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Cemgil, “Probabilistic latent tensor factorization
 in LVA/ICA, 2010
"... Abstract. We develop a probabilistic framework for multiway analysis of high dimensional datasets. By exploiting a link between graphical models and tensor factorization models we can realize any arbitrary tensor factorization structure, and many popular models such as CP or TUCKER models with Eucli ..."
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Cited by 13 (0 self)
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with Euclidean error and their nonnegative 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
Generalised Coupled Tensor Factorisation
"... We derive algorithms for generalised tensor factorisation (GTF) by building upon the wellestablished 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 fam ..."
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We derive algorithms for generalised tensor factorisation (GTF) by building upon the wellestablished 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
Nonnegative tensor factorisation for sound source separation
 IN: PROCEEDINGS OF IRISH SIGNALS AND SYSTEMS CONFERENCE
, 2005
"... ... 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, and the sepa ..."
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Cited by 28 (2 self)
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... 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
prediction via generalized coupled tensor factorisation
 in ECML/PKDDWorkshop on Collective Learning and Inference on Structured Data
, 2012
"... Abstract. This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as heterogeneous data, i.e., datasets in the form of ..."
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Cited by 4 (1 self)
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of matrices and higherorder 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 higherorder tensors/matrices with common latent factors
Shifted 2D Nonnegative Tensor Factorisation
"... ... developed as a means of separating harmonic instruments from single channel mixtures. This technique uses a model which is convolutive in both time and frequency, and so can capture instruments which have both timevarying spectra and timevarying fundamental frequencies simultaneously. However, ..."
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Cited by 5 (2 self)
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, in many cases two or more channels are available, in which case it would be advantageous to have a multichannel version of the algorithm. To this end, a shifted 2D Nonnegative Tensor Factorisation algorithm is derived, which extends Nonnegative Matrix Factor 2D Deconvolution to the multichannel case
User assisted separation using tensor factorisations
 in 20th European Signal Processing Conference (EUSIPCO 2012
, 2012
"... This Conference Paper is brought to you for free and open access by the ..."
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Cited by 1 (0 self)
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This Conference Paper is brought to you for free and open access by the
FACTORISED SOLUTIONS OF TEMPERLEYLIEB qKZ EQUATIONS ON A SEGMENT
, 2008
"... We study the qdeformed KnizhnikZamolodchikov equation in path representations of the TemperleyLieb algebras. We consider two types of open boundary conditions, and in both cases we derive factorised expressions for the solutions of the qKZ equation in terms of Baxterised DemazurreLusztig operat ..."
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Cited by 15 (3 self)
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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
Sound Source Separation using Shifted Nonnegative Tensor Factorisation
 Proceedings on the IEE Conference on Audio and Speech Signal Processing (ICASSP
, 2006
"... Recently, shifted Nonnegative Matrix Factorisation was developed as a means of separating harmonic instruments from single channel mixtures. However, in many cases two or more channels are available, in which case it would be advantageous to have a multichannel version of the algorithm. To this end ..."
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Cited by 15 (0 self)
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. To this end, a shifted Nonnegative Tensor Factorisation algorithm is derived, which extends shifted Nonnegative Matrix Factorisation to the multichannel case. The use of this algorithm for multichannel sound source separation of harmonic instruments is demonstrated. Further, it is shown that the algorithm
On Triple Factorisations of Finite Groups
, 2009
"... This paper introduces and develops a general framework for studying triple factorisations of the form G = ABA of finite groups G, with A and B subgroups of G. We call such a factorisation nondegenerate if G ̸ = AB. Consideration of the action of G by right multiplication on the right cosets of B lea ..."
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Cited by 2 (1 self)
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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.
Aggregation and Ordering in Factorised Databases
"... Acommonapproach todataanalysis involvesunderstanding andmanipulatingsuccinctrepresentationsofdata. Inearlier work, we put forward a succinct representation system for relational data called factorised databases and reported on the mainmemory query engine FDB for selectprojectjoin queries on such ..."
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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
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