single_layer_network.py

# Package imports
import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
import sklearn.linear_model
from common import *

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
    """
    n_x = X.shape[0]
    n_h = 4
    n_y = Y.shape[0]
    
    return (n_x, n_h, n_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:
    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)
    """    
    #(≈ 4 lines of code)
    # W1 = ...
    # b1 = ...
    # W2 = ...
    # b2 = ...
    # YOUR CODE STARTS HERE
    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))
    

    parameters = {"W1": W1,
                  "b1": b1,
                  "W2": W2,
                  "b2": b2}
    
    return parameters

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"

    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]
       
    # Implement Forward Propagation to calculate A2 (probabilities)

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

def compute_cost(A2, Y):
    """
    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)

    Returns:
    cost -- cross-entropy cost given equation (13)
    
    """
    
    m = Y.shape[1] # number of examples

    # Compute the cross-entropy cost
    # (≈ 2 lines of code)
    # logprobs = ...
    # cost = ...
    # YOUR CODE STARTS HERE
    logprobs = np.multiply(Y ,np.log(A2)) + np.multiply((1-Y), np.log(1-A2))
    cost = (-1/m) * np.sum(logprobs)
    
    
    
    cost = float(np.squeeze(cost))  # makes sure cost is the dimension we expect. 
                                    # E.g., turns [[17]] into 17 
    
    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".
    W1 = parameters["W1"]
    W2 = parameters["W2"]
    
        
    # Retrieve also A1 and A2 from dictionary "cache".
    A1 = cache["A1"]
    A2 = cache["A2"]
      
    # Backward propagation: calculate dW1, db1, dW2, db2. 

    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))
    
    
    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 a copy of each parameter from the dictionary "parameters". Use copy.deepcopy(...) for W1 and W2

    W1 = parameters["W1"]
    W2 = parameters["W2"]
    b1 = parameters["b1"]
    b2 = parameters["b2"]
      
    # Retrieve each gradient from the dictionary "grads"
    
    dW1  = grads["dW1"]
    dW2  = grads["dW2"]
    db1  = grads["db1"]
    db2  = grads["db2"]
    
    W1 = W1 - learning_rate*dW1
    W2 = W2 - learning_rate*dW2
    b1 = b1 - learning_rate*db1
    b2 = b2 - learning_rate*db2
     
    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]
    
    parameters = initialize_parameters(n_x, n_h, n_y)

    
    # Loop (gradient descent)

    for i in range(0, num_iterations):
         
        A2,cache = forward_propagation(X,parameters)
        cost = compute_cost(A2,Y)
        grads = backward_propagation(parameters,cache,X,Y)
        parameters = update_parameters(parameters,grads)

        # 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.

    A2, cache = forward_propagation(X, parameters)
    predictions = (A2 > 0.5)
      
    return predictions

X, Y = load_planar_dataset()
plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral)
m = X.shape[1]
shape_X = X.shape
shape_Y = Y.shape



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")

# 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)")


# 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, 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))

# 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}

# dataset = "noisy_moons"

# 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)