Tensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbations
Abstract
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the residual. We prove convergence to the globally optimal solution under natural incoherence conditions on the low rank component, and bounded level of sparse perturbations. We compare our method with natural baselines which apply robust matrix PCA either to the {\em flattened} tensor, or to the matrix slices of the tensor. Our method can provably handle a far greater level of perturbation when the sparse tensor is block-structured. This naturally occurs in many applications such as the activity detection task in videos. Our experiments validate these findings. Thus, we establish that tensor methods can tolerate a higher level of gross corruptions compared to matrix methods.
Additional Information
Animashree Anandkumar is supported in part by Microsoft Faculty Fellowship, NSF Career Award CCF-1254106, ONR Award N00014-14-1-0665, ARO YIP Award W911NF-13-1-0084, and AFOSR YIP FA9550-15-1-0221. Yang Shi is supported by NSF Career Award CCF-1254106 and ONR Award N00014-15-1-2737, Niranjan is supported by NSF BigData Award IIS-1251267 and ONR Award N00014-15-1-2737.Attached Files
Submitted - 1510.04747.pdf
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Additional details
- Eprint ID
- 94322
- Resolver ID
- CaltechAUTHORS:20190401-123303824
- Microsoft Faculty Fellowship
- CCF-1254106
- NSF
- N00014-14-1-0665
- Office of Naval Research (ONR)
- W911NF-13-1-0084
- Army Research Office (ARO)
- FA9550-15-1-0221
- Air Force Office of Scientific Research (AFOSR)
- N00014-15-1-2737
- Office of Naval Research (ONR)
- IIS-1251267
- NSF
- Created
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2019-04-01Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field