神经网络算法应用举例【Python实现】

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 npdef 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 NeuralNetworkimport numpy as npnn = 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8x8 

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：0,1,2,3,4,5,6,7,8,9import numpy as npfrom sklearn.datasets import load_digitsfrom sklearn.metrics import confusion_matrix, classification_reportfrom sklearn.preprocessing import LabelBinarizerfrom NeuralNetwork import NeuralNetworkfrom sklearn.cross_validation import train_test_splitdigits = load_digits()X = digits.datay = digits.targetX -= X.min()  # normalize the values to bring them into the range 0-1X /= 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：