算法主体

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
                #Computer the node value for each layer (O_i) using activation function
                a.append(self.activation(np.dot(a[l], self.weights[l])))  
            
            #Computer the error at the top layer
            error = y[i] - a[-1]  

            #For output layer, Err calculation (delta is updated error)
            deltas = [error * self.activation_deriv(a[-1])] 
            
            #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

简单测试

简单非线性关系数据集测试(XOR):

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] [ 0.00012519]
[0, 1] [ 0.99843015]
[1, 0] [ 0.99831681]
[1, 1] [ 0.00482466]

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

from sklearn.datasets import load_digits 
from sklearn.metrics import confusion_matrix, classification_report 
from sklearn.preprocessing import LabelBinarizer 
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))

start fitting
[[44  0  0  0  0  0  0  0  0  0]
    [ 0 41  0  0  0  1  1  0  0  3]
    [ 0  2 41  0  0  0  0  0  0  0]
    [ 0  0  1 35  0  3  0  2  1  1]
    [ 0  0  0  0 44  0  0  0  0  0]
    [ 1  0  0  0  0 36  0  0  0  0]
    [ 0  0  0  0  0  0 46  0  0  0]
    [ 0  0  0  0  1  0  0 48  1  0]
    [ 0  6  0  0  0  1  0  0 38  0]
    [ 0  1  0  1  1  1  0  0  5 43]]
                precision    recall  f1-score   support

            0       0.98      1.00      0.99        44
            1       0.82      0.89      0.85        46
            2       0.98      0.95      0.96        43
            3       0.97      0.81      0.89        43
            4       0.96      1.00      0.98        44
            5       0.86      0.97      0.91        37
            6       0.98      1.00      0.99        46
            7       0.96      0.96      0.96        50
            8       0.84      0.84      0.84        45
            9       0.91      0.83      0.87        52

avg / total       0.93      0.92      0.92       450