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I have observed that when I significantly reduce the dimensionality of my data that the silhouette score drastically increases. I have reduced the dimensionality so that only 10% of the variance is retained.

With no dimensionality reduction, I get on average silhouette scores ~0. With dimensionality reduction, only keeping 10% variance, I get a score of ~.78.

Based on the silhouette score, is the data actually better clustered in this low dimensionality, or have I manipulated the data too much for this score to be reliable?

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  • $\begingroup$ I tend to view "dimensionality reduction" as pertaining to variables (or features or vectors), and silhouette scores as pertaining to clustered objects (or cases or observations). Am I wrong? $\endgroup$
    – rolando2
    Commented Apr 18, 2017 at 23:29
  • $\begingroup$ That is correct. $\endgroup$
    – cosmosa
    Commented Apr 18, 2017 at 23:32

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Never compare silhouette scores of different preprocessing, in particular not of different features.

This is comparing apples and oranges.

If you want to see if the clusters after PCA are better, use the cluster labels with the original data for Silhouette.

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  • $\begingroup$ I'm not sure that I agree. Dimensionality reduction is considered feature extraction, meaning that you are extracting the essence of the data while minimizing redundancy. While I think that if dim. reduction only retains 10% of the original variance then it has become different data, dim. reduction that has retained 90% of the variance I think is the same data. $\endgroup$
    – cosmosa
    Commented Apr 19, 2017 at 13:54
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    $\begingroup$ If it actually retained 90%, the difference to using 100% when computing the Silhouette would not make much of a difference. But note that the variance measured by PCA is global. Local, you may be losing much more variance when you have clusters in your data. Also, PCA is commonly used with scaling, where the prime components (with most variance) get as much weight as the smaller components except those discarded. This has the odd effect of putting more weight on these smaller deviations, and the "90% retained" is not exactly true, because there is substantial distortion applied to these 90%. $\endgroup$
    – Has QUIT--Anony-Mousse
    Commented Apr 19, 2017 at 19:58
  • $\begingroup$ I agree with @Anony-Mousse on this (+1). The original data might be manipulated too much to make a silhouette score comparison reasonable. $\endgroup$
    – usεr11852
    Commented Apr 22, 2017 at 23:36
  • $\begingroup$ @cosmosa PCA does not do any feature extraction - what it does is to construct principal component(s) that are itself linear combination of the features in the (empirical) dataset. So, the number of principal components represents the number of dimensions in the Euclidean space onto which the (empirical) dataset is projected onto. $\endgroup$
    – Physkid
    Commented May 13, 2021 at 8:35

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