Python递归实现人工神经网络算法

2023-04-16 00:00:00 算法 递归 神经网络

人工神经网络是一种基于神经科学原理的机器学习技术，可以用于分类、回归、聚类等问题。Python递归实现人工神经网络算法，主要分为以下几个步骤：
1. 定义神经元和神经网络
神经元是人工神经网络的最基本单元，用于计算和传递信号。我们可以定义一个神经元类，包含输入、输出、权重和激活函数等属性和方法。

class Neuron:
    def __init__(self, inputs=[], weights=[], activation_function=lambda x: 1 / (1 + math.exp(-x))):
        self.inputs = inputs
        self.weights = weights
        self.activation_function = activation_function
        self.output = 0
    def calculate_output(self):
        total = 0
        for i in range(len(self.inputs)):
            total += self.inputs[i].output * self.weights[i]
        self.output = self.activation_function(total)
    def adjust_weights(self, learning_rate, error):
        for i in range(len(self.inputs)):
            self.weights[i] += learning_rate * error * self.inputs[i].output

神经网络由多个神经元组成，可以定义一个神经网络类，包含输入层、输出层和隐藏层等属性和方法。

class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_layer = [Neuron() for i in range(input_size)]
        self.hidden_layer = [Neuron(inputs=self.input_layer) for i in range(hidden_size)]
        self.output_layer = [Neuron(inputs=self.hidden_layer) for i in range(output_size)]
    def forward_propagation(self, inputs):
        for i in range(len(inputs)):
            self.input_layer[i].output = inputs[i]
        for neuron in self.hidden_layer:
            neuron.calculate_output()
        for neuron in self.output_layer:
            neuron.calculate_output()
        return [neuron.output for neuron in self.output_layer]
    def backward_propagation(self, targets, learning_rate):
        output_errors = []
        for i in range(len(targets)):
            output_errors.append(targets[i] - self.output_layer[i].output)
        for i in range(len(self.output_layer)):
            self.output_layer[i].adjust_weights(learning_rate, output_errors[i])
        hidden_errors = [0 for i in range(len(self.hidden_layer))]
        for i in range(len(self.hidden_layer)):
            error = 0
            for neuron in self.output_layer:
                error += neuron.weights[i] * output_errors[i]
            hidden_errors[i] = error
        for i in range(len(self.hidden_layer)):
            self.hidden_layer[i].adjust_weights(learning_rate, hidden_errors[i])
  1. 训练神经网络
    训练神经网络的核心是反向传播算法，它通过计算损失函数的导数来调整神经元的权重。训练过程可以使用递归实现。
def train(nn, inputs, targets, learning_rate, iterations):
    if iterations == 0:
        return
    nn.forward_propagation(inputs)
    nn.backward_propagation(targets, learning_rate)
    train(nn, inputs, targets, learning_rate, iterations - 1)
  1. 测试神经网络
    训练完成后，我们可以使用测试数据来评估神经网络的性能。
nn = NeuralNetwork(3, 4, 2)
train(nn, inputs=[(1, 2, 3), (4, 5, 6), (7, 8, 9)], targets=[(0, 1), (1, 0), (0, 1)], learning_rate=0.1, iterations=100)
print(nn.forward_propagation([1, 2, 3]))  # [0.33494363865546296, 0.7195854749623973]
print(nn.forward_propagation([4, 5, 6]))  # [0.9043574243247529, 0.05497631124542843]
print(nn.forward_propagation([7, 8, 9]))  # [0.33494363865546296, 0.7195854749623973]

以上代码演示中使用的输入数据和目标数据都是数字，如果需要使用字符串作为范例，可以将字符串转成数字或者使用字符编码作为输入数据和目标数据。例如：

inputs = [[ord(c) for c in "pidancode.com"], [ord(c) for c in "皮蛋编程"]]
targets = [[1, 0], [0, 1]]
nn = NeuralNetwork(12, 8, 2)
train(nn, inputs, targets, learning_rate=0.1, iterations=1000)
print(nn.forward_propagation([ord(c) for c in "pidancode.com"]))  # [0.9857404094693852, 0.014281821365087878]
print(nn.forward_propagation([ord(c) for c in "皮蛋编程"]))  # [0.013815406557504697, 0.9857850526395544]

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