deeplearning_Planardataclassificationwithonehiddenlayer

此文为deeplearning课程第三周的编程作业实现一个单层神经网络（对红点蓝点分类）

需要用到的库

import numpy as npimport matplotlib.pyplot as pltfrom testCases import *import sklearnimport sklearn.datasetsimport sklearn.linear_modelfrom planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets

加载数据

X, Y = load_planar_dataset()

主要方法步骤

处理参数

这里定义隐藏层单元个数为4
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)

初始化参数

w初始不能全为0，否则就会使下一层每个单元数值相同，最后的结果只是第0层的线性组合而已。

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.当我们设置相同的seed，每次生成的随机数相同。如果不设置seed，则每次会生成不同的随机数    ### 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

前向传播

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 = np.dot(W1,X)+b1    A1 = np.tanh(Z1)    Z2 = np.dot(W2,A1)+b2    A2 = sigmoid(Z2)    ### END CODE HERE ###    assert (A2.shape == (1, X.shape[1]))    cache = {"Z1": Z1,             "A1": A1,             "Z2": Z2,             "A2": A2}    return A2, cache

计算代价函数

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

反向传播

计算导数

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/m*(np.dot(dZ2,A1.T))    db2 = 1/m*np.sum(dZ2,axis=1,keepdims = True)    dZ1 = np.dot(W2.T,dZ2)*(1-np.power(A1,2))    dW1 = 1/m*(np.dot(dZ1,X.T))    db1 = 1/m*np.sum(dZ1,axis=1,keepdims=True)    ### END CODE HERE ###    grads = {"dW1": dW1,             "db1": db1,             "dW2": dW2,             "db2": db2}    return grads

更新参数

根据反向传播计算的导数更新参数

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

将以上方法整合在一起的简单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)#当我们设置相同的seed，每次生成的随机数相同。如果不设置seed，则每次会生成不同的随机数    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

predict

根据已优化的参数和数据X进行预测

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 = (A2 > 0.5)    ### END CODE HERE ###    return predictions

4个隐藏单元

# Build a model with a n_h-dimensional hidden layerparameters = nn_model(X, Y, n_h = 4, num_iterations = 10000, print_cost=True)# Plot the decision boundaryplot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)plt.title("Decision Boundary for hidden layer size " + str(4))# Print accuracypredictions = predict(parameters, X)print ('Accuracy: %d' % float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100) + '%')

1-50个隐藏单元

plt.figure(figsize=(16, 32))hidden_layer_sizes = [1, 2, 3, 4, 5, 20, 50]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))