no code implementations • 11 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.
no code implementations • 5 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.
no code implementations • 8 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 $G$.
no code implementations • 15 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.
no code implementations • 31 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.
no code implementations • 28 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.
no code implementations • 23 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).
no code implementations • 8 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.
no code implementations • 23 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.
no code implementations • 22 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.
no code implementations • 22 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.
no code implementations • 3 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.
no code implementations • 3 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.