How to use python artificial intelligence algorithm artificial neural network

Artificial Neural Network

(Artificial Neural Network, ANN) is a mathematical model that imitates the structure and function of biological neural networks. Its purpose is to be able to process unknown input data through learning and training. Carry out complex non-linear mapping relationships to achieve adaptive intelligent decision-making. It can be said that ANN is the most basic and core algorithm among artificial intelligence algorithms.

The basic structure of the ANN model includes input layer, hidden layer and output layer. The input layer receives input data, the hidden layer is responsible for multi-level, high-dimensional transformation and processing of data, and the output layer outputs the processed data. The training process of ANN is to continuously adjust the weights of each layer in the neural network through multiple iterations, so that the neural network can correctly predict and classify the input data.

Artificial Neural Network Algorithm Example

Next look at a simple artificial neural network algorithm example:

import numpy as np
class NeuralNetwork():
    def __init__(self, layers):
        """
        layers: 数组，包含每个层的神经元数量，例如 [2, 3, 1] 表示 3 层神经网络，第一层 2 个神经元，第二层 3 个神经元，第三层 1 个神经元。
        weights: 数组，包含每个连接的权重矩阵，默认值随机生成。
        biases: 数组，包含每个层的偏差值，默认值为 0。
        """
        self.layers = layers
        self.weights = [np.random.randn(a, b) for a, b in zip(layers[1:], layers[:-1])]
        self.biases = [np.zeros((a, 1)) for a in layers[1:]]
    def sigmoid(self, z):
        """Sigmoid 激活函数."""
        return 1 / (1 + np.exp(-z))
    def forward_propagation(self, a):
        """前向传播."""
        for w, b in zip(self.weights, self.biases):
            z = np.dot(w, a) + b
            a = self.sigmoid(z)
        return a
    def backward_propagation(self, x, y):
        """反向传播."""
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        a = x
        activations = [x]
        zs = []
        for w, b in zip(self.weights, self.biases):
            z = np.dot(w, a) + b
            zs.append(z)
            a = self.sigmoid(z)
            activations.append(a)
        delta = self.cost_derivative(activations[-1], y) * self.sigmoid_prime(zs[-1])
        nabla_b[-1] = delta
        nabla_w[-1] = np.dot(delta, activations[-2].transpose())
        for l in range(2, len(self.layers)):
            z = zs[-l]
            sp = self.sigmoid_prime(z)
            delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
            nabla_b[-l] = delta
            nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
        return (nabla_w, nabla_b)
    def train(self, x_train, y_train, epochs, learning_rate):
        """训练网络."""
        for epoch in range(epochs):
            nabla_w = [np.zeros(w.shape) for w in self.weights]
            nabla_b = [np.zeros(b.shape) for b in self.biases]
            for x, y in zip(x_train, y_train):
                delta_nabla_w, delta_nabla_b = self.backward_propagation(np.array([x]).transpose(), np.array([y]).transpose())
                nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
                nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
            self.weights = [w-(learning_rate/len(x_train))*nw for w, nw in zip(self.weights, nabla_w)]
            self.biases = [b-(learning_rate/len(x_train))*nb for b, nb in zip(self.biases, nabla_b)]
    def predict(self, x_test):
        """预测."""
        y_predictions = []
        for x in x_test:
            y_predictions.append(self.forward_propagation(np.array([x]).transpose())[0][0])
        return y_predictions
    def cost_derivative(self, output_activations, y):
        """损失函数的导数."""
        return output_activations - y
    def sigmoid_prime(self, z):
        """Sigmoid 函数的导数."""
        return self.sigmoid(z) * (1 - self.sigmoid(z))

Use the following code example to instantiate and use this simple neural network algorithm Network class:

x_train = [[0, 0], [1, 0], [0, 1], [1, 1]]
y_train = [0, 1, 1, 0]
# 创建神经网络
nn = NeuralNetwork([2, 3, 1])
# 训练神经网络
nn.train(x_train, y_train, 10000, 0.1)
# 测试神经网络
x_test = [[0, 0], [1, 0], [0, 1], [1, 1]]
y_test = [0, 1, 1, 0]
y_predictions = nn.predict(x_test)
print("Predictions:", y_predictions)
print("Actual:", y_test)

Output results:

Predictions: [0.011602156431658403, 0.9852717774725432, 0.9839448924887225, 0.020026540429992387]
Actual: [0, 1, 1, 0]

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