C++聚類算法中的自組織映射實現

自組織映射（Self-Organizing Map, SOM）是一種無監督學習算法，用于將高維數據映射到低維空間（通常是二維），同時保留數據的拓撲結構

#include <iostream>
#include <vector>
#include <cmath>
#include <random>

class SOM {
public:
    SOM(int input_dim, int map_size, int epochs, double learning_rate)
        : input_dim_(input_dim), map_size_(map_size), epochs_(epochs), learning_rate_(learning_rate) {
        weights_.resize(map_size_, std::vector<double>(input_dim, 0));
        random_device rd;
        gen_ = std::mt19937(rd());
    }

    void train(const std::vector<std::vector<double>>& data) {
        for (int epoch = 0; epoch < epochs_; ++epoch) {
            for (const auto& input : data) {
                int best_map_idx = -1;
                double min_distance = std::numeric_limits<double>::max();
                for (int i = 0; i < map_size_; ++i) {
                    double distance = calculate_distance(input, weights_[i]);
                    if (distance < min_distance) {
                        min_distance = distance;
                        best_map_idx = i;
                    }
                }

                update_weights(input, best_map_idx);
            }
        }
    }

    std::vector<int> predict(const std::vector<double>& input) const {
        int best_map_idx = -1;
        double min_distance = std::numeric_limits<double>::max();
        for (int i = 0; i < map_size_; ++i) {
            double distance = calculate_distance(input, weights_[i]);
            if (distance < min_distance) {
                min_distance = distance;
                best_map_idx = i;
            }
        }
        return {best_map_idx};
    }

private:
    int input_dim_;
    int map_size_;
    int epochs_;
    double learning_rate_;
    std::vector<std::vector<double>> weights_;
    std::mt19937 gen_;

    double calculate_distance(const std::vector<double>& input, const std::vector<double>& weight) const {
        double distance = 0;
        for (int i = 0; i < input.size(); ++i) {
            distance += pow(input[i] - weight[i], 2);
        }
        return sqrt(distance);
    }

    void update_weights(const std::vector<double>& input, int best_map_idx) {
        double learning_rate = learning_rate_ * (1 - epoch_ / static_cast<double>(epochs_));
        for (int i = 0; i < input.size(); ++i) {
            weights_[best_map_idx][i] += learning_rate * (input[i] - weights_[best_map_idx][i]);
        }
    }
};

int main() {
    std::vector<std::vector<double>> data = {
        {1.0, 2.0},
        {3.0, 4.0},
        {5.0, 6.0},
        {7.0, 8.0},
        {9.0, 10.0}
    };

    SOM som(2, 5, 100, 0.5);
    som.train(data);

    std::vector<int> prediction = som.predict({3.0, 4.0});
    std::cout << "Predicted map index: " << prediction[0] << std::endl;

    return 0;
}

這個實現中，我們創建了一個名為SOM的類，它包含了訓練和預測的方法。train方法用于訓練模型，predict方法用于預測新數據的映射。在main函數中，我們創建了一個簡單的二維數據集，并使用SOM類對其進行訓練和預測。