【机器学习】神经网络NeuralNetwork 算法 整理

人工神经网络（Artificial Neural Networks，ANN）是一种应用类似于大脑神经突触联接的结构进行信息处理的数学模型。在这种模型中，大量的节点（或称”神经元”，或”单元”）之间相互联接构成网络，即”神经网络”，以达到处理信息的目的。神经网络通常需要进行训练，训练的过程就是网络进行学习的过程。训练改变了网络节点的连接权的值使其具有分类的功能，经过训练的网络就可用于对象的识别。

目前，神经网络已有上百种不同的模型，常见的有BP网络、径向基RBF网络、Hopfield网络、随机神经网络（Boltzmann机）、竞争神经网络（Hamming网络，自组织映射网络）等。但是当前的神经网络仍普遍存在收敛速度慢、计算量大、训练时间长和不可解释等缺点。

1. 神经网络

这是一个常见的三层神经网络的基本构成，Layer L1是输入层，Layer L2是隐含层，Layer L3是隐含层，当我们输入x1,x2,x3等数据时，通过隐含层的计算、转换，输出你的期望，当你的输入和输出是一样的时候，成为自编码模型(Auto-Encoder),而当你输入和输出是不一致的时候，也就是我们常说的人工神经网络。

import numpy as np

def tanh(x): #双曲函数
    return np.tanh(x)

def tanh_deriv(x): #双曲函数导数
    return 1.0 - np.tanh(x)*np.tanh(x)

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

def logistic_derivative(x): # sigmoid 函数导数
    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): # add weights
            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) #转二维数组
        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])))  
            error = y[i] - a[-1]  #Computer the error at the top layer
			#For output layer, Err calculation (delta is updated error)
            deltas = [error * self.activation_deriv(a[-1])]

            #Start backprobagation 后向算法
            for l in range(len(a) - 2, 0, -1):
                #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

nn = NeuralNetwork([2, 2, 1], 'tanh')
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
print( np.atleast_2d(X))
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))