We introduce a compressive online decomposition via solving an nℓ1 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.
Luong, VH, Deligiannis, N, Forchhammer, S & Kaup, A 2018, Compressive online decomposition of dynamic signals via n-l1 minimization with clustered priors. in IEEE Statistical Signal Processing Workshop: SSP. pp. 1-5.
Luong, V. H., Deligiannis, N., Forchhammer, S., & Kaup, A. (2018). Compressive online decomposition of dynamic signals via n-l1 minimization with clustered priors. In IEEE Statistical Signal Processing Workshop: SSP (pp. 1-5)
@inproceedings{f25effccf6754478b4a8e56bd878cfba,
title = "Compressive online decomposition of dynamic signals via n-l1 minimization with clustered priors",
abstract = "We introduce a compressive online decomposition via solving an nℓ1 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.",
keywords = "Robust PCA, sparsity",
author = "Luong, \{Van Huynh\} and Nikolaos Deligiannis and Soren Forchhammer and Andr{\'e} Kaup",
year = "2018",
language = "English",
pages = "1--5",
booktitle = "IEEE Statistical Signal Processing Workshop",
}