Two Proposals for Robust PCA using Semidefinite Programming

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.

References in corpus (1)

• Principal Component Analysis with Contaminated Data: The High Dimensional Case

Cited by in corpus (21)

• Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery
• A Unified Framework for High-Dimensional Analysis of M-Estimators with Decomposable Regularizers
• Global rates of convergence for nonconvex optimization on manifolds
• Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions
• Optimal Algorithms for $L_1$-subspace Signal Processing
• Robust PCA via Nonconvex Rank Approximation
• An Online Algorithm for Separating Sparse and Low-dimensional Signal Sequences from their Sum
• Coherence Pursuit: Fast, Simple, and Robust Principal Component Analysis
• Efficient L1-Norm Principal-Component Analysis via Bit Flipping
• An Overview of Robust Subspace Recovery
• L1-norm Principal-Component Analysis of Complex Data
• A Simple and Fast Algorithm for L1-norm Kernel PCA
• Identifying Outliers in Large Matrices via Randomized Adaptive Compressive Sampling
• Fast, Robust and Non-convex Subspace Recovery
• lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers
• Iteratively Reweighted Least Squares Algorithms for L1-Norm Principal Component Analysis
• Simplicial faces of the set of correlation matrices
• Completing Low-Rank Matrices with Corrupted Samples from Few Coefficients in General Basis
• Closed-Form, Provable, and Robust PCA via Leverage Statistics and Innovation Search
• Optimization for L1-Norm Error Fitting via Data Aggregation
• Robust PCA via Regularized REAPER with a Matrix-Free Proximal Algorithm