神经网络解决手写数字识别问题

神经网络是深度学习的基础，其强大的拟合和学习能力，让其在图像识别，人工智能方面表现十分出众，这里不介绍神经网络的原理结构，(这一部分在网上非常多)，这里给出笔者利用纯python写的神经网络代码，实现了对sklearn库中的digits数据集的识别，准确率在93%以上

代码如下，详细见代码注释

import numpy as np
#激活函数tanh
def tanh(x):
    return np.tanh(x)
#tanh的导函数，为反向传播做准备
def tanh_deriv(x):
    return 1-np.tanh(x)*np.tanh(x)
#激活函数逻辑斯底回归函数
def logistic(x):
    return 1/(1+np.exp(-x))
#激活函数logistic导函数
def logistic_deriv(x):
    return logistic(x)*(1-logistic(x))
#神经网络类
class NeuralNetwork:
    def __init__(self,layers,activation='tanh'):
    #根据激活函数不同，设置不同的激活函数和其导函数
        if activation == 'logistic':
            self.activation = logistic
            self.activation_deriv = logistic_deriv
        elif activation == 'tanh':
            self.activation = tanh
            self.activation_deriv = tanh_deriv
       #初始化权重向量，从第一层开始初始化前一层和后一层的权重向量
        self.weights = []
        for i in range(1 , len(layers)-1):
         #权重的shape，是当前层和前一层的节点数目加１组成的元组
            self.weights.append((2*np.random.random((layers[i-1]+1,layers[i]+1))-1)*0.25)
            #权重的shape，是当前层加１和后一层组成的元组
            self.weights.append((2*np.random.random((layers[i]+1,layers[i+1]))-1)*0.25)
    #fit函数对元素进行训练找出合适的权重，X表示输入向量，y表示样本标签，learning_rate表示学习率
    #epochs表示循环训练次数
    def fit(self , X , y , learning_rate=0.2 , epochs=10000):
        X  = np.atleast_2d(X)#保证X是二维矩阵
        temp = np.ones([X.shape[0],X.shape[1]+1])
        temp[:,0:-1] = X
        X = temp #以上三步表示给Ｘ多加一列值为１
        y = np.array(y)#将y转换成np中array的形式
        #进行训练
        for k in range(epochs):
            i = np.random.randint(X.shape[0])#从0-epochs任意挑选一行
            a = [X[i]]#将其转换为list
            #前向传播
            for l in range(len(self.weights)):
                a.append(self.activation(np.dot(a[l],self.weights[l])))
            #计算误差
            error = y[i] - a[-1]
            deltas = [error * self.activation_deriv(a[-1])]
            #反向传播，不包括输出层
            for l in range(len(a)-2,0,-1):
                deltas.append(deltas[-1].dot(self.weights[l].T)*self.activation_deriv(a[l]))
            deltas.reverse()
            #更新权重
            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)
            
    #进行预测
    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

解决异或问题

if __name__ == '__main__':
    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)

解决识别手写数字

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

if __name__ == '__main__':
　　#加载数字数据集
    digits = load_digits()
    X = digits.data
    y = digits.target
    #对Ｘ进行最大最小值缩放
    X = MinMaxScaler().fit_transform(X)
    #生成一个64*100*10的神经网络，激活函数是logistic
    nn = NeuralNetwork([64,100,10],'logistic')
    X_train,X_test,y_train,y_test = train_test_split(X,y)
    #对标签进行标签化
    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))//选择概率最大的下标作为预测结果
    #预测结果
    print predictions
    #混淆矩阵
    print confusion_matrix(y_test,predictions)
    #分类报告
    print classification_report(y_test,predictions)