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I have to handle large binary dataset. That is one of the reasons I have to build my own Hierarchical Clustering. As I digged into the algorithms I was surprised and not ;) to find that it is possible to have multiple (not just two) vectors that have the same distance (hamming,overlap,...), so you can pair them differently in a 'correct' way.

F.e. using overlap as similarity mesaure ... the following 3 vectors have overlap of 2 and there are 2 different correct pairing.

 sequence : 110,101,111

what this means is that there is multiple ways to cluster those :

 ((110,111),101)  vs (110,(111,101))

 sequence : 110,101,111,011

 (110,((111,011),101))  vs ((110,(111,011)),101)

Let me illustrate it with integers :

 2,6,8,4
 (2,((4,6),8))  vs ((2,(4,6)),8) vs ....

What this means is that there are no canonical way of clustering/dendogram .

How do you handle that ? Is there a different type of clustering that can have canonical/single representation ?

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You can always adjust your algorithm to use a deterministic tie-breaking rule, e.g., sort the data points before applying the clustering algorithm, and always break ties in favor of the earliest/leftmost item. This yields a deterministic algorithm, so if you give it exactly the same input both times, it will produce the same clustering both times. I can't tell whether this is what you are looking for or not.

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  • $\begingroup$ good advice .. btw I'm doing online/incremental clustering, so it is by default deterministic, but I was hoping there will be some other "arrangement" that would fix the multiplicity problem ... multidimensional clustering or something ? $\endgroup$
    – sten
    May 12 at 23:34
  • $\begingroup$ @sten, I don't know, I can't understand what exactly the problem is or what the precise requirements are, so I'm not sure what to suggest. $\endgroup$
    – D.W.
    May 13 at 2:15
  • $\begingroup$ h-clustering that i know of pairs only 2 values .. i'm looking for clustering which can accommodate multi-pairing and is still hierarchical .. i imagine it is as multidimensional or some sort of fuzzy clustering ... $\endgroup$
    – sten
    May 13 at 21:07

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