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Very fast matlab implementation of kmedoids clustering algorithm

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This is a fully vectorized version kmedoids clustering methods ( It is usually more robust than kmeans algorithm. Please try following code for a demo:
close all; clear;
d = 2;
k = 3;
n = 500;
[X,label] = kmeansRnd(d,k,n);
y = kmedoids(X,k);
Input data are assumed COLUMN vectors!
You can only visualize 2d data!
This function is now a part of the PRML toolbox (

Comments and Ratings (21)

It was giving me the following error:

Error using +
Matrix dimensions must agree.

Error in kmedoids (line 20)
D = v+v'-2*(X'*X); % Euclidean distance matrix

So, instead of:
D = v+v'-2*(X'*X); % Euclidean distance matrix
it should be:
D = v'*v-2*(X'*X); % Euclidean distance matrix

And that fixed the issue for me.

Mo Chen

Mo Chen (view profile)

@yu dengxiu
@saeed safarian
This function requires Matlat version >= R2016b. X = X-mean(X,2) is a new syntax of R2016b. You can change this to X=bsxfun(@minus, X, mean(X,2)); for older version of Matlab

yu dengxiu

thanks for this code, but it doesent work correctly.
X = X-mean(X,2) in kmedoids function has an error that Matrix dimensions must agree.
How to fix it?

thanks for this code, but it doesent work correctly.
X = X-mean(X,2) in kmedoids function has an error that Matrix dimensions must agree.

Mark Ebden

Thanks for this code, but for some datasets it's hypersensitive to rounding errors: occasionally the slightly nonzero entries along D's diagonal lead to results that are surprisingly far from correct (eg the chance that given medoids are chosen increases or decreases). I can email code to demonstrate if needed.

The problem is fixed by adding a for-loop after D is defined:

for i=1:n,
D(i,i) = 0;

To confirm that this yields 'correct' results, I perturbed one of the problematic datasets by a tiny amount and compared medoids before-and-after.

Hope that helps.

Even though the code is lightning fast, the solution is not the proper one, hence this code is useless. See for example output of k = 6 for a naive (and very slow) implementation of the algorithm, and this submission. Obviously the naive is correct, this submission is incorrect.

Nonetheless thanks for the effort! It would be great if you could produce correct code that is still as fast.



I tested calling to kmedoids() function, it always returns
label = 2 1
energy = 0
index = 2 1
I believe it does not work. Thanks anyway.


SU Li (view profile)

Nice code. Very helpful. However, if the number of input data is large, then the D matrix is too large (n^2) which may make memory overflow.

Joao Henriques

Simple and elegant code, thanks!


Tong (view profile)

If I want to use the cosine distance between two vectors, What shold I do?


MUSA (view profile)


kannan (view profile)

if i want to apply kmedoids agorithm for X data in function [label, energy, index] = kmedoids(X,k) 3599*11 size data then it is not working properly can anybody of you give idea for this?

Nejc Ilc

Nejc Ilc (view profile)

Very compact and efficient coding. Nice job!
However, there is an error when k=1. I suggest to add the third parameter (dimension) to the calls of function min:
(Line 8): [~, label] = min(D(randsample(n,k),:),[],1);
(Line 11): [~, label] = [~, index] = min(D*sparse(1:n,label,1,n,k,n),[],1);


Tu (view profile)

Not working for my data as well.
My data was of the dimension 17-by-71.
wanted to find 4 or 6 clusters.
and spread did not work.


Graeme (view profile)

Undefined function 'randsample' for input arguments of type 'double'.

Error in kmedoids (line 8)
[~, label] = min(D(randsample(n,k),:));


huang (view profile)

Mo Chen

Mo Chen (view profile)

better post your error message

Dear Sir Pls help!!! My Matlab version is Matlab7.6.0..Is this the reason?
Pls reply when you free!!!

SIMPLY NOT working.
load data;





improved numerical stability, remove empty clusters


fix bug for k=1


correct description


significantly simplify the code

MATLAB Release
MATLAB 9.1 (R2016b)

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