Robust Kronecker component analysis
File(s)
Accepted version
Author(s)
Bahri, M
Panagakis, Y
Zafeiriou, SP
Type
Journal Article
Abstract
Dictionary learning and component analysis models are fundamental for learning compact representations relevant to a given task. The model complexity is encoded by means of structure, such as sparsity, low-rankness, or nonnegativity. Unfortunately, approaches like K-SVD that learn dictionaries for sparse coding via Singular Value Decomposition (SVD) are hard to scale, and fragile in the presence of outliers. Conversely, robust component analysis methods such as the Robust Principal Component Analysis (RPCA) are able to recover low-complexity representations from data corrupted with noise of unknown magnitude and support, but do not provide a dictionary that respects the structure of the data, and also involve expensive computations. In this paper, we propose a novel Kronecker-decomposable component analysis model, coined as Robust Kronecker Component Analysis (RKCA), that combines ideas from sparse dictionary learning and robust component analysis. RKCA has several appealing properties, including robustness to gross corruption; it can be used for low-rank modeling, and leverages separability to solve significantly smaller problems. We design an efficient learning algorithm by drawing links with tensor factorizations, and analyze its optimality and low-rankness properties. The effectiveness of the proposed approach is demonstrated on real-world applications, namely background subtraction and image denoising and completion, by performing a thorough comparison with the current state of the art.
Date Issued
2019-10-01
Date Acceptance
2018-11-06
Citation
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019, 41 (10), pp.2365-2379
ISSN
0162-8828
Publisher
Institute of Electrical and Electronics Engineers
Start Page
2365
End Page
2379
Journal / Book Title
IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume
41
Issue
10
Copyright Statement
© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor
Engineering & Physical Science Research Council (E
Identifier
https://ieeexplore.ieee.org/document/8536486
Grant Number
EP/N007743/1
Subjects
Artificial Intelligence & Image Processing
0801 Artificial Intelligence and Image Processing
0806 Information Systems
0906 Electrical and Electronic Engineering
Publication Status
Published
Date Publish Online
2018-11-14