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I am experimenting with clustering algorithms, like K-Means. Right now, I use all variables as input for the clustering algorithm. I am wondering if it is appropriate to do feature selection for clustering algorithms. That is, how can I find those variables that are most important or least important for clustering.

For the case where I know what the true clusters are, my idea would be to use increasing subsets of variable combinations as input for the clustering algorithm, compute a contingency table between predicted clusters and true groups are, apply some metric (like accuracy) in order to find those feature combinations that have the worst or best score.

Are you aware of some method to obtain the least and most important features after applying a clustering algorithm, like k-means?

I am new to this topic, so please be nice. :-)

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It is not straightforward to feature selection for k-menas clustering since it unsupervised.

One option is to loop through the features, leaving one out at a time. Select a criterion for better and worse clusterings, one example could be silhouette score. Then see which feature contributes the most or least to improving that criteria.

If you know what the true clusters are, then you have a classification problem. Should apply classification-based feature selection and algorithms.

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