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Institutional Repository [SANDBOX]
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/0AA164E5-8AD0-41D2-85D1-AB1786B7904C | ||
| Year | 2011 | ||
| Type of Item | Conference Full Paper | ||
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| Bibliographic Citation | M. Asteris, D. S. Papailiopoulos, and G. N. Karystinos, “Sparse principal component of a rank-deficient matrix,” in Proc. IEEE - Intern. Symp. Inform. Theory,(ISIT '11) pp. 673-677, doi: 10.1109/ISIT.2011.6034216 https://doi.org/10.1109/ISIT.2011.6034216 | ||
| Appears in Collections |
We consider the problem of identifying the sparse principal component of a rank-deficient matrix. We introduce auxiliary spherical variables and prove that there exists a set of candidate index-sets (that is, sets of indices to the nonzero elements of the vector argument) whose size is polynomially bounded, in terms of rank, and contains the optimal index-set, i.e. the index-set of the nonzero elements of the optimal solution. Finally, we develop an algorithm that computes the optimal sparse principal component in polynomial time for any sparsity degree.
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