KA算法 Matlab代码
时间: 2024-01-03 21:17:03 浏览: 30
以下是KA算法的Matlab代码实现:
```matlab
function [centers, memberships] = ka(data, num_clusters, m, max_iter, tol)
% data: 数据矩阵,每列为一个数据点
% num_clusters: 聚类中心个数
% m: 模糊指数
% max_iter: 最大迭代次数
% tol: 算法终止阈值
[n, d] = size(data);
% 初始化隶属度矩阵
memberships = rand(n, num_clusters);
memberships = memberships ./ sum(memberships, 2);
for i = 1:max_iter
% 计算聚类中心
centers = memberships' * data ./ sum(memberships, 1)';
% 计算距离矩阵
distances = zeros(n, num_clusters);
for j = 1:num_clusters
distances(:, j) = sqrt(sum((data - centers(j, :)) .^ 2, 2));
end
% 更新隶属度矩阵
new_memberships = 1 ./ distances .^ (2 / (m - 1));
new_memberships = new_memberships ./ sum(new_memberships, 2);
% 判断算法是否收敛
if max(max(abs(new_memberships - memberships))) < tol
break;
end
memberships = new_memberships;
end
end
```
其中,`data`是一个$n \times d$的矩阵,每列为一个数据点;`num_clusters`是聚类中心的个数;`m`是模糊指数;`max_iter`是最大迭代次数;`tol`是算法终止阈值。函数会返回`centers`和`memberships`,分别表示聚类中心和隶属度矩阵。