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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Bibliographic Details
Published in:Statistics and computing 2024, Vol.34 (5), Article 178
Main Authors: Roy, Subhrajyoty, Ghosh, Abhik, Basu, Ayanendranath
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Computer Science
Decomposition
Extreme values
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
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Summary: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.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-024-10493-7