T)
    print ('Accuracy of logistic regression: %d ' % float((np.dot(Y,LR_predictions) + np.dot(1-Y,1-LR_predictions))/float(Y.size)*100) +
       '% ' + "(percentage of correctly labelled datapoints)")

【注意】這裡因為我沒有使用IPython，所以顯示影象要刪掉頭部的“%matplotlib inline”，加一句“plt.show()”，下面同理。

執行結果：

可以看到，因為影象並不適合擬合線性迴歸，所以準確率僅為47%。

二、神經網路

這裡使用了含有隱藏層的神經網路來做預測：

#coding=utf-8
# Package imports
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from testCases import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets

np.random.seed(1) # set a seed so that the results are consistent

def layer_sizes(X, Y):
    """
    Arguments:
    X -- input dataset of shape (input size, number of examples)
    Y -- labels of shape (output size, number of examples)
    
    Returns:
    n_x -- the size of the input layer
    n_h -- the size of the hidden layer
    n_y -- the size of the output layer
    """
    ### START CODE HERE ### (≈ 3 lines of code)
    n_x = X.shape[0] # size of input layer
    n_h = 4
    n_y = Y.shape[0] # size of output layer

    ### END CODE HERE ###
    return (n_x, n_h, n_y)

# 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:
    params -- 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(2) # we set up a seed so that your output matches ours although the initialization is random.
    
    ### 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

    # GRADED FUNCTION: forward_propagation
def forward_propagation(X, parameters):
    """
    Argument:
    X -- input data of size (n_x, m)
    parameters -- python dictionary containing your parameters (output of initialization function)
    
    Returns:
    A2 -- The sigmoid output of the second activation
    cache -- a dictionary containing "Z1", "A1", "Z2" and "A2"
    """
    # Retrieve each parameter from the dictionary "parameters"
    ### START CODE HERE ### (≈ 4 lines of code)
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']
    ### END CODE HERE ###
    
    # Implement Forward Propagation to calculate A2 (probabilities)
    ### START CODE HERE ### (≈ 4 lines of code)
    Z1 = W1.dot(X) + b1
    A1 = np.tanh(Z1)
    Z2 = W2.dot(A1) + b2
    A2 = sigmoid(Z2)
    ### END CODE HERE ###
    '''print("Z1 = " + str(Z1))
    print("A1 = " + str(A1))
    print("Z2 = " + str(Z2))
    print("A2 = " + str(A2))'''
    assert(A2.shape == (1, X.shape[1]))
    
    cache = {"Z1": Z1,
             "A1": A1,
             "Z2": Z2,
             "A2": A2}
    
    return A2, cache

# GRADED FUNCTION: compute_cost

def compute_cost(A2, Y, parameters):
    """
    Computes the cross-entropy cost given in equation (13)
    
    Arguments:
    A2 -- The sigmoid output of the second activation, of shape (1, number of examples)
    Y -- "true" labels vector of shape (1, number of examples)
    parameters -- python dictionary containing your parameters W1, b1, W2 and b2
    
    Returns:
    cost -- cross-entropy cost given equation (13)
    """
    
    m = Y.shape[1] # number of example

    # Compute the cross-entropy cost
    ### START CODE HERE ### (≈ 2 lines of code)
    logprobs = np.multiply(np.log(A2),Y) + np.multiply(np.log(1 - A2),1 - Y)
    cost = - np.sum(logprobs) / m
    ### END CODE HERE ###
    
    cost = np.squeeze(cost)     # makes sure cost is the dimension we expect. 
                                # E.g., turns [[17]] into 17 
    assert(isinstance(cost, float))
    
    return cost

# GRADED FUNCTION: backward_propagation

def backward_propagation(parameters, cache, X, Y):
    """
    Implement the backward propagation using the instructions above.
    
    Arguments:
    parameters -- python dictionary containing our parameters 
    cache -- a dictionary containing "Z1", "A1", "Z2" and "A2".
    X -- input data of shape (2, number of examples)
    Y -- "true" labels vector of shape (1, number of examples)
    
    Returns:
    grads -- python dictionary containing your gradients with respect to different parameters
    """
    m = X.shape[1]
    
    # First, retrieve W1 and W2 from the dictionary "parameters".
    ### START CODE HERE ### (≈ 2 lines of code)
    W1 = parameters['W1']
    W2 = parameters['W2']
    ### END CODE HERE ###
        
    # Retrieve also A1 and A2 from dictionary "cache".
    ### START CODE HERE ### (≈ 2 lines of code)
    A1 = cache['A1']
    A2 = cache['A2']
    ### END CODE HERE ###
    
