Principal Component Analysis Based on L1-Norm Maximization

TLDR

The study proposes a principal component analysis method based on L1‑norm optimization. The method employs L1‑norm optimization, which is robust to outliers, rotation‑invariant, and is applied to multiple datasets for comparison with conventional PCA. The L1‑norm PCA is intuitive, simple, easy to implement, provably finds a locally maximal solution, and demonstrates competitive performance against conventional methods.

Abstract

A method of principal component analysis (PCA) based on a new L1-norm optimization technique is proposed. Unlike conventional PCA which is based on L2-norm, the proposed method is robust to outliers because it utilizes L1-norm which is less sensitive to outliers. It is invariant to rotations as well. The proposed L1-norm optimization technique is intuitive, simple, and easy to implement. It is also proven to find a locally maximal solution. The proposed method is applied to several datasets and the performances are compared with those of other conventional methods.