Fast Bayesian Non-Negative Matrix Factorisation and Tri-Factorisation

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). Rij ∼ N (Rij|U i · V j, τ−1) τ ∼ G(τ |α, β) Rij ∼ N (Rij|F i · S ·Gj, τ−1) τ ∼ G(τ |α, β) Uik ∼ E(Uik|λU) Vjk ∼ E(Vjk|λV ) Fik ∼ E(Fik|λF ) Skl ∼ E(Skl|λS) Gjl ∼ E(Gjl|λG)