    # Backward propagation: calculate dW1, db1, dW2, db2. 
    ### START CODE HERE ### (≈ 6 lines of code, corresponding to 6 equations on slide above)
    dZ2= A2 - Y
    dW2 = 1.0 / m * dZ2.dot(A1.T)
    db2 = 1.0 / m * np.sum(dZ2, axis = 1, keepdims = True)
    dZ1 = (W2.T).dot(dZ2) * (1 - np.power(A1, 2))
    dW1 = 1.0 / m * dZ1.dot(X.T)
    db1 = 1.0 / m * np.sum(dZ1, axis = 1, keepdims = True)
    ### END CODE HERE ###
    
    grads = {"dW1": dW1,
             "db1": db1,
             "dW2": dW2,
             "db2": db2}
    
    return grads

# GRADED FUNCTION: update_parameters

def update_parameters(parameters, grads, learning_rate = 1.2):
    """
    Updates parameters using the gradient descent update rule given above
    
    Arguments:
    parameters -- python dictionary containing your parameters 
    grads -- python dictionary containing your gradients 
    
    Returns:
    parameters -- python dictionary containing your updated parameters 
    """
    # Retrieve each parameter from the dictionary "parameters"
    ### START CODE HERE ### (≈ 4 lines of code)
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']
    ### END CODE HERE ###
    
    # Retrieve each gradient from the dictionary "grads"
    ### START CODE HERE ### (≈ 4 lines of code)
    dW1 = grads['dW1']
    db1 = grads['db1']
    dW2 = grads['dW2']
    db2 = grads['db2']
    ## END CODE HERE ###
    
    # Update rule for each parameter
    ### START CODE HERE ### (≈ 4 lines of code)
    W1 = W1-learning_rate * dW1
    b1 = b1-learning_rate * db1
    W2 = W2-learning_rate * dW2
    b2 = b2-learning_rate * db2
    
    ### END CODE HERE ###
    
    parameters = {"W1": W1,
                  "b1": b1,
                  "W2": W2,
                  "b2": b2}
    
    return parameters
 
# GRADED FUNCTION: nn_model

def nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False):
    """
    Arguments:
    X -- dataset of shape (2, number of examples)
    Y -- labels of shape (1, number of examples)
    n_h -- size of the hidden layer
    num_iterations -- Number of iterations in gradient descent loop
    print_cost -- if True, print the cost every 1000 iterations
    
    Returns:
    parameters -- parameters learnt by the model. They can then be used to predict.
    """
    
    np.random.seed(3)
    n_x = layer_sizes(X, Y)[0]
    n_y = layer_sizes(X, Y)[2]
    
    # Initialize parameters, then retrieve W1, b1, W2, b2. Inputs: "n_x, n_h, n_y". Outputs = "W1, b1, W2, b2, parameters".
    ### START CODE HERE ### (≈ 5 lines of code)
    parameters = initialize_parameters(n_x, n_h, n_y)
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]
    ### END CODE HERE ###
    
    # Loop (gradient descent)

    for i in range(0, num_iterations):
         
        ### START CODE HERE ### (≈ 4 lines of code)
        # Forward propagation. Inputs: "X, parameters". Outputs: "A2, cache".
        A2, cache = forward_propagation(X, parameters)
        
        # Cost function. Inputs: "A2, Y, parameters". Outputs: "cost".
        cost = compute_cost(A2, Y, parameters)
 
        # Backpropagation. Inputs: "parameters, cache, X, Y". Outputs: "grads".
        grads = backward_propagation(parameters, cache, X, Y)
 
        # Gradient descent parameter update. Inputs: "parameters, grads". Outputs: "parameters".
        parameters = update_parameters(parameters, grads)
        
        ### END CODE HERE ###
        
        # Print the cost every 1000 iterations
        if print_cost and i % 1000 == 0:
            print ("Cost after iteration %i: %f" %(i, cost))

    return parameters
 
# GRADED FUNCTION: predict

def predict(parameters, X):
    """
    Using the learned parameters, predicts a class for each example in X
    
    Arguments:
    parameters -- python dictionary containing your parameters 
    X -- input data of size (n_x, m)
    
    Returns
    predictions -- vector of predictions of our model (red: 0 / blue: 1)
    """
    
    # Computes probabilities using forward propagation, and classifies to 0/1 using 0.5 as the threshold.
    ### START CODE HERE ### (≈ 2 lines of code)
    A2, cache = forward_propagation(X, parameters)
    predictions = np.rint(A2)
    ### END CODE HERE ###
    
    return predictions

if __name__=='__main__':
    X, Y = load_planar_dataset()
    
