矢量量化分裂算法C++程序

矢量量化分裂算法（Vector Quantization Splitting Algorithm，简称VQSA）是一种用于将数据压缩的算法。下面是一个简单的C++实现：

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

using namespace std;

struct point {
    double x, y;
    point() {}
    point(double _x, double _y) : x(_x), y(_y) {}
};

const int N = 10000;
const int K = 16;   // 簇的个数
const int MAX_ITER = 100;   // 最大迭代次数

vector<point> data(N);
vector<point> centroids(K);

// 计算两个点之间的距离
double distance(const point& p1, const point& p2) {
    double dx = p1.x - p2.x;
    double dy = p1.y - p2.y;
    return sqrt(dx * dx + dy * dy);
}

// 初始化聚类中心
void init() {
    for (int i = 0; i < K; i++) {
        centroids[i] = data[i];
    }
}

// 分配每个点到最近的簇
vector<int> assign_clusters() {
    vector<int> clusters(N);
    for (int i = 0; i < N; i++) {
        double min_dist = 1e9;
        int min_idx = 0;
        for (int j = 0; j < K; j++) {
            double dist = distance(data[i], centroids[j]);
            if (dist < min_dist) {
                min_dist = dist;
                min_idx = j;
            }
        }
        clusters[i] = min_idx;
    }
    return clusters;
}

// 更新聚类中心
void update_centroids(const vector<int>& clusters) {
    vector<int> counts(K, 0);
    vector<point> sums(K, point(0, 0));
    for (int i = 0; i < N; i++) {
        int c = clusters[i];
        counts[c]++;
        sums[c].x += data[i].x;
        sums[c].y += data[i].y;
    }
    for (int i = 0; i < K; i++) {
        if (counts[i] > 0) {
            centroids[i].x = sums[i].x / counts[i];
            centroids[i].y = sums[i].y / counts[i];
        }
    }
}

// 分裂簇
void split_cluster() {
    int max_idx = 0;
    double max_dist = 0;
    for (int i = 0; i < K; i++) {
        for (int j = i + 1; j < K; j++) {
            double dist = distance(centroids[i], centroids[j]);
            if (dist > max_dist) {
                max_dist = dist;
                max_idx = i;
            }
        }
    }
    centroids[max_idx].x += max_dist / 2;
    centroids[max_idx + 1].x -= max_dist / 2;
}

// 计算聚类误差平方和
double compute_error(const vector<int>& clusters) {
    double error = 0;
    for (int i = 0; i < N; i++) {
        int c = clusters[i];
        error += pow(distance(data[i], centroids[c]), 2);
    }
    return error;
}

int main() {
    // 生成随机数据
    srand(time(0));
    for (int i = 0; i < N; i++) {
        data[i] = point(rand() % 100, rand() % 100);
    }

    // 初始化聚类中心
    init();

    // 迭代优化
    for (int iter = 0; iter < MAX_ITER; iter++) {
        vector<int> clusters = assign_clusters();
        update_centroids(clusters);
        if (iter % 10 == 9) {
            split_cluster();
        }
        double error = compute_error(clusters);
        cout << "Iteration " << iter << ", error = " << error << endl;
    }

    return 0;
}

该程序生成了10000个随机点，将它们分为16个簇，并且在每10次迭代后分裂一个簇。在每次迭代后，程序计算聚类误差平方和并输出。