Nonnegative Matrix Factorization (NMF) can be used to approximate a large nonnegative matrix as a product of two smaller nonnegative matrices. This paper shows in detail how an NMF algorithm based on Newton iteration can be derived utilizing the general Karush-KuhnTucker (KKT) conditions for first-order optimality. This algorithm is suited for parallel execution on shared-memory systems. It was...

Matrix factorization or factor analysis is an important task helpful in the analysis of high dimensional real world data. There are several well known methods and algorithms for factorization of real data but many application areas including information retrieval, pattern recognition and data mining often require processing of binary rather than real data. Unfortunately, the methods used for re...

We give an algorithm for computing approximate PSD factorizations of nonnegative matrices. The running time of the algorithm is polynomial in the dimensions of the input matrix, but exponential in the PSD rank and the approximation error. The main ingredient is an exact factorization algorithm when the rows and columns of the factors are constrained to lie in a general polyhedron. This strictly...

This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an m-by-n nonnegative matrix X and an integer k, the PSD factorization problem consists in finding, if possible, symmetric k-by-k positive semidefinite matrices {A, ..., A} and {B, ..., B} such that Xi,j = trace(AB) for i = 1, ...,m, and ...

Nonnegative matrix factorization (NMF) is an unsupervised technique to represent nonnegative data as linear combinations of nonnegative bases, which has shown impressive performance for source separation. However, its source separation performance degrades when one signal can also be described well with the bases for the interfering source signals. In this paper, we propose a discriminative NMF...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author He Zhang Name of the doctoral dissertation Advances in Nonnegative Matrix Decomposition with Application to Cluster Analysis Publisher School of Science Unit Department of Information and Computer Science Series Aalto University publication series DOCTORAL DISSERTATIONS 127/2014 Field of research Machine Learning Manuscript su...