dnn_app_utils.py

# Deep neural network utilities based on 'Neural Networks and Deep Learning'
# class assignments taught by Andrew Ng from deeplearning.ai
# https://www.coursera.org/learn/neural-networks-deep-learning
#
# Extended by Johann Steinbrecher (@hansman) to support one vs
# all classification. This file implements paramter initialization,
# forward propagation, cost computation, backward propagation, paramters
# update and class prediction.


import numpy as np
import json
from pprint import pprint


def sigmoid(Z):
    '''
    Implements the sigmoid activation in numpy

    Arguments:
    Z -- numpy array of any shape

    Returns:
    A -- output of sigmoid(z), same shape as Z
    cache -- returns Z as well, useful during backpropagation
    '''

    A = 1/(1+np.exp(-Z))
    cache = Z

    return A, cache

def relu(Z):
    '''
    Implement the RELU function.

    Arguments:
    Z -- Output of the linear layer, of any shape

    Returns:
    A -- Post-activation parameter, of the same shape as Z
    cache -- a python dictionary containing 'A' ; stored for computing the backward pass efficiently
    '''

    A = np.maximum(0,Z)

    assert(A.shape == Z.shape)

    cache = Z
    return A, cache


def relu_backward(dA, cache):
    '''
    Implement the backward propagation for a single RELU unit.

    Arguments:
    dA -- post-activation gradient, of any shape
    cache -- 'Z' where we store for computing backward propagation efficiently

    Returns:
    dZ -- Gradient of the cost with respect to Z
    '''

    Z = cache
    dZ = np.array(dA, copy=True) # just converting dz to a correct object.

    # When z <= 0, you should set dz to 0 as well.
    dZ[Z <= 0] = 0

    assert (dZ.shape == Z.shape)

    return dZ

def sigmoid_backward(dA, cache):
    '''
    Implement the backward propagation for a single SIGMOID unit.

    Arguments:
    dA -- post-activation gradient, of any shape
    cache -- 'Z' where we store for computing backward propagation efficiently

    Returns:
    dZ -- Gradient of the cost with respect to Z
    '''

    Z = cache

    s = 1/(1+np.exp(-Z))
    dZ = dA * s * (1-s)

    assert (dZ.shape == Z.shape)

    return dZ


def load_data(mepId):

    with open('./samples/' + str(mepId) + '.json') as data_file:
        examples = json.load(data_file)

        samples = examples['samples']
        labels = examples['labels']

        assert(len(samples) == len(labels))

        trainSize = int(len(labels) * 0.7)

        train_y = np.array(labels[:trainSize]).T
        # train_y = np.array(examples['train_y']).T
        test_y = np.array(labels[trainSize:]).T
        # test_y = np.array(examples['test_y']).T

        train_x = np.array(samples[:trainSize])
        # train_x = np.array(examples['train_x'])
        test_x = np.array(samples[trainSize:])
        # test_x = np.array(examples['test_x'])

    return train_x, train_y, test_x, test_y




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:
    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)

    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))

    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


def 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(1)
    parameters = {}
    L = len(layer_dims)            # number of layers in the network

    for l in range(1, L):
        parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l-1]) / np.sqrt(layer_dims[l-1]) #*0.01
        parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))

        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

def 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
    '''
    # print ('A shape: ' + str(A.shape))
    # print ('W shape: ' + str(W.shape))
    # print ('b shape: ' + str(b.shape))
    Z = W.dot(A) + b

    assert(Z.shape == (W.shape[0], A.shape[1]))
    cache = (A, W, b)

    return Z, cache

def 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'.
        Z, linear_cache = linear_forward(A_prev, W, b)
        A, activation_cache = sigmoid(Z)

    elif activation == 'relu':
        # Inputs: 'A_prev, W, b'. Outputs: 'A, activation_cache'.
        Z, linear_cache = linear_forward(A_prev, W, b)
        A, activation_cache = relu(Z)

    assert (A.shape == (W.shape[0], A_prev.shape[1]))
    cache = (linear_cache, activation_cache)

    return A, cache

def 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
        A, cache = linear_activation_forward(A_prev, parameters['W' + str(l)], parameters['b' + str(l)], activation = 'relu')
        caches.append(cache)

