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On the monoidal structure of matrix bifactorisations
, 2009
"... 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 a ..."
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Cited by 14 (5 self)
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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
SCORE GUIDED AUDIO RESTORATION VIA GENERALISED COUPLED TENSOR FACTORISATION
"... 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 spectrogr ..."
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Cited by 5 (1 self)
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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
USING TENSOR FACTORISATION MODELS TO SEPARATE DRUMS FROM POLYPHONIC MUSIC
"... This paper describes the use of Nonnegative Tensor Factorisation models for the separation of drums from polyphonic audio. Improved separation of the drums is achieved through the incorporation of Gamma Chain priors into the Nonnegative Tensor Factorisation framework. In contrast to many previo ..."
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Cited by 5 (1 self)
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This paper describes the use of Nonnegative Tensor Factorisation models for the separation of drums from polyphonic audio. Improved separation of the drums is achieved through the incorporation of Gamma Chain priors into the Nonnegative Tensor Factorisation framework. In contrast to many
Musical Source Separation using Generalised NonNegative Tensor Factorisation models
"... A shiftinvariant nonnegative 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 note ..."
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Cited by 2 (2 self)
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A shiftinvariant nonnegative 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
Extended Nonnegative Tensor Factorisation models for Musical Sound Source Separation
"... 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 logfrequency spectrograms to allow shift invariance in frequency which causes problems when attemp ..."
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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 logfrequency spectrograms to allow shift invariance in frequency which causes problems when
Unique factorisation of additive inducedhereditary properties
"... An additive hereditary graph property is a set of graphs, closed under isomorphism and under taking subgraphs and disjoint unions. Let P1,...,Pn be additive hereditary graph properties. A graph G has property (P1 ◦ · · · ◦ Pn) if there is a partition (V1,...,Vn) of V (G) into n sets such that, f ..."
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Cited by 6 (5 self)
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, 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
Matrix WienerHopf factorisation II by
, 1984
"... A direct method is described for effecting the explicit WienerHopf 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 problem ..."
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A direct method is described for effecting the explicit WienerHopf 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
General tensor discriminant analysis and Gabor featuresforgaitrecognition,”IEEE Trans
 Pattern Anal. Mach. Intell
, 2007
"... Abstract — The traditional image representations are not suited to conventional classification methods, such as the linear discriminant analysis (LDA), because of the under sample problem (USP): the dimensionality of the feature space is much higher than the number of training samples. Motivated by ..."
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Cited by 105 (11 self)
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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
Tensor decompositions for learning latent variable models
, 2014
"... This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models—including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation—which exploits a certain tensor structure in their loworder observable mo ..."
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Cited by 83 (7 self)
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moments (typically, of second and thirdorder). Specifically, parameter estimation is reduced to the problem of extracting a certain (orthogonal) decomposition of a symmetric tensor derived from the moments; this decomposition can be viewed as a natural generalization of the singular value decomposition
Discriminant analysis with tensor representation
 in Proc. IEEE Conf. Comput. Vision Pattern Recognit., 2005
, 2005
"... In this paper, we present a novel approach to solving the supervised dimensionality reduction problem by encoding an image object as a general tensor of 2nd or higher order. First, we propose a Discriminant Tensor Criterion (DTC), whereby multiple interrelated lowerdimensional discriminative subspa ..."
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Cited by 53 (13 self)
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; 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
Results 11  20
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1,602