Nonnegative matrix factorisation and tri-factorisation Nonnegative matrix factorisation (NMF) and tri-factorisation (NMTF) methods decompose a given matrix R into two or three smaller matrices so that R ≈ UV T or R ≈ FSG , respectively. Schmidt, Winther and Hansen (2009) introduced a Bayesian version of nonnegative matrix factorisation (left), which we extend to matrix tri-factorisation (right)...

Let V ∈ R be a nonnegative matrix. The nonnegative matrix factorization (NNMF) problem consists of finding nonnegative matrix factors W ∈ R and H ∈ R such that V ≈ WH. Lee and Seung proposed two algorithms which find nonnegative W and H such that ‖V −WH‖F is minimized. After examining the case in which r = 1 about which a complete characterization of the solution is possible, we consider the ca...

We construct new families of symplectic 4-manifolds with nonnegative signature that are interesting with respect to the geography problem. In particular, we construct an irreducible symplectic 4-manifold that is homeomorphic to mCP#mCP for each odd integer m satisfying m ≥ 49.

In non-negative matrix factorization, it is difficult to find the optimal non-negative factor matrix in each iterative update. However, with the help of transformation matrix, it is able to derive the optimal non-negative factor matrix for the transformed cost function. Transformation matrix based nonnegative matrix factorization method is proposed and analyzed. It shows that this new method, w...

Nonnegative matrix factorization (NMF) aims at factoring a data matrix into low-rank latent factor matrices with nonnegativity constraints on (one or both of) the factors. Specifically, given a data matrix X ∈ RM×N and a target rank R, NMF seeks a factorization model X ≈WH>, W ∈ RM×R, H ∈ RN×R, to ‘explain’ the data matrix X, where W ≥ 0 and/or H ≥ 0 and R ≤ min{M,N}. At first glance, NMF is no...

Nonnegative matrix factorization (NMF) has become a prominent signal processing and data analysis technique. To address streaming data, online methods for NMF have been introduced recently, mainly restricted to the linear model. In this paper, we propose a framework for online nonlinear NMF, where the factorization is conducted in a kernel-induced feature space. By exploring recent advances in ...

Boolean control networks (BCNs) are recently attracting considerable interest as computational models for genetic and cellular networks. Addressing control-theoretic problems in BCNs may lead to a better understanding of the intrinsic control in biological systems, as well as to developing suitable protocols for manipulating biological systems using exogenous inputs. We introduce two definition...