Comments for Suresh Venkatasubramanian

Comment on The Johnson-Lindenstrauss Transform: An Empirical Study by suresh

suresh — Tue, 02 Nov 2010 18:02:46 +0000

Sam, that statement is not true. PCA is not optimal for the distance function you mention. Moreover, JL results are for minimizing the max ratio, not the average difference.

Comment on The Johnson-Lindenstrauss Transform: An Empirical Study by Sam

Sam — Tue, 02 Nov 2010 17:39:02 +0000

PCA should be optimal (among all linear projections) if you minimize \sum (d(y_i, y_j)^2 – \delta(x_i, x_j)^2)^2, the squared distances. What is the intuition why it behaves badly for the distances itself?

Comment on The Johnson-Lindenstrauss Transform: An Empirical Study by suresh

suresh — Thu, 07 Oct 2010 04:40:15 +0000

We could I guess. There are two reasons not to though: firstly, PCA doesn’t actually preserve distances, and secondly, we have a fair bit of evidence (from the MDS paper) that PCA does a terrible job at distances (which motivated the iterative improvement schemes we use there).

But if you’re think of the larger picture of ‘dimensionality reduction’, then yes, PCA is a player. Maybe we’ll add something in before we arxiv it.

Comment on The Johnson-Lindenstrauss Transform: An Empirical Study by Sariel

Sariel — Thu, 07 Oct 2010 04:15:29 +0000

You should compare to PCA, no?