I found a reference quoting that there are approximately ways of partitioning n data points into k clusters, assuming hard partitioning.
hi every body.
i want to cluster a graph with n nodes to k clusters.
for example suppose that n=10, k=3. some different clustering could be:
clustering 1:
c1={n1,n2,n3} , c2={n4,n5}, c3={n6,n7,n8,n9,n10}
clustering 2:
c1={n1,n2,n10} , c2={n4,n5}, c3={n6,n7,n8,n9,n3}
clustering 3:
c1={n1,n2} , c2={n4,n5}, c3={n6,n7,n8,n9,n3,n10}
i want to know how many different clusters is possible?
tanks in advance.
Is a cluster allowed to be empty? If we switch c1 and c2, do we get an equivalent or a distinct clustering?
Assuming that switching c1 and c2 produces an equivalent clustering, what you are doing is equivalent to placing n distinguishable objects into k indistinguishable bins. There is more info here
http://www.johndcook.com/TwelvefoldWay.pdf