Search Results for author: Alejandro Parada-Mayorga

Found 13 papers, 0 papers with code

Sampling and Uniqueness Sets in Graphon Signal Processing

no code implementations11 Jan 2024 Alejandro Parada-Mayorga, Alejandro Ribeiro

We state the formal definition of a $\Lambda-$removable set and conditions under which a bandlimited graphon signal can be represented in a unique way when its samples are obtained from the complement of a given $\Lambda-$removable set in the graphon.

Non Commutative Convolutional Signal Models in Neural Networks: Stability to Small Deformations

no code implementations5 Oct 2023 Alejandro Parada-Mayorga, Landon Butler, Alejandro Ribeiro

In this paper we discuss the results recently published in~[1] about algebraic signal models (ASMs) based on non commutative algebras and their use in convolutional neural networks.

Lie Group Algebra Convolutional Filters

no code implementations8 May 2023 Harshat Kumar, Alejandro Parada-Mayorga, Alejandro Ribeiro

We show that traditional group convolutions are one particular instantiation of a more general Lie group algebra homomorphism associated to an algebraic signal model rooted in the Lie group algebra $L^{1}(G)$ for given Lie group $G$.

Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs

no code implementations15 Dec 2022 Alejandro Parada-Mayorga, Zhiyang Wang, Alejandro Ribeiro

In this paper we propose a pooling approach for convolutional information processing on graphs relying on the theory of graphons and limits of dense graph sequences.

Dimensionality Reduction

Algebraic Convolutional Filters on Lie Group Algebras

no code implementations31 Oct 2022 Harshat Kumar, Alejandro Parada-Mayorga, Alejandro Ribeiro

Group convolutional neural networks are a useful tool for utilizing symmetries known to be in a signal; however, they require that the signal is defined on the group itself.

Learning with Multigraph Convolutional Filters

no code implementations28 Oct 2022 Landon Butler, Alejandro Parada-Mayorga, Alejandro Ribeiro

In this paper, we introduce a convolutional architecture to perform learning when information is supported on multigraphs.

Convolutional Learning on Multigraphs

no code implementations23 Sep 2022 Landon Butler, Alejandro Parada-Mayorga, Alejandro Ribeiro

In this paper, we develop convolutional information processing on multigraphs and introduce convolutional multigraph neural networks (MGNNs).

Stability of Aggregation Graph Neural Networks

no code implementations8 Jul 2022 Alejandro Parada-Mayorga, Zhiyang Wang, Fernando Gama, Alejandro Ribeiro

We also conclude that in Agg-GNNs the selectivity of the mapping operators is tied to the properties of the filters only in the first layer of the CNN stage.

Convolutional Filtering and Neural Networks with Non Commutative Algebras

no code implementations23 Aug 2021 Alejandro Parada-Mayorga, Landon Butler, Alejandro Ribeiro

In this paper we introduce and study the algebraic generalization of non commutative convolutional neural networks.

Stability of Algebraic Neural Networks to Small Perturbations

no code implementations22 Oct 2020 Alejandro Parada-Mayorga, Alejandro Ribeiro

Algebraic neural networks (AlgNNs) are composed of a cascade of layers each one associated to and algebraic signal model, and information is mapped between layers by means of a nonlinearity function.

Quiver Signal Processing (QSP)

no code implementations22 Oct 2020 Alejandro Parada-Mayorga, Hans Riess, Alejandro Ribeiro, Robert Ghrist

In this paper we state the basics for a signal processing framework on quiver representations.

Algebraic Neural Networks: Stability to Deformations

no code implementations3 Sep 2020 Alejandro Parada-Mayorga, Alejandro Ribeiro

An AlgNN is a stacked layered information processing structure where each layer is conformed by an algebra, a vector space and a homomorphism between the algebra and the space of endomorphisms of the vector space.

Graphon Pooling in Graph Neural Networks

no code implementations3 Mar 2020 Alejandro Parada-Mayorga, Luana Ruiz, Alejandro Ribeiro

In this work, we propose a new strategy for pooling and sampling on GNNs using graphons which preserves the spectral properties of the graph.

Dimensionality Reduction

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