    # Implement LINEAR -> SIGMOID. Add 'cache' to the 'caches' list.
    AL, cache = linear_activation_forward(A, parameters['W' + str(L)], parameters['b' + str(L)], activation = 'sigmoid')
    caches.append(cache)

    # print ('AL shape: ' + str(AL.shape))

    assert(AL.shape == (1,X.shape[1]))

    return AL, caches

def compute_cost(AL, Y):
    # print ('compute_cost Y shape: ' + str(Y.shape))
    '''
    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[0]

    # Compute loss from aL and y.
    cost = (1./m) * (-np.dot(Y,np.log(AL).T) - np.dot(1-Y, np.log(1-AL).T))

    cost = np.squeeze(cost)      # To make sure your cost's shape is what we expect (e.g. this turns [[17]] into 17).
    return np.asscalar(cost)

def 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]

    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)

    assert (dA_prev.shape == A_prev.shape)
    assert (dW.shape == W.shape)
    assert (db.shape == b.shape)

    return dA_prev, dW, db

def 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':
        dZ = relu_backward(dA, activation_cache)
        dA_prev, dW, db = linear_backward(dZ, linear_cache)

    elif activation == 'sigmoid':
        dZ = sigmoid_backward(dA, activation_cache)
        dA_prev, dW, db = linear_backward(dZ, linear_cache)

    return dA_prev, dW, db

def 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' (there are (L-1) or them, indexes from 0 to L-2)
                the cache of linear_activation_forward() with 'sigmoid' (there is one, index 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
    dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))

    # Lth layer (SIGMOID -> LINEAR) gradients. Inputs: 'AL, Y, caches'. Outputs: 'grads['dAL'], grads['dWL'], grads['dbL']
    current_cache = caches[L-1]
    grads['dA' + str(L)], grads['dW' + str(L)], grads['db' + str(L)] = linear_activation_backward(dAL, current_cache, activation = 'sigmoid')

    for l in reversed(range(L-1)):
        # lth layer: (RELU -> LINEAR) gradients.
        current_cache = caches[l]
        dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads['dA' + str(l + 2)], current_cache, activation = 'relu')
        grads['dA' + str(l + 1)] = dA_prev_temp
        grads['dW' + str(l + 1)] = dW_temp
        grads['db' + str(l + 1)] = db_temp

    return grads

def 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.
    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)]

    return parameters

def predict(X, y, parameters, K):
    '''
    This function is used to predict the results of a  L-layer neural network.

    Arguments:
    X -- data set of examples you would like to label
    parameters -- parameters of the trained model

    Returns:
    p -- predictions for the given dataset X
    '''
    m = X.shape[1]

    probas = np.zeros([3, m])

    for k in range(0, K):

        n = len(parameters[k]) // 2 # number of layers in the neural network
        p = np.zeros((1, m),dtype=int)

        # Forward propagation
        p, caches = L_model_forward(X, parameters[k])

        probas[k,:] = p[0,:]


    score = 0
    for i in range(0, m):
        k = np.argmax(probas[:,i])
        if y[k,i] == 1:
            score+=1

    # print('Accuracy: %s' % str(score/float(m)))
    return p

def print_mislabeled_images(classes, X, y, p):
    '''
    Plots images where predictions and truth were different.
    X -- dataset
    y -- true labels
    p -- predictions
    '''
    a = p + y
    mislabeled_indices = np.asarray(np.where(a == 1))
    plt.rcParams['figure.figsize'] = (40.0, 40.0) # set default size of plots
    num_images = len(mislabeled_indices[0])
    for i in range(num_images):
        index = mislabeled_indices[1][i]

        plt.subplot(2, num_images, i + 1)
        plt.imshow(X[:,index].reshape(64,64,3), interpolation='nearest')
        plt.axis('off')
        plt.title('Prediction: ' + classes[int(p[0,index])].decode('utf-8') + ' \n Class: ' + classes[y[0,index]].decode('utf-8'))