Selecting K with elbow method for K-modes (binary or nominal data)

I have run the k-modes algorithm on my nominal data set, which I converted to a dummy matrix (binary). As for K-Means, one can perform the elbow method by looking at the elbow method using, according to Wikipedia, the Percentage of variance explained is the ratio of the between-group variance to the total variance, also known as an F-test source.

How would one compute the between-group variance ratio or simply the SS(W) for a nominal/binary data set? Are there available approaches?

Thanks for any help and insights!

PS: I have already performed the silhouette score using jaccard index or dice from the using scipy library and would like to compute the elbow method as well.

• Variance is for continuous variables, not nominal data. – Has QUIT--Anony-Mousse Sep 10 '17 at 8:40
• @Anony-Mousse Hence my question. Is there a comparable approach for nominal data? I have encountered Unalikeability (Kader et al 2007; ww2.amstat.org/publications/jse/v15n2/kader.pdf) but I am unsure if one could employ it in a similar fashion – dmeu Sep 11 '17 at 14:04
• Well, many distance-based methods like Silhouette can still be used if you have a distance function. But that doesn't mean they will be very reliable, but mostly can serve as a first guess. Some of these will require you finding an "elbow" too... – Has QUIT--Anony-Mousse Sep 11 '17 at 18:47
• Refer to the below link might be of some help. kaggle.com/ashydv/bank-customer-clustering-k-modes-clustering/… – Rick.code Jun 17 at 18:05