Python写一个简单的神经网络

简单的神经网络算法，包括基本的后向传播BP算法，前向传播算法，更新权重使用的梯度下降算法，基本的框架算是有了，学习使用。

注意输入每一行数据时候在神经网络中会加入bias偏量，神经网络的层数和每层个数为自定义，搞了很久才知道输入矩阵多了一个维度，权重和后向传播更新的delta都是每列神经元之间的关系，关于s形函数暂时用了两种，分别是logistic() 和 tanh() 效果差不多，简单的模型作为笔记学习使用。下面附上代码。

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'):
        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[-2] + 1, layers[-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])))
            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])]
            # Staring backprobagation
            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()
            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, 3, 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))