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Technical University of Crete
Technical University of Crete
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| URI | http://purl.tuc.gr/dl/dias/13F9D7BC-B98C-40E2-9705-5E257B3D5EFE | - |
| Identifier | https://doi.org/10.1109/TIT.2014.2303975 | - |
| Language | en | - |
| Extent | 9 | en |
| Title | The sparse principal component of a constant-rank matrix | en |
| Creator | Asteris Megasthenis | en |
| Creator | Αστερης Μεγασθενης | el |
| Creator | Papailiopoulos, D.S | en |
| Creator | Karystinos Georgios | en |
| Creator | Καρυστινος Γεωργιος | el |
| Publisher | Institute of Electrical and Electronics Engineers | en |
| Description | Δημοσίευση σε επιστημονικό περιοδικό | el |
| Content Summary | The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem NP-hard. In this paper, we prove that, if the matrix is positive semidefinite and its rank is constant, then its sparse principal component is polynomially computable. Our proof utilizes the auxiliary unit vector technique that has been recently developed to identify problems that are polynomially solvable. In addition, we use this technique to design an algorithm which, for any sparsity value, computes the sparse principal component with complexity O(ND+1), where N and D are the matrix size and rank, respectively. Our algorithm is fully parallelizable and memory efficient. | en |
| Type of Item | Peer-Reviewed Journal Publication | en |
| Type of Item | Δημοσίευση σε Περιοδικό με Κριτές | el |
| License | http://creativecommons.org/licenses/by/4.0/ | en |
| Date of Item | 2015-10-23 | - |
| Date of Publication | 2014 | - |
| Subject | Eigenvalues and eigenfunctions | en |
| Subject | feature extraction | en |
| Subject | information processing | en |
| Subject | machine learning algorithms | en |
| Subject | principal component analysis | en |
| Subject | signal processing algorithms | en |
| Bibliographic Citation | M. Asteris, D. S. Papailiopoulos, and G. N. Karystinos, "The sparse principal component of a constant-rank matrix," IEEE Transactions on Information Theory,vol. 60, no. 4, pp. 2281 - 2290, Apr. 2014. doi: 10.1109/TIT.2014.2303975 | en |
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