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Compressive Online Decomposition of Dynamic Signals Via N-ℓ1 Minimization With Clustered Priors

Authors
  • Luong, Huynh Van
  • Deligiannis, Nikos
  • Forchhammer, Søren
  • Kaup, Andre
Publication Date
Jan 01, 2018
Source
Online Research Database In Technology
Keywords
Language
English
License
Unknown
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Abstract

We introduce a compressive online decomposition via solving an n-ℓ1 cluster-weighted minimization to decompose a sequence of data vectors into sparse and low-rank components. In contrast to conventional batch Robust Principal Component Analysis (RPCA)-which needs to access full data-our method processes a data vector of the sequence per time instance from a small number of measurements. The n-ℓ1 cluster-weighted minimization promotes (i) the structure of the sparse components and (ii) their correlation with multiple previously-recovered sparse vectors via clustering and re-weighting iteratively. We establish guarantees on the number of measurements required for successful compressive decomposition under the assumption of slowly-varying low-rank components. Experimental results show that our guarantees are sharp and the proposed algorithm outperforms the state of the art.

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