我如何在Matlab中使用轮廓函数

Question

I have a question on how to use silhouette function in matlab

if i have my correlation matrix X = 90x90 and my cluster membership numbers for my data ; say i have five clusters. This is defined as cidx which is length 90x1 each value is assigned a number from 1 to 5.

Can I just pass the correlation matrix and cidx to the silhouette function and specify the measure as 'correlation' or should i be passing in my returns matrix instead?

Thanks for your help!

Answer 1

First of all you need to make your clusters. For example kmeans function in matlab does this for you.

cidx = kmeans(X,2,'distance','Euclidean');

According to MATLAB:

IDX = kmeans(X,k) partitions the points in the n-by-p data matrix X into k clusters. This iterative partitioning minimizes the sum, over all clusters, of the within-cluster sums of point-to-cluster-centroid distances. Rows of X correspond to points, columns correspond to variables. kmeans returns an n-by-1 vector IDX containing the cluster indices of each point.

so here cidx is the n-by-1 cluster indices. After finding the indices you can pass the X and the cidx to the silhouette function:

s = silhouette(X,cidx,'Euclidean')

s is the silhouette values in the n-by-1 vector.

Answer 2

Silhouette is used to determine the quality of clustering. The way this function works is illustrated below using a matrix of 100*3 size. Example -

NofClusters=3;

numObservarations = 100;
dimensions = 3;
data = rand([numObservarations dimensions]);
numObservarations = length(data);

%% cluster
opts = statset('MaxIter', 500, 'Display', 'iter');
[clustIDX, clusters, interClustSum, Dist] = kmeans(data, K, 'options',opts, ...
    'distance','sqEuclidean', 'EmptyAction','singleton', 'replicates',3);
%% plot data+clusters
figure, hold on
scatter3(data(:,1),data(:,2),data(:,3), 50, clustIDX, 'filled')
scatter3(clusters(:,1),clusters(:,2),clusters(:,3), 200, (1:K)', 'filled')
hold off, xlabel('x'), ylabel('y'), zlabel('z')

%% plot clusters quality
figure
[silh,h] = silhouette(data, clustIDX);
avrgScore = mean(silh);