Efficient L1-Norm Principal-Component Analysis via Bit Flipping

6 Oct 2016Panos P. MarkopoulosSandipan KunduShubham ChamadiaDimitris A. Pados

It was shown recently that the $K$ L1-norm principal components (L1-PCs) of a real-valued data matrix $\mathbf X \in \mathbb R^{D \times N}$ ($N$ data samples of $D$ dimensions) can be exactly calculated with cost $\mathcal{O}(2^{NK})$ or, when advantageous, $\mathcal{O}(N^{dK - K + 1})$ where $d=\mathrm{rank}(\mathbf X)$, $K<d$ [1],[2]. In applications where $\mathbf X$ is large (e.g., "big" data of large $N$ and/or "heavy" data of large $d$), these costs are prohibitive... (read more)

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