# Why is fanny() producing tied maximal group probabilities?

I have a matrix of pairwise Gower dissimilarities (i.e. a non-Euclidean metric) among 48 objects derived from observations of 54 variables.

I want to use fuzzy clustering to obtain a matrix of group membership probabilities for these objects.

I successfully applied function fanny() from package {cluster} with k (number of groups) = 4.

However, for each sample, the resulting group membership probabilities for groups 1, 2 and 4 are identical. That is, they differ between samples, but within a sample they are identical, and differ from the membership probability for group 3.

I tested the function with k of 5, 6 and 7 and obtained the same result. For each k, the group membership probabilities were identical (within an object), except for group 3.

Does anyone know why this might be happening? I've read up on the fanny() algorithm a little but I'm out of my depth.

Reproducible code (NB: actual data follow due to size):

install.packages("cluster")
library("cluster")
WRS_fanny <- fanny(WRS_abiotic_gower, k = 4, memb.exp = 1.6)
boxplot(WRS_fanny\$membership) # Note identical probabilities except group 3


Used dump() to generate this expression to recreate my data (warning: 294 lines):

WRS_abiotic_gower <-
structure(c(0.146778126529408, 0.233395130892759, 0.230707834408444,
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))


## migrated from stackoverflow.comJun 10 '16 at 13:51

This question came from our site for professional and enthusiast programmers.

• try to change the value of memb.exp, it should help – Cath Jun 10 '16 at 7:17
• Alas, it does not. – mixtrak Jun 10 '16 at 11:58
• I tried with memb.exp=1.1 and membership probabilities are much more "drastic"... (around 98%-99% for the first objects) – Cath Jun 10 '16 at 13:23
• Thanks - I jumped to conclusions and didn't explore a wide enough range of memb.exp values. Turns out, below about 1.5, the group memberships begin to diverge. Any idea why? If this was posted as a solution, it would be accepted ;) – user119630 Jun 11 '16 at 9:02
• If I had to guess, I'd imagine this is complete fuzziness for all group memberships except one, which would explain why increasing crispness resolves the tie. I suppose that implies the clustering is only robust for one group, and the others should be interpreted with caution? – user119630 Jun 11 '16 at 9:09

The parameter memb.exp determines the degree of fuzziness. depending on your data, the best value can be 1.8 or 1.05, hence there is no perfect value. The higher the value is, the more fuzziness you introduce in the clustering.

You can have a look at Bora et al., which discusses more thoroughly about the topic.

I hope this helps you at least a bit.