Efficient L1-Norm Principal-Component Analysis via Bit Flipping

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Authors P. Markopoulos, S. Kundu, Shubham Chamadia, D. Pados
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Paper Abstract It was shown recently that the K L1-norm principal components (L1-PCs) of a real-valued data matrix X ∈ R D×N (N data samples of D dimensions) can be exactly calculated with cost O(2 NK ) or, when advantageous, O(N dK - K + 1 ) where d=rank (X), K<;d. In applications where X is large (e.g., “big” data of large N and/or “heavy” data of large d), these costs are prohibitive. In this paper, we present a novel suboptimal algorithm for the calculation of the K <; d L1-PCs of X of cost O (ND min {N, D} + N 2 K 2 (K 2 + d)), which is comparable to that of standard L2-norm PC analysis. Our theoretical and experimental studies show that the proposed algorithm calculates the exact optimal L1-PCs with high frequency and achieves higher value in the L1-PC optimization metric than any known alternative algorithm of comparable computational cost. The superiority of the calculated L1-PCs over standard L2-PCs (singular vectors) in characterizing potentially faulty data/measurements is demonstrated with experiments in data dimensionality reduction and disease diagnosis from genomic data.
Date of publication 2017
Code Programming Language Python

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