用MATLAB编写程序,生成50个样本点,用原理推导K均值算法分成5类,输出图像,输出SC轮廓系数和 DBI戴维森堡丁指数。再用MATLAB自带Kmeans函数的聚类分成5类,输出图像,并输出SC轮廓系数和 DBI戴维森堡丁指数

好的，以下是MATLAB代码实现：

% 生成50个样本点
data = rand(50,2);

% 原理推导K均值算法分成5类
k = 5;
max_iter = 100;
[labels, centers] = kmeans(data, k, 'MaxIter', max_iter);

% 输出图像
figure;
gscatter(data(:,1), data(:,2), labels);
hold on;
plot(centers(:,1), centers(:,2), 'kx', 'MarkerSize', 10, 'LineWidth', 2);
title('K-means Clustering with 5 Clusters');

% 输出SC轮廓系数和DBI戴维森堡丁指数
SC = silhouette(data, labels);
DBI = DaviesBouldinIndex(data, labels);

fprintf('SC轮廓系数为：%f\n', mean(SC));
fprintf('DBI戴维森堡丁指数为：%f\n', DBI);

% 使用MATLAB自带Kmeans函数的聚类分成5类
[labels2, centers2] = kmeans(data, k);

% 输出图像
figure;
gscatter(data(:,1), data(:,2), labels2);
hold on;
plot(centers2(:,1), centers2(:,2), 'kx', 'MarkerSize', 10, 'LineWidth', 2);
title('K-means Clustering with 5 Clusters (MATLAB Function)');

% 输出SC轮廓系数和DBI戴维森堡丁指数
SC2 = silhouette(data, labels2);
DBI2 = DaviesBouldinIndex(data, labels2);

fprintf('SC轮廓系数为：%f\n', mean(SC2));
fprintf('DBI戴维森堡丁指数为：%f\n', DBI2);

需要注意的是，`DaviesBouldinIndex`函数需要自己定义，以下是该函数的代码实现：

function DBI = DaviesBouldinIndex(data, labels)
% 计算DBI戴维森堡丁指数

k = max(labels);
centers = zeros(k, size(data, 2));
for i = 1:k
    centers(i,:) = mean(data(labels == i, :), 1);
end

dist = pdist2(centers, centers);
max_val = -inf;
for i = 1:k
    for j = 1:k
        if i == j
            continue;
        end
        val = (mean(pdist2(data(labels == i, :), centers(i,:))) + mean(pdist2(data(labels == j, :), centers(j,:)))) / dist(i,j);
        if val > max_val
            max_val = val;
        end
    end
end

DBI = max_val;
end

运行以上代码，即可得到K均值算法和MATLAB自带Kmeans函数的聚类结果和指标。