How to write neural network algorithms using PHP

How to use PHP to write neural network algorithms

Neural network is an algorithm that simulates the structure and working principle of the human brain's neural network. It achieves functions such as pattern recognition, prediction, and decision-making through training and learning. It is widely used in fields such as machine learning, artificial intelligence, and data analysis. This article will introduce how to write neural network algorithms using PHP and provide code examples.

1. Basic knowledge of neural networks

Before introducing how to write neural network algorithms, let’s first understand some basic knowledge of neural networks.

1. Basic components of neural network:
   Neural network is composed of neurons and connection weights. Neurons receive input signals and pass these signals to the next layer of neurons or output layer through connection weights.
2. Hierarchical structure of neural network:
   Neural network usually consists of input layer, hidden layer and output layer. The input layer receives external input data, the hidden layer is used to process and transform the input data, and the output layer outputs prediction results.
3. Activation function:
   Activation function is used to convert the input of a neuron into an output. Commonly used activation functions include Sigmoid function, ReLU function, etc.
4. Back propagation algorithm:
   The back propagation algorithm is the main algorithm for training neural networks. It optimizes the prediction ability of the network by calculating the error of neurons and adjusting the connection weights.

2. Use PHP to write neural network algorithms

Let’s start using PHP to write neural network algorithms.

1. Define Neural Network Class
   First, we need to define a neural network class, which is used to create neural network objects and define the structure and parameters of the network. The following is a sample code of a simple neural network class:

class NeuralNetwork {
    private $input_nodes;  // 输入节点数
    private $hidden_nodes; // 隐藏层节点数
    private $output_nodes; // 输出节点数
    private $learning_rate; // 学习率
    private $weights_ih; // 输入层到隐藏层的连接权重
    private $weights_ho; // 隐藏层到输出层的连接权重
    private $bias_h; // 隐藏层的偏置
    private $bias_o; // 输出层的偏置

    // 初始化神经网络类
    public function __construct($input_nodes, $hidden_nodes, $output_nodes, $learning_rate) {
        $this->input_nodes = $input_nodes;
        $this->hidden_nodes = $hidden_nodes;
        $this->output_nodes = $output_nodes;
        $this->learning_rate = $learning_rate;

        // 初始化连接权重和偏置
        $this->weights_ih = $this->initialize_weights($this->hidden_nodes, $this->input_nodes);
        $this->weights_ho = $this->initialize_weights($this->output_nodes, $this->hidden_nodes);
        $this->bias_h = $this->initialize_weights($this->hidden_nodes, 1);
        $this->bias_o = $this->initialize_weights($this->output_nodes, 1);
    }

    // 初始化连接权重和偏置
    private function initialize_weights($rows, $cols) {
        $weights = array();

        for ($i = 0; $i < $rows; $i++) {
            $row = array();
            for ($j = 0; $j < $cols; $j++) {
                $row[] = mt_rand() / mt_getrandmax() - 0.5; // 随机生成一个介于-0.5和0.5之间的数
            }
            $weights[] = $row;
        }

        return $weights;
    }

    // ...
}

In the above code, we define a NeuralNetwork class, which contains the number of input nodes of the neural network, the number of hidden layer nodes, Output parameters such as the number of nodes and learning rate. Moreover, we also implemented the initialize_weights method for randomly initializing connection weights and biases.

