(2)逻辑函数,本文上面用的就是逻辑函数
五、BP神经网络的python实现
需要先导入numpy模块
import numpy as np
定义非线性转化函数,由于还需要用到给函数的导数形式,因此一起定义
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))
设计BP神经网络的形式(几层,每层多少单元个数),用到了面向对象,主要是选择哪种非线性函数,以及初始化权重。layers是一个list,里面包含每一层的单元个数。
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)
实现算法
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 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)): a.append(self.activation(np.dot(a[l], self.weights[l]))) error = y[i] - a[-1] deltas = [error * self.activation_deriv(a[-1])] 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)
实现预测
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
我们给出一组数进行预测,我们上面的程序文件保存名称为BP
from BP 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([1,0,0,1]) nn.fit(x,y,0.1,10000) for i in [[0,0], [0,1], [1,0], [1,1]]: print(i, nn.predict(i))
结果如下:
([0, 0], array([ 0.99738862])) ([0, 1], array([ 0.00091329])) ([1, 0], array([ 0.00086846])) ([1, 1], array([ 0.99751259]))
相关推荐:
Python中关于numpy灵活定义神经网络结构的实例
Python中递归神经网络实现的简单示例分享
JavaScript 实现简单的神经网络算法图文详解
以上就是详解神经网络理论基础及Python实现方法的详细内容,更多请关注Gxl网其它相关文章!
查看更多关于详解神经网络理论基础及Python实现方法的详细内容...
声明:本文来自网络,不代表【好得很程序员自学网】立场,转载请注明出处:http://haodehen.cn/did81684