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Monday, February 18
Calculating a Symmetry Preserving Singular Value DecompositionMili Shah, Loyola University Maryland, Baltimore
Computer Science and Mathematics Division Seminar
10:00 AM — 11:00 AM, Research Office Building (5700), Room L-204
Contact: Chris Baker (email@example.com), 865.576.7110
AbstractThe symmetry preserving singular value decomposition (SPSVD) produces the best symmetric (low rank) approximation to a set of data. These symmetric approximations are characterized via an invariance under the action of a symmetry group on the set of data. The symmetry groups of interest consist of all the non-spherical symmetry groups in three dimensions. This set includes the rotational, reflectional, dihedral, and inversion symmetry groups. In order to calculate the best symmetric (low rank) approximation, the symmetry of the data set must be determined. Therefore, matrix representations for each of the non-spherical symmetry groups have been formulated. These new matrix representations lead directly to a novel reweighting iterative method to determine the symmetry of a given data set by solving a series of minimization problems. Once the symmetry of the data set is found, the best symmetric (low rank) approximation can be established by using the SPSVD. Applications of the SPSVD to protein dynamics problems as well as facial recognition will be presented.