# Efficient L1-Norm Principal-Component Analysis via Bit Flipping

@article{Markopoulos2017EfficientLP, title={Efficient L1-Norm Principal-Component Analysis via Bit Flipping}, author={Panos P. Markopoulos and Sandipan Kundu and Shubham Chamadia and Dimitris A. Pados}, journal={IEEE Transactions on Signal Processing}, year={2017}, volume={65}, pages={4252-4264} }

It was shown recently that the <inline-formula><tex-math notation="LaTeX">$K$</tex-math></inline-formula> L1-norm principal components (L1-PCs) of a real-valued data matrix <inline-formula><tex-math notation="LaTeX">$\mathbf X \in \mathbb {R}^{D \times N}$</tex-math></inline-formula> (<inline-formula><tex-math notation="LaTeX">$N$</tex-math> </inline-formula> data samples of <inline-formula><tex-math notation="LaTeX">$D$</tex-math></inline-formula> dimensions) can be exactly calculated with…

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L1-BF is presented: a novel, near-optimal algorithm that calculates the K L1-PCs of X with cost O (NDmin{N, D} + N2(K4 + DK2) + DNK3), comparable to that of standard (L2-norm) Principal-Component Analysis.

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