The sparse principal component of a constant-rank matrixThe sparse principal component of a constant-rank matrix Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-232014enThe 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.Δημοσίευση σε επιστημονικό περιοδικό http://creativecommons.org/licenses/by/4.0/IEEE Transactions on Information Theory4602281 - 2290 Asteris Megasthenis Αστερης Μεγασθενης Papailiopoulos, D.S Karystinos Georgios Καρυστινος Γεωργιος Institute of Electrical and Electronics Engineers Eigenvalues and eigenfunctions feature extraction information processing machine learning algorithms principal component analysis signal processing algorithms