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arXiv · 1708.01249

L1-norm Principal-Component Analysis of Complex Data

Nicholas Tsagkarakis·Panos P. Markopoulos·Dimitris A. Pados
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Abstract

L1-norm Principal-Component Analysis (L1-PCA) of real-valued data has attracted significant research interest over the past decade. However, L1-PCA of complex-valued data remains to date unexplored despite the many possible applications (e.g., in communication systems). In this work, we establish theoretical and algorithmic foundations of L1-PCA of complex-valued data matrices. Specifically, we first show that, in contrast to the real-valued case for which an optimal polynomial-cost algorithm was recently reported by Markopoulos et al., complex L1-PCA is formally NP-hard in the number of data points. Then, casting complex L1-PCA as a unimodular optimization problem, we present the first two suboptimal algorithms in the literature for its solution. Our experimental studies illustrate the sturdy resistance of complex L1-PCA against faulty measurements/outliers in the processed data.

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Nicholas Tsagkarakis, Panos P. Markopoulos, Dimitris A. Pados. 2017-08-03. L1-norm Principal-Component Analysis of Complex Data. https://doi.org/10.1109/tsp.2018.2821641

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