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 ?