OPIT: A Simple but Effective Method for Sparse Subspace Tracking in High-Dimension and Low-Sample-Size Context

被引：0

作者：

Le, Thanh Trung ^{[1
,2
]}

Abed-Meraim, Karim ^{[2
,3
]}

Trung, Nguyen Linh ^{[1
]}

Hafiane, Adel ^{[2
]}

机构：

[1] VNU Univ Engn & Technol, Hanoi 100000, Vietnam

[2] Univ Orleans, PRISME, INSA CVL, F-45100 Orleans, France

[3] Acad Inst France, F-75005 Paris, France

来源：

IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2024年 / 72卷

关键词：

Sparse subspace tracking; data streams; high dimensions; thresholding; power iteration; OPTIMAL RATES; POWER METHOD; SEMIDEFINITE RELAXATIONS; ROBUST-PCA; PRINCIPAL; COVARIANCE; ALGORITHM; CONVERGENCE; CONSISTENCY;

D O I：

10.1109/TSP.2023.3349070

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

In recent years, sparse subspace tracking has attracted increasing attention in the signal processing community. In this paper, we propose a new provable effective method called OPIT (which stands for Online Power Iteration via Thresholding) for tracking the sparse principal subspace of data streams over time. Particularly, OPIT introduces a new adaptive variant of power iteration with space and computational complexity linear to the data dimension. In addition, a new column-based thresholding operator is developed to regularize the subspace sparsity. Utilizing both advantages of power iteration and thresholding operation, OPIT is capable of tracking the underlying subspace in both the classical regime and high dimensional regime. We also present a theoretical result on its convergence to verify its consistency in high dimensions. Several experiments are carried out on both synthetic and real data to demonstrate the performance of OPIT.

引用

页码：521 / 534

页数：14