C++聚類算法與網格搜索的參數優化

在C++中，聚類算法和網格搜索是機器學習中兩個重要的概念

1. 聚類算法：

聚類是一種無監督學習方法，用于將數據集中的樣本分成不同的組或簇。常用的C++聚類算法有K-means、DBSCAN等。以下是K-means算法的簡單實現：

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

using namespace std;

struct Point {
    double x, y;
};

double distance(const Point& a, const Point& b) {
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}

vector<Point> kmeans(const vector<Point>& points, int k, int max_iterations = 100) {
    random_device rd;
    mt19937 gen(rd());
    uniform_int_distribution<> dis(0, points.size() - 1);

    vector<Point> centroids(k);
    vector<int> labels(points.size(), -1);

    for (int i = 0; i < max_iterations; ++i) {
        vector<Point> clusters[k];

        for (int j = 0; j < points.size(); ++j) {
            int closest_centroid = dis(gen);
            clusters[closest_centroid].push_back(points[j]);
            labels[j] = closest_centroid;
        }

        bool converged = true;
        for (int j = 0; j < k; ++j) {
            if (clusters[j].size() == 0) {
                // Find the largest cluster and take its centroid as the new centroid
                int max_cluster_index = 0;
                for (int l = 1; l < k; ++l) {
                    if (clusters[l].size() > clusters[max_cluster_index].size()) {
                        max_cluster_index = l;
                    }
                }
                centroids[j] = clusters[max_cluster_index][0];
                clusters[max_cluster_index].clear();
            } else {
                Point new_centroid = {0, 0};
                for (const auto& point : clusters[j]) {
                    new_centroid.x += point.x;
                    new_centroid.y += point.y;
                }
                new_centroid.x /= clusters[j].size();
                new_centroid.y /= clusters[j].size();
                centroids[j] = new_centroid;
            }

            for (int j = 0; j < points.size(); ++j) {
                double min_distance = DBL_MAX;
                int closest_centroid = -1;
                for (int l = 0; l < k; ++l) {
                    double dist = distance(points[j], centroids[l]);
                    if (dist < min_distance) {
                        min_distance = dist;
                        closest_centroid = l;
                    }
                }
                if (closest_centroid != labels[j]) {
                    converged = false;
                    break;
                }
            }

            if (!converged) break;
        }

        if (converged) break;
    }

    return centroids;
}

2. 網格搜索：

網格搜索是一種參數優化方法，用于在給定的參數空間中搜索最佳參數組合。常用的C++網格搜索庫有GridSearchCV（基于Scikit-learn）和mlpack等。以下是使用Scikit-learn的GridSearchCV進行參數優化的示例：

#include <iostream>
#include <vector>
#include <algorithm>
#include <random>
#include <chrono>
#include <sklearn/model_selection/grid_search.hpp>
#include <sklearn/svm/svc.hpp>

using namespace std;
using namespace sklearn::model_selection;
using namespace sklearn::svm;

int main() {
    // 生成隨機數據集
    random_device rd;
    mt19937 gen(rd());
    uniform_int_distribution<> dis(0, 100);
    vector<vector<double>> X(100, vector<double>(2));
    vector<double> y(100);
    for (int i = 0; i < 100; ++i) {
        X[i][0] = dis(gen);
        X[i][1] = dis(gen);
        y[i] = dis(gen) % 2;
    }

    // 定義參數網格
    param_grid grid = {{0, 1}, {1, 2}, {2, 3}};

    // 創建SVM分類器
    SVC classifier;

    // 創建網格搜索對象
    GridSearchCV grid_search(classifier, grid, cv::evaluate_classification, vector<double>());

    // 開始網格搜索
    auto start = chrono::high_resolution_clock::now();
    grid_search.fit(X, y);
    auto end = chrono::high_resolution_clock::now();

    // 輸出最佳參數組合和對應的得分
    cout << "Best parameters: " << grid_search.best_params_ << endl;
    cout << "Best score: " << grid_search.best_score_ << endl;
    cout << "Time taken: " << chrono::duration<double, milli>(end - start).count() << " ms" << endl;

    return 0;
}

這個示例使用了Scikit-learn的GridSearchCV類來進行SVM分類器的參數優化。首先，我們生成了一個隨機數據集，然后定義了參數網格，接著創建了一個SVM分類器和一個網格搜索對象。最后，我們調用fit方法開始網格搜索，并輸出了最佳參數組合和對應的得分。