Conference paper
Compressive Online Decomposition of Dynamic Signals Via N-ℓ1 Minimization With Clustered Priors
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.
| Language: | English |
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| Publisher: | IEEE |
| Year: | 2018 |
| Pages: | 846-50 |
| Proceedings: | 2018 IEEE Workshop on Statistical Signal Processing |
| ISBN: | 1538615703 , 1538615711 , 153861572X , 153861572x , 9781538615706 , 9781538615713 , 9781538615720 and 9781538615703 |
| Types: | Conference paper |
| DOI: | 10.1109/SSP.2018.8450742 |
| ORCIDs: | Forchhammer, Søren |
Clustering algorithms Conferences Correlation Minimization Signal processing Signal processing algorithms Sparse matrices batch robust principal component analysis cluster-weighted minimization clustered priors clustering compressive decomposition compressive online decomposition data compression data vector dynamic signals iterative methods low-rank model n-ℓ<sub>1 </sub>minimization n-ℓ<sub>1</sub> cluster-weighted minimization optimisation pattern clustering prior information slowly-varying low-rank components source separation sparse components sparse signal sparse vectors vectors
