A few days ago I bashed PCA on various grounds, in particular that it ranks components by their contribution to the data variance, and it is rarely the data variance about which one cares. Today in discussions with Tsalmantza I realized that one could rank components by the kurtosis of their amplitudes (rather than the variance), and lowest first. This has a number of advantages, but one is that (uninteresting) data artifacts and outliers tend to create high-kurtosis directions in data space, and another is that if there are directions that are multi-modal, they tend also to be low in kurtosis (think the color distribution of galaxies, which is bimodal and low in kurtosis). It is still a very frequentist
approach, but a search for minimal kurtosis directions in data space might be productive. Tsalmantza and I hope to give it a shot next week.
2008-07-10
kurtosis
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Interesting idea. I found your weblog and I think I'll subscribe :-)
ReplyDeleteAre you thinking of computing a cokurtosis matrix and finding its eigenvectors as the directions of minimal/maximal kurtosis? Same scheme as with PCA but with cokurtosis instead of covariance.