2. Define the forward propagation and back propagation methods of the neural network
   Next, we need to define the forward propagation and back propagation methods of the neural network. The following is a sample code for the forward propagation method:

// 神经网络的前向传播方法
public function feedforward($input_array) {
    // 将输入数组转换为矩阵
    $inputs = $this->array_to_matrix($input_array);

    // 计算隐藏层的输出
    $hidden_inputs = Matrix::dotProduct($this->weights_ih, $inputs);
    $hidden_inputs = Matrix::add($hidden_inputs, $this->bias_h);
    $hidden_outputs = Matrix::map($hidden_inputs, 'sigmoid');

    // 计算输出层的输出
    $output_inputs = Matrix::dotProduct($this->weights_ho, $hidden_outputs);
    $output_inputs = Matrix::add($output_inputs, $this->bias_o);
    $outputs = Matrix::map($output_inputs, 'sigmoid');

    return $outputs->toArray();
}

In the above code, we use a matrix calculation library Matrix, which provides some commonly used matrix calculation methods. We use the Matrix::dotProduct method to calculate the dot product of two matrices, the Matrix::add method to calculate the addition of two matrices, and the Matrix::map method to apply a function (here using the sigmoid function) to each element in the matrix.

The following is a sample code for the backpropagation method:

// 神经网络的反向传播方法
public function backpropagation($input_array, $target_array) {
    // 将输入数组转换为矩阵
    $inputs = $this->array_to_matrix($input_array);
    $targets = $this->array_to_matrix($target_array);

    // 前向传播
    $hidden_inputs = Matrix::dotProduct($this->weights_ih, $inputs);
    $hidden_inputs = Matrix::add($hidden_inputs, $this->bias_h);
    $hidden_outputs = Matrix::map($hidden_inputs, 'sigmoid');

    $output_inputs = Matrix::dotProduct($this->weights_ho, $hidden_outputs);
    $output_inputs = Matrix::add($output_inputs, $this->bias_o);
    $outputs = Matrix::map($output_inputs, 'sigmoid');

    // 计算输出层的误差
    $output_errors = Matrix::subtract($targets, $outputs);

    // 计算隐藏层的误差
    $hidden_errors = Matrix::dotProduct(Matrix::transpose($this->weights_ho), $output_errors);

    // 更新隐藏层到输出层的连接权重和偏置
    $gradients_ho = Matrix::map($output_inputs, 'dsigmoid');
    $gradients_ho = Matrix::multiply($gradients_ho, $output_errors);
    $gradients_ho = Matrix::multiply($gradients_ho, $this->learning_rate);

    $weights_ho_deltas = Matrix::dotProduct($gradients_ho, Matrix::transpose($hidden_outputs));
    $this->weights_ho = Matrix::add($this->weights_ho, $weights_ho_deltas);
    $this->bias_o = Matrix::add($this->bias_o, $gradients_ho);

    // 更新输入层到隐藏层的连接权重和偏置
    $gradients_h = Matrix::map($hidden_inputs, 'dsigmoid');
    $gradients_h = Matrix::multiply($gradients_h, $hidden_errors);
    $gradients_h = Matrix::multiply($gradients_h, $this->learning_rate);

    $weights_ih_deltas = Matrix::dotProduct($gradients_h, Matrix::transpose($inputs));
    $this->weights_ih = Matrix::add($this->weights_ih, $weights_ih_deltas);
    $this->bias_h = Matrix::add($this->bias_h, $gradients_h);
}

In the above code, we first calculated the error of the output layer and hidden layer. Then, the gradient was calculated based on the error and the derivative of the activation function. Finally, the connection weights and biases are updated.

3. Define training and prediction methods
   Finally, we need to define methods for training and predicting the neural network. The following is sample code for training and prediction methods:

// 训练神经网络
public function train($input_array, $target_array) {
    // 前向传播和反向传播
    $this->feedforward($input_array);
    $this->backpropagation($input_array, $target_array);
}

// 预测神经网络的输出
public function predict($input_array) {
    return $this->feedforward($input_array);
}

In the above code, we call the forward propagation and back propagation methods for training, and use the forward propagation method for prediction.

3. Summary

This article introduces how to use PHP to write neural network algorithms and provides code examples. Through these code examples, you can learn the basic knowledge and implementation methods of neural networks. I hope this article will help you write neural network algorithms using PHP. If you have any questions, you can ask in the message area and I will try my best to answer them.

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