Energy-based sequential sampling for low-rank PSD-matrix approximation
Résumé
We introduce a pseudoconvex differentiable relaxation of the column-sampling problem for the Nyström approximation of positive-semidefinite (PSD) matrices. The relaxation is based on the interpretation of PSD matrices as integral operators, and uses the supports of measures to characterise samples of columns. We describe a class of gradient-based sequential sampling strategies which leverages the properties of the considered framework and demonstrate its ability to produce accurate Nyström approximations. As an important feature, the proposed strategies rely on an isometric representation of weighted PSD matrices as potentials to efficiently handle matrices of very large scale.
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