MATLAB 中的层次聚类

Question

我通过以下方式使用层次聚类对我的数据 X 进行了聚类：

X = [1 1 1;
     2 2 2;
     1 1 0;
     1 2 2];
Y = pdist(X);
T = linkage(Y, 'complete');
c = cluster(T,'maxclust',2);

所以，X(1,:) 和 X(3,:) 属于集群 #1，其他属于 集群 #2。

如何确定应该将新数据点（不在 X 中）分配到哪个集群？例如 [1 0 1] 属于哪个集群？

Answer 1

简单的解决方案是找到最近的集群质心。

最近的质心

x_new = [1 0 1];

% Find cluster centroid
X_c = zeros(numel(unique(c)), size(X,2));
for cid = unique(c)'
   X_c(cid,:) = mean(X(c == cid,:)); 
end

% Find closest centroid
[~,c_new] = min(pdist2(x_new,X_c));

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如果您有更多样本并且想要考虑方差，您可以计算欧几里得距离的 z 分数

距离的 Z 分数

x_new = [1 0 1];
X_means = zeros(1,numel(unique(c)));
X_stds = zeros(1,numel(unique(c)));
X_c = zeros(numel(unique(c)), size(X,2));
for cid = unique(c)'
   distances = pdist2(X(c == cid,:),mean(X(c == cid,:))); 
   X_means(cid) = mean(distances);
   X_stds(cid) = std(distances);

   X_c(cid,:) = mean(X(c == cid,:)); 
end
[~,c_new] = min((pdist2(x_new,X_c) - X_means)./X_stds);

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如果您想考虑组件方差，您可以获取组件距离的 Z 分数（我不确定此结果与上述结果有什么不同...）

组件距离的平均 Z 分数

x_new = [1 0 1];
X_means = zeros(numel(unique(c)),size(X,2));
X_stds = zeros(numel(unique(c)),size(X,2));
X_c = zeros(numel(unique(c)), size(X,2));
for cid = unique(c)'
   comp_distances = abs(X(c == cid,:) - repmat(mean(X(c == cid,:)),[numel(find(c==cid)),1])); 
   X_means(cid,:) = mean(comp_distances);
   X_stds(cid,:) = std(comp_distances);

   X_c(cid,:) = mean(X(c == cid,:)); 
end
[~,c_new] = min(mean(((repmat(x_new,[size(X_c,1),1])-X_c) - X_means)./X_stds,2));