Neural Network (Week 3) : One hidden layer

# ## 1 - Packages ##

# Package imports
import numpy as np
import matplotlib.pyplot as plt
from testCases_v2 import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets

get_ipython().magic('matplotlib inline')
np.random.seed(1)


# ## 2 - Dataset ##
X, Y = load_planar_dataset()
# Visualize the data:
plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);
shape_X = np.shape(X)
shape_Y = np.shape(Y)
m = np.shape(X)[1]  # training set size


# ## 3 - Simple Logistic Regression
# Train the logistic regression classifier
clf = sklearn.linear_model.LogisticRegressionCV();
clf.fit(X.T, Y.T);
plot_decision_boundary(lambda x: clf.predict(x), X, Y)

# 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)")

# ## 4 - Neural Network model
def layer_sizes(X, Y):
    n_x = np.shape(X)[0] # size of input layer
    n_h = 4
    n_y = np.shape(Y)[0] # size of output layer
    return (n_x, n_h, n_y)


# ### 4.2 - Initialize the model's parameters ####
def initialize_parameters(n_x, n_h, n_y):
    np.random.seed(2) 
    
    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


# ### 4.3 - The Loop ####
def forward_propagation(X, parameters):
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]
    
    Z1 = np.dot(W1, X) + b1
    A1 = np.tanh(Z1)
    Z2 = np.dot(W2, A1) + b2
    A2 = sigmoid(Z2)
    
    cache = {"Z1": Z1, "A1": A1, "Z2": Z2, "A2": A2}
    return A2, cache


def compute_cost(A2, Y, parameters):
    m = Y.shape[1] # number of example

    logprobs = np.multiply(Y, np.log(A2)) + np.multiply(1-Y, np.log(1-A2))
    cost = -(1/m)*np.sum(logprobs)
    
    cost = np.squeeze(cost)
    return cost


def backward_propagation(parameters, cache, X, Y):
    m = X.shape[1]
    
    W1 = parameters["W1"]
    W2 = parameters["W2"]
    A1 = cache["A1"]
    A2 = cache["A2"]
    
    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


def update_parameters(parameters, grads, learning_rate = 1.2):
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]
    
    dW1 = grads["dW1"]
    db1 = grads["db1"]
    dW2 = grads["dW2"]
    db2 = grads["db2"]
    
    W1 = W1 - learning_rate * dW1
    b1 = b1 - learning_rate * db1
    W2 = W2 - learning_rate * dW2
    b2 = b2 - learning_rate * db2
    
    parameters = {"W1": W1, "b1": b1, "W2": W2, "b2": b2}
    return parameters


def nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False):
    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)
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]
    
    for i in range(0, num_iterations):
        A2, cache = forward_propagation(X, parameters)
        cost = compute_cost(A2, Y, parameters)
        grads = backward_propagation(parameters, cache, X, Y)

        parameters = update_parameters(parameters, grads)
        return parameters


# ### 4.5 Predictions
def predict(parameters, X):
    A2, cache = forward_propagation(X, parameters)
    predictions = (A2 > 0.5)
    return 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) + '%')


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))