用python实现一个神经网络

原文：http://www.wildml.com/2015/09/implementing-a-neural-network-from-scratch/

体验一下神经网络

# -*- coding: utf-8 -*-
"""
Created on Fri Jul  7 15:37:41 2017

@author: bryan
"""

import numpy as np
from matplotlib import pyplot as plt
import sklearn

np.random.seed(0)
X, y = sklearn.datasets.make_moons(200, noise=0.20)

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

#Gradient descent parameters
eta=0.01
reg_lambda=0.01

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)

def calculate_loss(model):
    W1,b1,W2,b2=model['W1'],model['b1'],model['W2'],model['b2']
    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)
    corect_logprobs=-np.log(probs[range(num_examples),y])
    data_loss = np.sum(corect_logprobs)
    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']
    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=True):
    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={}
    # Gradient descent. For each batch...
    for i in range(0,num_passes):
        # 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)
        
        # Backpropagation
        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)
        
        # Add regularization terms (b1 and b2 don't have regularization terms)
        dW2+=reg_lambda*W2
        dW1+=reg_lambda*W1
        
        # Gradient descent parameter update
        W1+=-eta*dW1
        b1+=-eta*db1
        W2+=-eta*dW2
        b2+=-eta*db2
        
        model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}
        
        # Optionally print the loss.
        # This is expensive because it uses the whole dataset, so we don't want to do it too often.
        if print_loss and i % 1000 == 0:
            print( "%i hidden_layers' Loss after iteration %i: %f" %(nn_hdim,i, calculate_loss(model)))
    return model
 
# Build a model with a 3-dimensional hidden layer
#model = build_model(3, print_loss=True)
 # Plot the decision boundary
#plot_decision_boundary(lambda x: predict(model, x))
#plt.title("Decision Boundary for hidden layer size 3")
plt.figure(figsize=(16, 32))
hidden_layer_dimensions = [1, 2, 3, 4, 5, 20, 50]
for i, nn_hdim in enumerate(hidden_layer_dimensions):
    plt.subplot(5, 2, i+1)
    plt.title('Hidden Layer size %d' % nn_hdim)
    model = build_model(nn_hdim)
    plot_decision_boundary(lambda x: predict(model, x))
plt.show()