with Euclidean error and their non-negative variants with KL error appear as special cases. Due to the duality between exponential families and Bregman divergences, we can cast the problem as inference in a model with Gaussian or Poisson components, where tensor factorisation reduces to a parameter estimation

We derive algorithms for generalised tensor factorisation (GTF) by building upon the well-established theory of Generalised Linear Models. Our algorithms are general in the sense that we can compute arbitrary factorisations in a message passing framework, derived for a broad class of exponential

... is introduced which extends current matrix factorisation techniques to deal with tensors. The effectiveness of the algorithm is then demonstrated through tests on synthetic data. The algorithm is then employed as a means of performing sound source separation on two channel mixtures

of matrices and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com-mon latent factors

, in many cases two or more channels are available, in which case it would be advantageous to have a multi-channel version of the algorithm. To this end, a shifted 2D Non-negative Tensor Factorisation algorithm is derived, which extends Non-negative Matrix Factor 2D Deconvolution to the multi-channel case

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-Lusztig operators. These expressions are alternative to known integral solutions for tensor product representations. The factorised expressions reveal the algebraic structure within the qKZ equation, and effectively reduce it to a set of truncation conditions on a single scalar function. The factorised expressions

. To this end, a shifted Non-negative Tensor Factorisation algorithm is derived, which extends shifted Non-negative Matrix Factorisation to the multi-channel case. The use of this algorithm for multi-channel sound source separation of harmonic instruments is demonstrated. Further, it is shown that the algorithm

is given for reducing the study of nondegenerate triple factorisations to those in which G acts faithfully and primitively on the cosets of A. This involves study of a wreath product construction for triple factorisations.

on such databases. In this paper, we extend FDB to support a larger class of practical queries with aggregates and ordering. This requires novel optimisation and evaluation techniques. We show how factorisation coupled with partial aggregation can effectively reduce the number of operations needed for query