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The traditional method of computing singular value decomposition (SVD) of adata matrix is based on a least squares principle, thus, is very sensitive tothe presence of outliers. Hence the resulting inferences across differentapplications using the classical SVD are extremely degraded in the presence ofdata contamination (e.g., video surveillance background modelling tasks, etc.).A robust singular value decomposition method using the minimum density powerdivergence estimator (rSVDdpd) has been found to provide a satisfactorysolution to this problem and works well in applications. For example, itprovides a neat solution to the background modelling problem of videosurveillance data in the presence of camera tampering. In this paper, weinvestigate the theoretical properties of the rSVDdpd estimator such asconvergence, equivariance and consistency under reasonable assumptions. Sincethe dimension of the parameters, i.e., the number of singular values and thedimension of singular vectors can grow linearly with the size of the data, theusual M-estimation theory has to be suitably modified with concentration boundsto establish the asymptotic properties. We believe that we have been able toaccomplish this satisfactorily in the present work. We also demonstrate theefficiency of rSVDdpd through extensive simulations.

Analysis of the rSVDdpd Algorithm: A Robust Singular Value Decomposition Method using Density Power Divergence