Robust singular value decomposition with application to video surveillance background modelling

The traditional method of computing singular value decomposition (SVD) of a data matrix is based on the least squares principle and is, therefore, very sensitive to the presence of outliers. Hence, the resulting inferences across different applications using the classical SVD are extremely degraded...

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Published in:	Statistics and computing Vol. 34; no. 5
Main Authors:	Roy, Subhrajyoty, Ghosh, Abhik, Basu, Ayanendranath
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.10.2024 Springer Nature B.V
Subjects:	Algorithms Artificial Intelligence Computer Science Decomposition Matrices (mathematics) Modelling Original Paper Probability and Statistics in Computer Science Robustness Singular value decomposition Statistical Theory and Methods Statistics and Computing/Statistics Programs Surveillance Video data Robust matrix factorization Robust SVD Density power divergence Background modelling Singular value decomposition
ISSN:	0960-3174, 1573-1375
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Abstract	The traditional method of computing singular value decomposition (SVD) of a data matrix is based on the least squares principle and is, therefore, very sensitive to the presence of outliers. Hence, the resulting inferences across different applications using the classical SVD are extremely degraded in the presence of data contamination. In particular, background modelling of video surveillance data in the presence of camera tampering cannot be reliably solved by the classical SVD. In this paper, we propose a novel robust singular value decomposition technique based on the popular minimum density power divergence estimator. We have established the theoretical properties of the proposed estimator such as convergence, equivariance and consistency under the high-dimensional regime where both the row and column dimensions of the data matrix approach infinity. We also propose a fast and scalable algorithm based on alternating weighted regression to obtain the estimate. Within the scope of our fairly extensive simulation studies, our method performs better than existing robust SVD algorithms. Finally, we present an application of the proposed method on the video surveillance background modelling problem.
AbstractList	The traditional method of computing singular value decomposition (SVD) of a data matrix is based on the least squares principle and is, therefore, very sensitive to the presence of outliers. Hence, the resulting inferences across different applications using the classical SVD are extremely degraded in the presence of data contamination. In particular, background modelling of video surveillance data in the presence of camera tampering cannot be reliably solved by the classical SVD. In this paper, we propose a novel robust singular value decomposition technique based on the popular minimum density power divergence estimator. We have established the theoretical properties of the proposed estimator such as convergence, equivariance and consistency under the high-dimensional regime where both the row and column dimensions of the data matrix approach infinity. We also propose a fast and scalable algorithm based on alternating weighted regression to obtain the estimate. Within the scope of our fairly extensive simulation studies, our method performs better than existing robust SVD algorithms. Finally, we present an application of the proposed method on the video surveillance background modelling problem.
ArticleNumber	178
Author	Roy, Subhrajyoty Basu, Ayanendranath Ghosh, Abhik
Author_xml	– sequence: 1 givenname: Subhrajyoty surname: Roy fullname: Roy, Subhrajyoty email: roysubhra98@gmail.com organization: Interdisciplinary Statistical Research Unit, Indian Statistical Institute – sequence: 2 givenname: Abhik surname: Ghosh fullname: Ghosh, Abhik organization: Interdisciplinary Statistical Research Unit, Indian Statistical Institute – sequence: 3 givenname: Ayanendranath surname: Basu fullname: Basu, Ayanendranath organization: Interdisciplinary Statistical Research Unit, Indian Statistical Institute
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Cites_doi	10.3390/e13010134 10.1109/ISIT.2010.5513535 10.1137/090771806 10.1007/978-3-642-37410-4_25 10.48550/arXiv.1211.7102 10.1007/BFb0021444 10.1016/j.cosrev.2019.100204 10.1142/9789814324359_0111 10.1073/pnas.1733249100 10.1561/2200000058 10.1109/CVPR.2005.309 10.1093/biomet/85.3.549 10.1214/aos/1176346793 10.18637/jss.v089.i11 10.1214/aos/1176342503 10.1214/13-AOAS649 10.1016/j.cosrev.2014.04.001 10.1214/aos/1176343347 10.1093/bioinformatics/btm069 10.32614/CRAN.package.rpca 10.1007/BF02163027 10.3390/data2030029 10.1101/gr.277525.122 10.1016/j.camwa.2005.08.009 10.32614/CRAN.package.rsvddpd 10.1109/CVPR.2012.6247848 10.5220/0007392100850095 10.1016/j.sigpro.2007.04.004 10.1006/jmva.1999.1873 10.32614/CRAN.package.pcaone 10.1137/1.9781611976465.32 10.1007/s11042-018-6165-4 10.1016/j.cviu.2013.11.009 10.1080/01621459.1993.10476301 10.1007/s40304-020-00221-8 10.1198/jasa.2009.tm08024 10.1080/10556788.2012.700713 10.1109/ICASSP.2017.7952994 10.1109/AVSS.2019.8909856 10.1214/08-AOAS227 10.1109/TIT.2011.2173156 10.1109/TPAMI.2009.112 10.1214/13-EJS847 10.3390/e22030304 10.1109/TSP.2012.2197748 10.1201/9781315369983
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Snippet	The traditional method of computing singular value decomposition (SVD) of a data matrix is based on the least squares principle and is, therefore, very...
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SubjectTerms	Algorithms Artificial Intelligence Computer Science Decomposition Matrices (mathematics) Modelling Original Paper Probability and Statistics in Computer Science Robustness Singular value decomposition Statistical Theory and Methods Statistics and Computing/Statistics Programs Surveillance Video data
Title	Robust singular value decomposition with application to video surveillance background modelling
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