回归模型——多维BP神经网络模型 C++带类实现及案例

多维BP神经网络模型是一种常见的回归模型，用于解决多维输入与输出之间的映射关系。下面是使用C++带类实现多维BP神经网络模型的示例代码：

#include <iostream>
#include <vector>
#include <cmath>
#include <ctime>
#include <cstdlib>

using namespace std;

class Neuron {
public:
    Neuron(int num_inputs) {
        for (int i = 0; i < num_inputs; i++) {
            weights.push_back(rand() / double(RAND_MAX));
        }
        bias = rand() / double(RAND_MAX);
    }

    double fire(vector<double>& inputs) {
        double activation = 0.0;
        for (int i = 0; i < inputs.size(); i++) {
            activation += inputs[i] * weights[i];
        }
        activation += bias;
        return activation;
    }

    void update_weights(vector<double>& inputs, double delta, double learning_rate) {
        for (int i = 0; i < inputs.size(); i++) {
            weights[i] += learning_rate * delta * inputs[i];
        }
        bias += learning_rate * delta;
    }

private:
    vector<double> weights;
    double bias;
};

class NeuralNetwork {
public:
    NeuralNetwork(int num_inputs, int num_hidden, int num_outputs, double learning_rate) :
            learning_rate(learning_rate), hidden_layer(num_hidden, Neuron(num_inputs)),
            output_layer(num_outputs, Neuron(num_hidden)) {}

    vector<double> predict(vector<double>& inputs) {
        vector<double> hidden_activations;
        for (int i = 0; i < hidden_layer.size(); i++) {
            hidden_activations.push_back(sigmoid(hidden_layer[i].fire(inputs)));
        }

        vector<double> output_activations;
        for (int i = 0; i < output_layer.size(); i++) {
            output_activations.push_back(sigmoid(output_layer[i].fire(hidden_activations)));
        }

        return output_activations;
    }

    void train(vector<double>& inputs, vector<double>& targets) {
        vector<double> hidden_activations;
        for (int i = 0; i < hidden_layer.size(); i++) {
            hidden_activations.push_back(sigmoid(hidden_layer[i].fire(inputs)));
        }

        vector<double> output_activations;
        for (int i = 0; i < output_layer.size(); i++) {
            output_activations.push_back(sigmoid(output_layer[i].fire(hidden_activations)));
        }

        vector<double> output_deltas;
        for (int i = 0; i < output_layer.size(); i++) {
            double error = targets[i] - output_activations[i];
            output_deltas.push_back(error * sigmoid_derivative(output_activations[i]));
        }

        vector<double> hidden_deltas;
        for (int i = 0; i < hidden_layer.size(); i++) {
            double error = 0.0;
            for (int j = 0; j < output_layer.size(); j++) {
                error += output_deltas[j] * output_layer[j].get_weight(i);
            }
            hidden_deltas.push_back(error * sigmoid_derivative(hidden_activations[i]));
        }

        for (int i = 0; i < output_layer.size(); i++) {
            output_layer[i].update_weights(hidden_activations, output_deltas[i], learning_rate);
        }

        for (int i = 0; i < hidden_layer.size(); i++) {
            hidden_layer[i].update_weights(inputs, hidden_deltas[i], learning_rate);
        }
    }

private:
    double learning_rate;
    vector<Neuron> hidden_layer;
    vector<Neuron> output_layer;

    double sigmoid(double x) {
        return 1.0 / (1.0 + exp(-x));
    }

    double sigmoid_derivative(double x) {
        return sigmoid(x) * (1.0 - sigmoid(x));
    }
};

int main() {
    srand(time(NULL));

    vector<vector<double>> inputs = {{0, 0}, {0, 1}, {1, 0}, {1, 1}};
    vector<vector<double>> targets = {{0}, {1}, {1}, {0}};

    NeuralNetwork nn(2, 10, 1, 0.1);

    for (int i = 0; i < 10000; i++) {
        int rand_index = rand() % inputs.size();
        nn.train(inputs[rand_index], targets[rand_index]);
    }

    for (int i = 0; i < inputs.size(); i++) {
        vector<double> output = nn.predict(inputs[i]);
        cout << "Input: " << inputs[i][0] << ", " << inputs[i][1] <<
             " Output: " << output[0] << endl;
    }

    return 0;
}

该示例代码实现了一个多维BP神经网络模型，用于解决XOR运算问题。其中，Neuron类表示神经元，NeuralNetwork类表示神经网络。在Neuron类中，weights表示每个输入的权重，bias表示偏差。在NeuralNetwork类中，hidden_layer和output_layer分别表示隐藏层和输出层。predict方法用于进行预测，train方法用于训练模型。sigmoid函数和sigmoid_derivative函数分别表示激活函数和激活函数的导数。在main函数中，我们使用该模型解决XOR运算问题。