神经网络（Neural Network）

#!/usr/bin/env python
# -*- coding: utf-8 -*-
import numpy as np#矩阵运算

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

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

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

def logistic_derivative(x):#对s函数求导
    return logistic(x)*(1-logistic(x))

class NeuralNetwork:#面向对象定义一个神经网络类
    def __init__(self, layers, activation=‘tanh‘):#下划线构造函数self 相当于本身这个类的指针 layer就是一个list 数字代表神经元个数
        """
        :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#之前定义的s函数
            self.activation_deriv = logistic_derivative#求导函数
        elif activation == ‘tanh‘:
            self.activation = tanh#双曲线函数
            self.activation_deriv = tanh_deriv#求导双曲线函数

        self.weights = []#初始化一个list作为   权重
        #初始化权重两个值之间随机初始化
        for i in range(1, len(layers) - 1):#有几层神经网络 除去输出层
            #i-1层 和i层之间的权重 随机生成layers[i - 1] + 1 *  layers[i] + 1 的矩阵 -0.25-0.25
            self.weights.append((2*np.random.random((layers[i - 1] + 1, layers[i] + 1))-1)*0.25)
            #i层和i+1层之间的权重
            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):#训练神经网络
        #learning rate
        X = np.atleast_2d(X)#x至少2维
        temp = np.ones([X.shape[0], X.shape[1]+1])#初始化一个全为1的矩阵
        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])#随机选行
            a = [X[i]]

            for l in range(len(self.weights)):  #going forward network, for each layer
                #选择一条实例与权重点乘 并且将值传给激活函数，经过a的append 使得所有神经元都有了值（正向）
                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 真实值与计算值的差（向量）
            #通过求导 得到权重应当调整的误差
            deltas = [error * self.activation_deriv(a[-1])] #For output layer, Err calculation (delta is updated error)

            #Staring backprobagation 更新weight
            for l in range(len(a) - 2, 0, -1): # we need to begin at the second to last layer 每次减一
                #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

　异或运算　

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))

([0, 0], array([-0.00475208]))
([0, 1], array([ 0.99828477]))
([1, 0], array([ 0.99827186]))
([1, 1], array([-0.00776711]))　　

　手写体识别

#!/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.model_selection 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)

confusion_matrix

precision    recall  f1-score   support

          0       1.00      0.97      0.99        34
          1       0.75      0.91      0.82        46
          2       1.00      0.92      0.96        50
          3       1.00      0.92      0.96        51
          4       0.94      0.91      0.92        53
          5       0.95      0.96      0.96        57
          6       0.97      0.95      0.96        38
          7       0.88      1.00      0.93        35
          8       0.88      0.83      0.85        42
          9       0.86      0.82      0.84        44

avg / total       0.92      0.92      0.92       450