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I want to cluster a data set where all variables are categorical.

Which would be more effective for doing so, k - means or k - medoids?

The data set is linked below.

https://archive.ics.uci.edu/ml/datasets/congressional+voting+records

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As K-medoids minimizes a sum of pairwise dissimilarities instead K-means minimizes sum of squared Euclidean distances.

If the data is categorical the medoids are more perfect as it is more robust towards outlier and noise.

So use K-medoids

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K-means needs to compute means.

Hence it cannot be used on categoricial data.

You can do hacks such as one-hot encoding but these have their own issues. That is why method such as k-modes exist...

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