Efficient L1-Norm Principal-Component Analysis via Bit Flipping

no code implementations • 6 Oct 2016 • Panos P. Markopoulos, Sandipan Kundu, Shubham Chamadia, Dimitris 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].

Dimensionality Reduction