Iteratively Reweighted Least Squares Algorithms for L1-Norm Principal Component Analysis

TL;DR

This paper introduces new iteratively reweighted least squares algorithms for L1-norm PCA, providing convergence analysis and demonstrating superior performance over existing methods through computational experiments.

Contribution

It presents both exact and approximate algorithms for L1 PCA based on reweighted least squares, with proven convergence and improved efficiency.

Findings

Proposed algorithms outperform benchmarks in computational tests.

Algorithms demonstrate consistent convergence behavior.

L1 PCA effectively reduces data dimensionality with robust error measurement.

Abstract

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of the reconstructed data, we propose an exact reweighted and an approximate algorithm based on iteratively reweighted least squares. We provide convergence analyses, and compare their performance against benchmark algorithms in the literature. The computational experiment shows that the proposed algorithms consistently perform best.