Coursera-Deep Learning Specialization 课程之（一）：Neural Networks and Deep Learning-weak4编程作业

Building your Deep Neural Network: Step by Step

1 - Packages

import numpy as npimport h5pyimport matplotlib.pyplot as pltfrom testCases_v3 import *from dnn_utils_v2 import sigmoid, sigmoid_backward, relu, relu_backward%matplotlib inlineplt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plotsplt.rcParams['image.interpolation'] = 'nearest'plt.rcParams['image.cmap'] = 'gray'%load_ext autoreload%autoreload 2np.random.seed(1)

2 - Outline of the Assignment

3 - Initialization

3.1 - 2-layer Neural Network

# GRADED FUNCTION: initialize_parametersdef 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 

parameters = initialize_parameters(3,2,1)print("W1 = " + str(parameters["W1"]))print("b1 = " + str(parameters["b1"]))print("W2 = " + str(parameters["W2"]))print("b2 = " + str(parameters["b2"]))

3.2 - L-layer Neural Network

# GRADED FUNCTION: initialize_parameters_deepdef 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

parameters = initialize_parameters_deep([5,4,3])print("W1 = " + str(parameters["W1"]))print("b1 = " + str(parameters["b1"]))print("W2 = " + str(parameters["W2"]))print("b2 = " + str(parameters["b2"]))

4 - Forward propagation module

4.1 - Linear Forward

# GRADED FUNCTION: linear_forwarddef 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

A, W, b = linear_forward_test_case()Z, linear_cache = linear_forward(A, W, b)print("Z = " + str(Z))

4.2 - Linear-Activation Forward

# GRADED FUNCTION: linear_activation_forwarddef 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

d) L-Layer Model

# GRADED FUNCTION: L_model_forwarddef 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)], activation = "relu")        caches.append(cache)        ### 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

5 - Cost function

# GRADED FUNCTION: compute_costdef 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 = (-1/m)*np.sum(np.dot(Y,np.log(AL).T)+np.dot((1-Y),np.log(1-AL).T))    ### 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

Y, AL = compute_cost_test_case()print("cost = " + str(compute_cost(AL, Y)))

6 - Backward propagation module

# GRADED FUNCTION: linear_backwarddef 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 = (1/m)*np.dot(dZ,A_prev.T)    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

# Set up some test inputsdZ, linear_cache = linear_backward_test_case()dA_prev, dW, db = linear_backward(dZ, linear_cache)print ("dA_prev = "+ str(dA_prev))print ("dW = " + str(dW))print ("db = " + str(db))

6.2 - Linear-Activation backward

# GRADED FUNCTION: linear_activation_backwarddef 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

AL, linear_activation_cache = linear_activation_backward_test_case()dA_prev, dW, db = linear_activation_backward(AL, linear_activation_cache, activation = "sigmoid")print ("sigmoid:")print ("dA_prev = "+ str(dA_prev))print ("dW = " + str(dW))print ("db = " + str(db) + "\n")dA_prev, dW, db = linear_activation_backward(AL, linear_activation_cache, activation = "relu")print ("relu:")print ("dA_prev = "+ str(dA_prev))print ("dW = " + str(dW))print ("db = " + str(db))

6.3 - L-Model Backward

# GRADED FUNCTION: L_model_backwarddef 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

AL, Y_assess, caches = L_model_backward_test_case()grads = L_model_backward(AL, Y_assess, caches)print_grads(grads)

6.4 - Update Parameters

# GRADED FUNCTION: update_parametersdef 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

parameters, grads = update_parameters_test_case()parameters = update_parameters(parameters, grads, 0.1)print ("W1 = "+ str(parameters["W1"]))print ("b1 = "+ str(parameters["b1"]))print ("W2 = "+ str(parameters["W2"]))print ("b2 = "+ str(parameters["b2"]))

Deep Neural Network for Image Classification: Application

1 - Packages

import timeimport numpy as npimport h5pyimport matplotlib.pyplot as pltimport scipyfrom PIL import Imagefrom scipy import ndimagefrom dnn_app_utils_v2 import *%matplotlib inlineplt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plotsplt.rcParams['image.interpolation'] = 'nearest'plt.rcParams['image.cmap'] = 'gray'%load_ext autoreload%autoreload 2np.random.seed(1)

2 - Dataset

# Example of a pictureindex = 10plt.imshow(train_x_orig[index])print ("y = " + str(train_y[0,index]) + ". It's a " + classes[train_y[0,index]].decode("utf-8") +  " picture.")

3 - Architecture of your model

3.1 - 2-layer neural network

3.2 - L-layer deep neural network

3.3 - General methodology

As usual you will follow the Deep Learning methodology to build the model:
1. Initialize parameters / Define hyperparameters
2. Loop for num_iterations:
a. Forward propagation
b. Compute cost function
c. Backward propagation
d. Update parameters (using parameters, and grads from backprop)
4. Use trained parameters to predict labels

4 - Two-layer neural network

# GRADED FUNCTION: two_layer_modeldef 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

parameters = two_layer_model(train_x, train_y, layers_dims = (n_x, n_h, n_y), num_iterations = 2500, print_cost=True)

5 - L-layer Neural Network

# GRADED FUNCTION: L_layer_modeldef 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