We investigate tensor products of matrix factorisations. This is most naturally done by formulating matrix factorisations in terms of bimodules instead of modules. If the underlying ring is�[x1,...,xN] we show that bimodule matrix factorisations form a monoidal category. This monoidal category has

Generalised coupled tensor factorisation is a recently proposed algorithmic framework for simultaneously estimating tensor factorisation models where several observed tensors can share a set of latent factors. This paper proposes a model in this framework for coupled factorisation of piano

This paper describes the use of Non-negative Tensor Factorisation models for the separation of drums from polyphonic audio. Im-proved separation of the drums is achieved through the incorpo-ration of Gamma Chain priors into the Non-negative Tensor Fac-torisation framework. In contrast to many

A shift-invariant non-negative tensor factorisation algorithm for musical source separation is proposed which generalises previous work by allowing each source to have its own parameters rather a fixed set of parameters for all sources. This allows independent control of the number of allowable

Recently, shift invariant tensor factorisation algorithms have been proposed for the purposes of sound source separation of pitched musical instruments. However, existing algorithms require the use of log-frequency spectrograms to allow shift invariance in frequency which causes problems when

, for all i, the induced subgraph G[Vi] is in Pi. A property P is reducible if there are properties Q, R such that P = Q ◦ R; otherwise it is irreducible. Mihók, Semaniˇsin and Vasky [J. Graph Theory 33 (2000), 44–53] gave a factorisation for any additive hereditary property P into a given number dc

A direct method is described for effecting the explicit Wiener-Hopf factorisation of a class of (2 x 2}—matrices. The class is determined such that the factorisation problem can be reduced to a matrix Hilbert problem which involves an upper or lower triangular matrix. Then the matrix Hilbert

by the successes of the two dimensional LDA (2DLDA) for face recognition, we develop a general tensor discriminant analysis (GTDA) as a preprocessing step for LDA. The benefits of GTDA compared with existing preprocessing methods, e.g., principal component analysis (PCA) and 2DLDA, include 1) the USP is reduced

moments (typically, of second- and third-order). Specifically, parameter estimation is reduced to the problem of extracting a certain (orthog-onal) decomposition of a symmetric tensor derived from the moments; this decomposition can be viewed as a natural generalization of the singular value decomposition

; and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in generalized eigenvalue decomposition. We provide extensive experiments by encoding face images as 2nd or 3rd order tensors to demonstrate that the proposed DATER algorithm based