Two Proposals for Robust PCA using Semidefinite Programming

TL;DR

This paper introduces two new robust PCA methods based on semidefinite programming that effectively handle outliers, providing improved data decomposition and direction estimation with efficient algorithms.

Contribution

It presents two novel SDP-based robust PCA approaches, MDR and LLD, with computational methods and experimental validation, advancing outlier-resistant data analysis.

Findings

MDR identifies directions of large spread while reducing outlier influence

LLD separates corrupted observations to produce a low-rank data model

Numerical experiments demonstrate the effectiveness of the proposed methods

Abstract

The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation rounding (MDR), seeks directions of large spread in the data while damping the effect of outliers. The second method produces a low-leverage decomposition (LLD) of the data that attempts to form a low-rank model for the data by separating out corrupted observations. This paper also presents efficient computational methods for solving these SDPs. Numerical experiments confirm the value of these new techniques.