# How to compare two cluster solutions ?

Hello all,

I have two ways to cluster a set of objects, and now I want to compare my two clusters so to measure how "similar" the resulting clusters are.

I found there is a variety of validation criteria (Hubert's gamma coefficient, the Dunn index and the corrected rand index), but the implementation I found for them rely on knowing a distance matrix for pairs of objects (which I don't have).

(As can be seen here - see last paragraph)

My question is if other measures exist? (such that don't require the knowledge of the distance matrix)

(I already found one such solution, using a measure called Bk, from C mallow in 1983 - but would like to know of other solutions that came to be since then)

Thanks,

Tal

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This question borders on philosophy. clusteringtheory.org –  Shiva Kaul Apr 21 '10 at 18:55
Is it not said that all of math borders on philosophy? –  Tal Galili Apr 22 '10 at 12:08

Kappa_max proposed by Reilly et al uses kappa (well known for comparing raters). They cross-tabulate the two cluster solutions, and permute the columns to find the permutation that maximises kappa, hence kappa_max. For clusters with up to 8 or 10 categories, it is possible to use brute force to examine all permutation, but they present code that does a search through the permutation space for larger cluster solutions.

@Article{reilly05:_rapid_method_for_compar_of_clust_analy, author = {Cavan Reilly and Changchun Wang and Mark Rutherford}, title = {A Rapid Method for the Comparison of Cluster Analyses}, journal = {Statistica Sinica}, year = 2005, volume = 15, number = 1, pages = {19-33}, month = {January} }

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You can use all the indexes listed in Quick-R page.

If you look into stat package there's a function dist. This function calculates the distance matrix between your data elements. Such matrix is the matrix you need to run the function cluster.stats.

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