Robust Sparse Subspace Tracking from Corrupted Data Observations

2025-09-20

AI Summary

This work addresses the problem of robust dynamic subspace estimation and tracking in high-dimensional data streams corrupted by non-Gaussian noise and sparse outliers. To tackle this, we propose a novel online algorithm grounded in α-divergence minimization. By incorporating α-divergence into the subspace optimization objective, the method explicitly enhances robustness against heavy-tailed noise and impulsive data corruptions. Further, it integrates sparse subspace modeling with a low-rank iterative update scheme, ensuring theoretical convergence while substantially reducing computational and memory complexity. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed approach achieves significantly lower subspace tracking error and higher direction-of-arrival (DOA) estimation accuracy compared to state-of-the-art robust PCA and adaptive subspace methods. These results validate its effectiveness and practicality for dynamic signal processing under challenging non-Gaussian and sparse corruption conditions.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Subspace tracking is a fundamental problem in signal processing, where the goal is to estimate and track the underlying subspace that spans a sequence of data streams over time. In high-dimensional settings, data samples are often corrupted by non-Gaussian noises and may exhibit sparsity. This paper explores the alpha divergence for sparse subspace estimation and tracking, offering robustness to data corruption. The proposed method outperforms the state-of-the-art robust subspace tracking methods while achieving a low computational complexity and memory storage. Several experiments are conducted to demonstrate its effectiveness in robust subspace tracking and direction-of-arrival (DOA) estimation.

Problem

• Tracking sparse subspaces from corrupted high-dimensional data streams
• Developing robust subspace estimation using alpha divergence method
• Achieving low computational complexity in subspace tracking applications

Innovation

• Uses alpha divergence for robust subspace tracking
• Handles sparse data with non-Gaussian noise corruption
• Achieves low computational complexity and memory usage