# L1-norm Principal-Component Analysis of Complex Data

arXiv: https://arxiv.org/abs/1708.01249 · HTML: https://mlsanity.com/paper/1708.01249/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2017.

## Built on by (most cited first, 1 of 1)

- [On Finite-Step Convergence of the Non-Greedy Algorithm and Proximal Alternating Minimization Method with Extrapolation for L1-Norm PCA](https://mlsanity.com/paper/2302.07712/) (2023)

## Abstract (arXiv)

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.