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I am using k-modes for clustering unlabeled categorical data. Since the data is not labeled, I fear that my knowledge of suitable valuation indices is limited. So far I have used silhouette score with a precomputed matrix of Ng's dissimilarity measure as presented in: Ng, M. K., Li, M. J., Huang, J. Z., & He, Z. (2007). On the impact of dissimilarity measure in k-modes clustering algorithm. IEEE transactions on pattern analysis and machine intelligence, 29(3), 503-507.

  • My first question is whether it is valid to use the silhouette score with a self-defined dissimilarity measure. So far I just assumed that it is, because the python implementation sklearn.metrics.silhouette_score allows it.
  • My second question is whether I can also use indices like Calinski-Harabasz, or Davies-Bouldin, as these are actually based on distances in Euclidean space, but I use it for categorical data clusters. My assumption so far is that it can still be used as a quality measure for the results of the k-modes algorithm.
  • My last question is whether you have any better suggestions for a suitable method for evaluating the cluster results of categorical data.
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My method isn't traditional and it isn't numeric.

I look at various clusterings and ask whether they tell me anything I didn't know before, give me insight into the data, answer my research questions, and so on. I don't run any tests or indices. If there is one set of clusters that meets the above, or meets it better than the others, I use that one. Ideally, one clustering yields an AHA moment, or, at least, stimulates thought.

I may use numerical measures of each cluster to help me answer the above questions. Since you have categorical data, you could look at proportions of people with each variable in each cluster. You could look at crosstabs of pairs of variables. Mosaic plots of triplets or quadruplets of variables might also be helpful.

Sometimes, the clustering that is chosen by any numeric measure is blazingly obvious. Other times, it is so obscure as to be useless.

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