Apparaît dans la collection : Geometry of Nonnegative Matrix Rank

One of many definitions gives the rank of an m x n matrix M as the smallest natural number r such that M can be factorized as AB, where A and B are m x r and r x n matrices respectively. In many applications, we are interested in factorizations of a particular form. For example, factorizations with nonnegative entries define the nonnegative rank which is notion that is used in data mining applications, statistics, complexity theory etc. We will define nonnegative rank, discuss its properties and applications. We will explain a geometric characterization of nonnegative rank using nested polytopes. Finally, we will explore uniqueness of nonnegative factorizations and how it relates to the boundaries of the set of matrices of given nonnegative rank.