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Poster
Approximating Sparse PCA from Incomplete Data
ABHISEK KUNDU · Petros Drineas · Malik Magdon-Ismail

Wed Dec 09 04:00 PM -- 08:59 PM (PST) @ 210 C #62 #None
in Poster Session »

We study how well one can recover sparse principal componentsof a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems,if the sketch is close (in the spectral norm) to the original datamatrix, then one can recover a near optimal solution to the optimizationproblem by using the sketch. In particular, we use this approach toobtain sparse principal components and show that for \math{m} data pointsin \math{n} dimensions,\math{O(\epsilon^{-2}\tilde k\max{m,n})} elements gives an\math{\epsilon}-additive approximation to the sparse PCA problem(\math{\tilde k} is the stable rank of the data matrix).We demonstrate our algorithms extensivelyon image, text, biological and financial data.The results show that not only are we able to recover the sparse PCAs from the incomplete data, but by using our sparse sketch, the running timedrops by a factor of five or more.

Author Information

ABHISEK KUNDU (RENSSELAER POLYTECHNIC INST)
Petros Drineas (Rensselaer Polytechnic Institute)
Malik Magdon-Ismail (RPI)

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