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Sparse principal component of a rank-deficient matrix

Asteris Megasthenis, Papailiopoulos Dimitrios, Karystinos Georgios

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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
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Summary

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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