神经网络算法应用举例子

理论参加上一篇博客。

1. 关于非线性转化方程(non-linear transformation function)
sigmoid函数(S 曲线)用来作为activation function:
     1.1 双曲函数(tanh)
   
     1.2  逻辑函数(logistic function)
2. 实现一个简单的神经网络算法

import numpy as np


def tanh(x):
    return np.tanh(x)


def tanh_deriv(x):
    return 1.0 - np.tanh(x)*np.tanh(x)


def logistic(x):
    return 1/(1 + np.exp(-x))


def logistic_derivative(x):
    return logistic(x)*(1-logistic(x))


class NeuralNetwork:
    def __init__(self, layers, activation='tanh'):
        """
        :param layers: A list containing the number of units in each layer.
        Should be at least two values
        :param activation: The activation function to be used. Can be
        "logistic" or "tanh"
        """
        if activation == 'logistic':
            self.activation = logistic
            self.activation_deriv = logistic_derivative
        elif activation == 'tanh':
            self.activation = tanh
            self.activation_deriv = tanh_deriv

        self.weights = []
        for i in range(1, len(layers) - 1):
            self.weights.append((2*np.random.random((layers[i - 1] + 1, layers[i] + 1))-1)*0.25)
            self.weights.append((2*np.random.random((layers[i] + 1, layers[i + 1]))-1)*0.25)

    def fit(self, X, y, learning_rate=0.2, epochs=10000):
        X = np.atleast_2d(X)
        temp = np.ones([X.shape[0], X.shape[1]+1])
        temp[:, 0:-1] = X  # adding the bias unit to the input layer
        X = temp
        y = np.array(y)

        for k in range(epochs):
            i = np.random.randint(X.shape[0])
            a = [X[i]]

            for l in range(len(self.weights)):  #going forward network, for each layer
                a.append(self.activation(np.dot(a[l], self.weights[l])))  #Computer the node value for each layer (O_i) using activation function
            error = y[i] - a[-1]  #Computer the error at the top layer
            deltas = [error * self.activation_deriv(a[-1])] #For output layer, Err calculation (delta is updated error)

            #Staring backprobagation
            for l in range(len(a) - 2, 0, -1): # we need to begin at the second to last layer
                #Compute the updated error (i,e, deltas) for each node going from top layer to input layer

                deltas.append(deltas[-1].dot(self.weights[l].T)*self.activation_deriv(a[l]))
            deltas.reverse()
            for i in range(len(self.weights)):
                layer = np.atleast_2d(a[i])
                delta = np.atleast_2d(deltas[i])
                self.weights[i] += learning_rate * layer.T.dot(delta)

    def predict(self, x):
        x = np.array(x)
        temp = np.ones(x.shape[0]+1)
        temp[0:-1] = x
        a = temp
        for l in range(0, len(self.weights)):
            a = self.activation(np.dot(a, self.weights[l]))
        return a

3.应用

3.1   简单非线性关系数据集测试(XOR):

X:                  Y 0 0                 0 0 1                 1 1 0                 1 1 1                 0
代码：

from NeuralNetwork import NeuralNetwork
import numpy as np

nn = NeuralNetwork([2, 2, 1], 'tanh')
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([0, 1, 1, 0])
nn.fit(X, y)
for i in [[0, 0], [0, 1], [1, 0], [1, 1]]:
    print(i, nn.predict(i))

运行截图：

3.2 

 手写数字识别：
每个图片8×8 
识别数字：0,1,2,3,4,5,6,7,8,9
代码：

#!/usr/bin/python
# -*- coding:utf-8 -*-

# 每个图片8x8  识别数字：0,1,2,3,4,5,6,7,8,9

import numpy as np
from sklearn.datasets import load_digits
from sklearn.metrics import confusion_matrix, classification_report
from sklearn.preprocessing import LabelBinarizer
from NeuralNetwork import NeuralNetwork
from sklearn.cross_validation import train_test_split


digits = load_digits()
X = digits.data
y = digits.target
X -= X.min()  # normalize the values to bring them into the range 0-1
X /= X.max()

nn = NeuralNetwork([64, 100, 10], 'logistic')
X_train, X_test, y_train, y_test = train_test_split(X, y)
labels_train = LabelBinarizer().fit_transform(y_train)
labels_test = LabelBinarizer().fit_transform(y_test)
print ("start fitting")
nn.fit(X_train, labels_train, epochs=3000)
predictions = []
for i in range(X_test.shape[0]):
    o = nn.predict(X_test[i])
    predictions.append(np.argmax(o))
print (confusion_matrix(y_test, predictions))
print (classification_report(y_test, predictions))

运行截图：