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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| Vydané v: | Statistics and computing Ročník 34; číslo 5 |
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01.10.2024
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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. |
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| 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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| Keywords | Robust matrix factorization Robust SVD Density power divergence Background modelling Singular value decomposition |
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| Title | Robust singular value decomposition with application to video surveillance background modelling |
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