基于轮盘赌算法的k-means++的算法复杂度（matlab程序）

Question

% k-means++算法，选择尽可能距离远的初始聚类中心
function center = KmeansPPFun(data,K)
    % Choose the first inital centroid randomly
    center = data(randperm(size(data,1),1)',:); 

    % Select remaining initial centroids (a total number of k-1)
    for i = 2:K
        distance_matrix = zeros(size(data,1),i-1); % size(data,1)是数据点个数N
        for j = 1:size(distance_matrix,1) % size(distance_matrix,1) 是数据点个数N
            for m = 1:size(distance_matrix,2) % size(distance_matrix,2)是当前已经选好的聚类中心个数
                distance_matrix(j,m) = sum((data(j,:)-center(m,:)) .^ 2);
            end
        end
        % Choose next centroid according to distances between points and
        % previous cluster centroids.
        index = Roulettemethod(distance_matrix); % 轮盘赌算法
        center(i,:) = data(index,:);
    end

% 轮盘赌算法
function [index] = Roulettemethod(distance_matrix)

% Find shortest distance between one sample and its closest cluster centroid
[min_distance,~] = min(distance_matrix,[],2);

% Normalize for further operations
min_distance = min_distance ./ sum(min_distance);

% Construct roulette according to min_distance
temp_roulette = zeros(size(distance_matrix,1),1);
for i = 1:size(distance_matrix,1) % size(distance_matrix,1)是数据点个数N
    temp_roulette(i,1) = sum(min_distance(1:i,:));
end

% Generate a random number for selection
temp_rand = rand();

% Find the corresponding index
for i = 1:size(temp_roulette,1) % size(temp_roulette,1)是数据点个数N
    if((i == 1) && temp_roulette(i,1) > temp_rand)
        index = 1;
    elseif((temp_roulette(i,1) > temp_rand) && (temp_roulette(i-1,1) < temp_rand))
        index = i;
    end
end
end

Answer 1

这个算法主要分析的是初始聚类中心和迭代更新聚类中心各自的时间复杂度，但是你代码的逻辑很乱，比如这里为什么要用三层循环，明明用矩阵运算就可以做的，大致只能看出你要用距离信息选择下一个聚类中心，先交给GPT去解释代码吧，逻辑弄清楚才能分析复杂度