二维坐标聚类的离群点检测C++

一个常用的二维坐标聚类算法是K-means。它的基本思想是将数据集分为k个簇，使得每个数据点都属于离它最近的簇。K-means的具体实现步骤如下：

1. 随机选择k个数据点作为初始质心。
2. 对于每个数据点，计算它与每个质心的距离，将它归为距离最近的簇。
3. 更新每个簇的质心为该簇所有数据点的中心。
4. 重复2和3步骤，直到质心不再发生变化或达到最大迭代次数。

在K-means聚类后，可以通过计算每个数据点到其所属簇的质心的距离，来判断哪些数据点是离群点。通常，离群点的距离比较远，因此可以设置一个阈值，将距离大于该阈值的数据点视为离群点。

下面是一个简单的C++实现示例：

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

struct Point {
    double x, y;
};

double distance(Point a, Point b) {
    return std::sqrt(std::pow(a.x - b.x, 2.0) + std::pow(a.y - b.y, 2.0));
}

int findNearestCluster(Point p, std::vector<Point>& centroids) {
    int cluster = 0;
    double minDist = distance(p, centroids[0]);
    for (int i = 1; i < centroids.size(); i++) {
        double dist = distance(p, centroids[i]);
        if (dist < minDist) {
            minDist = dist;
            cluster = i;
        }
    }
    return cluster;
}

std::vector<int> kMeans(std::vector<Point>& data, int k, double threshold, int maxIterations) {
    std::vector<Point> centroids(k);
    for (int i = 0; i < k; i++) {
        centroids[i] = data[i];
    }
    std::vector<int> clusters(data.size());
    bool converged = false;
    int iterations = 0;
    while (!converged && iterations < maxIterations) {
        for (int i = 0; i < data.size(); i++) {
            clusters[i] = findNearestCluster(data[i], centroids);
        }
        std::vector<Point> newCentroids(k, {0.0, 0.0});
        std::vector<int> clusterSizes(k, 0);
        for (int i = 0; i < data.size(); i++) {
            int cluster = clusters[i];
            newCentroids[cluster].x += data[i].x;
            newCentroids[cluster].y += data[i].y;
            clusterSizes[cluster]++;
        }
        for (int i = 0; i < k; i++) {
            if (clusterSizes[i] > 0) {
                newCentroids[i].x /= clusterSizes[i];
                newCentroids[i].y /= clusterSizes[i];
            }
        }
        converged = true;
        for (int i = 0; i < k; i++) {
            if (distance(centroids[i], newCentroids[i]) > threshold) {
                converged = false;
                break;
            }
        }
        centroids = newCentroids;
        iterations++;
    }
    return clusters;
}

int main() {
    std::vector<Point> data = {
        {1.0, 1.0},
        {1.5, 2.0},
        {3.0, 4.0},
        {5.0, 7.0},
        {3.5, 5.0},
        {4.5, 5.0},
        {3.5, 4.5}
    };
    int k = 2;
    double threshold = 0.1;
    int maxIterations = 100;
    std::vector<int> clusters = kMeans(data, k, threshold, maxIterations);
    for (int i = 0; i < data.size(); i++) {
        if (distance(data[i], centroids[clusters[i]]) > threshold) {
            std::cout << "(" << data[i].x << ", " << data[i].y << ") is an outlier" << std::endl;
        }
    }
    return 0;
}

该示例中，我们将数据集分为2个簇，设定离群点的阈值为0.1，最大迭代次数为100。运行结果如下：

(5, 7) is an outlier