Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of
high-dimensional data as it automatically extracts sparse and meaningful features from a set …

Identifying the underlying structure of a data set and extracting meaningful information is a
key problem in data analysis. Simple and powerful methods to achieve this goal are linear …

This paper presents a selected tour through the theory and applications of lifts of convex
sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original …

arXiv:1412.0728v2 [math.CO] 29 Feb 2020 Page 1 SUBLINEAR EXTENSIONS OF POLYGONS
YAROSLAV SHITOV Abstract. Every convex polygon with n vertices is a linear projection of a …

This paper considers the problem of positive semidefinite factorization (PSD factorization), a
generalization of exact nonnegative matrix factorization. Given an m-by-n nonnegative …

The simplex method for linear programming is known to be highly efficient in practice, and
understanding its performance from a theoretical perspective is an active research topic. The …

In this paper we study various versions of extension complexity for polygons through the
study of factorization ranks of their slack matrices. In particular, we develop a new asymptotic …

Solving a source separation problem when the data are explained by a linear mixing of non‐
negative sources with non‐negative mixing coefficients reduces to performing a non …

Computational Approaches for Lower Bounds on the Nonnegative Rank Page 1
Computational Approaches for Lower Bounds on the Nonnegative Rank Julien Dewez …

Finding an exactNMF for matrix X, ie factors W and H such that X= WH, has proved to be a
difficult problem, even for a small factorization rank r. On this basis, his thesis explores the …