  


A Projective Approach to Nonnegative Matrix Factorization
Patrick Groetzner(patrick.groetznermath.uniaugsburg.de) Abstract: Nonnegative matrix factorization as a tool in data science to analyse the structure of the underlying dataset appears in various applications and enjoys great popularity. Consider a given square matrix $A$. The symmetric nonnegative matrix factorization aims for a nonnegative lowrank approximation $A\approx XX^T$ to $A$, where $X$ is entrywise nonnegative and of given order. This setting can be seen as demanding a socalled completely positive approximation of $A$. In this paper we introduce an alternating projection type approach to this setting in order to obtain symmetric nonnegative matrix factorizations. Moreover, considering a general rectangular input matrix $A$, the general nonnegative matrix factorization again aims for a nonnegative lowrank approximation to $A$ which is now of the type $A\approx XY$ for entrywise nonnegative matrices $X,Y$ of given order. Here we introduce a new perspective motivated by our results in the symmetric case in order to derive nonnegative matrix factorizations even in this general setting. Keywords: nonnegative matrix factorization, symmetric nonnegative matrix factorization, lowrank approximation, completely positive matrices Category 1: Linear, Cone and Semidefinite Programming Category 2: Applications  Science and Engineering Citation: P. Groetzner, A Projective Approach to Nonnegative Matrix Factorization. Preprint, 2019. Download: [PDF] Entry Submitted: 04/23/2019 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  