neural_net_3layer.py

import pandas as pd
import matplotlib.pyplot as plt 
import numpy as np 
import sklearn 
import sklearn.datasets 
import sklearn.linear_model 
import matplotlib 

get_ipython().run_line_magic('matplotlib', 'inline')
matplotlib.rcParams['figure.figsize'] = (10.0, 8.0)

##

def plot_decision_boundary(pred_func): 
    # Set min and max values and give it some padding 
    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5 
    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5 
    h = 0.01 
    # Generate a grid of points with distance h between them 
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) 
    # Predict the function value for the whole gid 
    Z = pred_func(np.c_[xx.ravel(), yy.ravel()]) 
    Z = Z.reshape(xx.shape) 
    # Plot the contour and training examples 
    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral) 
    plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral) 

##

np.random.seed(9)
#X, y = datasets.make_moons(200, noise=0.10)
X, y = datasets.make_moons(250, noise=0.2)
plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral);

##

clf = linear_model.LogisticRegressionCV()
clf.fit(X, y)

plot_decision_boundary(lambda x: clf.predict(x))
plt.title("Logistic Regression")


# # ---------------------------------------------------------

# # FUNCTIONS TO TRAIN MODEL

# In[45]:


num_examples = len(X)
nn_input_dim = 2
nn_output_dim = 2

epsilon = 0.01
reg_lambda = 0.01

def calculate_loss(model):
    W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
    # Forward propagation to calculate our predictions
    z1 = X.dot(W1) + b1
    a1 = np.tanh(z1)
    z2 = a1.dot(W2) + b2
    exp_scores = np.exp(z2)
    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
    # Calculating the loss
    corect_logprobs = -np.log(probs[range(num_examples), y])
    data_loss = np.sum(corect_logprobs)
    # Add regulatization term to loss (optional)
    data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))
    return 1./num_examples * data_loss

def predict(model, x):
    W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
    # Forward propagation
    z1 = x.dot(W1) + b1
    a1 = np.tanh(z1)
    z2 = a1.dot(W2) + b2
    exp_scores = np.exp(z2)
    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
    return np.argmax(probs, axis=1)

##

def build_model(nn_hdim, num_passes=20000, print_loss=False):
    
    np.random.seed(0)
    W1 = np.random.randn(nn_input_dim, nn_hdim) / np.sqrt(nn_input_dim)
    b1 = np.zeros((1, nn_hdim))
    W2 = np.random.randn(nn_hdim, nn_output_dim) / np.sqrt(nn_hdim)
    b2 = np.zeros((1, nn_output_dim))
    
    model = {}
    
    for i in range(0, num_passes):
        z1 = X.dot(W1) + b1
        a1 = np.tanh(z1)
        z2 = a1.dot(W2) + b2
        exp_scores = np.exp(z2)
        probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
        
        delta3 = probs
        delta3[range(num_examples), y] -= 1
        dW2 = (a1.T).dot(delta3) 
        db2 = np.sum(delta3, axis=0, keepdims=True) 
        
        delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))
        dW1 = np.dot(X.T, delta2)
        db1 = np.sum(delta2, axis=0)
 
        dW2 += reg_lambda * W2
        dW1 += reg_lambda * W1
 
        W1 += -epsilon * dW1
        b1 += -epsilon * db1
        W2 += -epsilon * dW2
        b2 += -epsilon * db2
        
        model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}
        
        if print_loss and i % 1000 == 0:
          print("Loss after iteration %i: %f" %(i, calculate_loss(model)))
    
    return model


# # BUILDING THE MODEL

# In[46]:


model = build_model(5, num_passes=30000, print_loss=True)

plot_decision_boundary(lambda x: predict(model, x))
plt.title("Decision Boundary for Hidden Layer (size: 3)")