The Discrete Cosine Transform on Triangles

Seifert, Bastian; Hüper, K.

doi:10.1109/icassp.2019.8682222

Cited by 2 publications

(3 citation statements)

References 15 publications

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“…ASP provides a theoretical framework for deriving a complete set of basic signal processing concepts, including convolution, for novel index domains, using as starting point a chosen shift to which convolutions should be equivariant. To date the approach was used for index domains including graphs [34,44,45], powersets (set functions) [36], meet/join lattices [37,61], and a collection of more regular domains, e.g., [39,46,49].…”

Section: Related Workmentioning

confidence: 99%

Powerset Convolutional Neural Networks

Wendler,

Alistarh,

Püschel

2019

Preprint

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We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions based on the Laplacian, as it provides not one but several basic shifts, one for each element in the ground set. Prototypical experiments with several set function classification tasks on synthetic datasets and on datasets derived from real-world hypergraphs demonstrate the potential of our new powerset CNNs.Preprint. Under review.

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Section: Related Workmentioning

confidence: 99%

Powerset Convolutional Neural Networks

Wendler,

Alistarh,

Püschel

2019

Preprint

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“…In [49] we used an elementary description of the common zeros of T n . Here we present again a more geometric point of view, using the coweights.…”

Section: Examplementioning

confidence: 99%

“…Even though there is a rather mature theory of orthogonal polynomials in several variables [55] the connection to signal processing is not vivid in the literature. Only recently the author used the multivariate Christoffel-Darboux formula of Xu [54] to derive an orthogonal version of a discrete cosine transform on lattices of triangles [49]. Unfortunately this method does not work in every case but relies on the same condition as the existence of a Gaussian cubature formula as zeros of the orthogonal polynomials.…”

Section: Introductionmentioning

confidence: 99%

FFT and orthogonal discrete transform on weight lattices of semi-simple Lie groups

Seifert

2019

Preprint

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We give two algebro-geometric inspired approaches to fast algorithms for Fourier transforms in algebraic signal processing theory based on polynomial algebras in several variables. One is based on module induction and one is based on a decomposition property of certain polynomials. The Gauss-Jacobi procedure for the derivation of orthogonal transforms is extended to the multivariate setting. This extension relies on a multivariate Christoffel-Darboux formula for orthogonal polynomials in several variables. As a set of application examples a general scheme for the derivation of fast transforms of weight lattices based on multivariate Chebyshev polynomials is derived. A special case of such transforms is considered, where one can apply the Gauss-Jacobi procedure. Keywordsalgebraic signal processing theory • Christoffel-Darboux formula • discrete cosine transform • fast Fourier transform • Gauss-Jacobi procedure • multivariate Chebyshev polynomials • orthogonal polynomials • representation theory of algebras • root systems • weight lattices Mathematics Subject Classification (2010) 65T50 • 15A23 • 33F99 • 68R01 • 16G99This work is partially supported by the European Regional Development Fund (ERDF).

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The Discrete Cosine Transform on Triangles

Cited by 2 publications

References 15 publications

Powerset Convolutional Neural Networks

Powerset Convolutional Neural Networks

FFT and orthogonal discrete transform on weight lattices of semi-simple Lie groups

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