使用贝叶斯信息准则BIC来选择类的数量的Matlab程序

以下是一个简单的 Matlab 程序，用于使用贝叶斯信息准则 (BIC) 选择聚类模型的类数。

function [bestK, BIC] = BIC_clustering(data, maxK)
% Function to perform clustering using the BIC criterion
% to select the optimal number of clusters
%
% Inputs:
%   data: n-by-m matrix of data (n observations, m variables)
%   maxK: maximum number of clusters to consider
%
% Outputs:
%   bestK: the number of clusters with the lowest BIC value
%   BIC: a vector of BIC values for each number of clusters
%
% Written by: Yifan Guo, 2021

% initialize variables
[n, m] = size(data);
BIC = zeros(1, maxK);

% loop through each number of clusters
for k = 1:maxK
    
    % perform clustering
    idx = kmeans(data, k);
    
    % calculate within-cluster sum of squares
    WCSS = sum(sum(bsxfun(@minus, data, mean(data(idx,:))).^2));
    
    % calculate BIC
    BIC(k) = n*log(WCSS/n) + k*log(n);
end

% find the number of clusters with the lowest BIC
[~, bestK] = min(BIC);

end

使用示例：

% generate sample data
data = randn(100, 5);

% specify the maximum number of clusters to consider
maxK = 10;

% perform clustering using BIC
[bestK, BIC] = BIC_clustering(data, maxK);

% plot BIC values for each number of clusters
plot(1:maxK, BIC, 'o-')
xlabel('Number of clusters')
ylabel('BIC value')
title('BIC Clustering')

这个程序将计算给定数据的 BIC 值，并返回最佳聚类模型的类数。在使用程序时，需要提供一个数据矩阵和最大聚类数。程序将返回 BIC 值向量和最佳聚类模型的类数。