Critical Points of Matrix Least Square Distance Functions

Critical points of distance functions and applications to geometry

8. Introduction Critical points of distance functions Toponogov's theorem; first application:a Background on finiteness theorems Homotopy Finiteness Appendix. Some volume estimates Betti numbers and rank Appendix: The generalized Mayer-Vietoris estimate Rank, curvature and diameter Ricci curvature, volume and the Laplacian Appendix. The maximum principle Ricci curvature, diameter growth and fin...

A Generalized Least-Square Matrix Decomposition

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Critical points of simple functions

Critical Points for Least - Squares ProblemsInvolving

This paper deals with nonlinear least-squares problems involving the tting to data of parameterized analytic functions. For generic regression data, a general result establishes the countability, and under stronger assumptions niteness, of the set of functions giving rise to critical points of the quadratic loss function. In the special case of what are usually called \single-hidden layer neura...

A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem.  At each step of ALS algorithms two convex least square problems should be solved, which causes high com...