    X_assess, Y_assess = layer_sizes_test_case()
    (n_x, n_h, n_y) = layer_sizes(X_assess, Y_assess)
    print("The size of the input layer is: n_x = " + str(n_x))
    print("The size of the hidden layer is: n_h = " + str(n_h))
    print("The size of the output layer is: n_y = " + str(n_y))

    n_x, n_h, n_y = initialize_parameters_test_case()

    parameters = initialize_parameters(n_x, n_h, n_y)
    print("W1 = " + str(parameters["W1"]))
    print("b1 = " + str(parameters["b1"]))
    print("W2 = " + str(parameters["W2"]))
    print("b2 = " + str(parameters["b2"]))
    
    X_assess, parameters = forward_propagation_test_case()
    A2, cache = forward_propagation(X_assess, parameters)
    # Note: we use the mean here just to make sure that your output matches ours. 
    print(np.mean(cache['Z1']) ,np.mean(cache['A1']),np.mean(cache['Z2']),np.mean(cache['A2']))
 
    A2, Y_assess, parameters = compute_cost_test_case()
    print("cost = " + str(compute_cost(A2, Y_assess, parameters)))

    parameters, cache, X_assess, Y_assess = backward_propagation_test_case()
    grads = backward_propagation(parameters, cache, X_assess, Y_assess)
    print ("dW1 = "+ str(grads["dW1"]))
    print ("db1 = "+ str(grads["db1"]))
    print ("dW2 = "+ str(grads["dW2"]))
    print ("db2 = "+ str(grads["db2"]))

    parameters, grads = update_parameters_test_case()
    parameters = update_parameters(parameters, grads)
    print("W1 = " + str(parameters["W1"]))
    print("b1 = " + str(parameters["b1"]))
    print("W2 = " + str(parameters["W2"]))
    print("b2 = " + str(parameters["b2"]))

    X_assess, Y_assess = nn_model_test_case()
    parameters = nn_model(X_assess, Y_assess, 4, num_iterations=10000, print_cost=False)
    print("W1 = " + str(parameters["W1"]))
    print("b1 = " + str(parameters["b1"]))
    print("W2 = " + str(parameters["W2"]))
    print("b2 = " + str(parameters["b2"]))

    parameters, X_assess = predict_test_case()
    predictions = predict(parameters, X_assess)
    print("predictions mean = " + str(np.mean(predictions)))

    # Build a model with a n_h-dimensional hidden layer
    parameters = nn_model(X, Y, n_h = 4, num_iterations = 10000, print_cost=True)
    # Plot the decision boundary
    plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
    plt.title("Decision Boundary for hidden layer size " + str(4))

    # Print accuracy
    predictions = predict(parameters, X)
    print ('Accuracy: %d' % float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100) + '%')

    # This may take about 2 minutes to run
    plt.figure(figsize=(16, 32))
    hidden_layer_sizes = [1, 2, 3, 4, 5, 20, 40]
    for i, n_h in enumerate(hidden_layer_sizes):
        plt.subplot(5, 2, i+1)
        plt.title('Hidden Layer of size %d' % n_h)
        parameters = nn_model(X, Y, n_h, num_iterations = 5000)
        plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
        predictions = predict(parameters, X)
        accuracy = float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100)
        print ("Accuracy for {} hidden units: {} %".format(n_h, accuracy))

    # Datasets
    noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure = load_extra_datasets()
    datasets = {"noisy_circles": noisy_circles,
            "noisy_moons": noisy_moons,
            "blobs": blobs,
            "gaussian_quantiles": gaussian_quantiles}
    ### START CODE HERE ### (choose your dataset)
    dataset = "noisy_moons"
    ### END CODE HERE ###
    
    X, Y = datasets[dataset]
    X, Y = X.T, Y.reshape(1, Y.shape[0])
    # make blobs binary
    if dataset == "blobs":
        Y = Y%2

    # Visualize the data
    plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);
    plt.show()

【注意1】在步驟進行到對於4.3 - The Loop 部分的 “def forward_propagation(X, parameters)”函式時，因為我的程式碼跑出來的結果和expected不同，找bug找了很久，最後實在找不出來就硬著頭皮接著敲下面的部分，居然發現後面的結果都和expected相同……(｡•́︿•̀｡)大膽猜測一下，是不是原expected出錯了呢……？

（1）原expected：

（2）我的output：

【注意2】預測值四捨五入的時候，最好不要使用“np.round()”，而是使用“np.rint()”，原因。

【注意3】後面我是測試了“hidden_layer_sizes = [1, 2, 3, 4, 5, 20, 40]”這幾種不同隱藏層層數的神經網路，，預測準確率提高到了90%以上。當層數增大的時候，丟擲 Memory Error 超出記憶體。

執行結果：