Hypercomplex-valued neural networks: beyond complex numbers and quaternions

• Grant number: 22/01831-2
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2022
• End date: June 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcos Eduardo Ribeiro Do Valle Mesquita
• Grantee: Marcos Eduardo Ribeiro Do Valle Mesquita
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• City of the host institution: Campinas

Abstract

Artificial neural networks (ANNs), including convolutional neural networks, have demonstrated outstanding results in several application areas, including image detection and classification. Concomitantly, hypercomplex-valued neural networks showed competitive or superior performance but with fewer parameters than their equivalent neural networks defined on the real numbers. Among the advantages of hypercomplex-valued ANNs, reducing the number of parameters and treating multiple values as a single entity stand out. Despite significant advances in hypercomplex-valued ANNs, most research in the area focuses on networks based on complex numbers and quaternions. However, alternative hypercomplex number algebras such as hyperbolic numbers, tessarines, and coquaternions can result in efficient hypercomplex-valued ANNs. In this context, this research project aims to investigate ANNs defined in alternative hypercomplex number algebras, considering both theoretical and practical aspects of these models. (AU)

Scientific publications

(6)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

OLIVEIRA, ANGELICA LOURENCO; VALLE, MARCOS EDUARDO; XAVIER-JUNIOR, JC; RIOS, RA. Least-Squares Linear Dilation-Erosion Regressor Trained Using a Convex-Concave Procedure. INTELLIGENT SYSTEMS, PT II, v. 13654, p. 14-pg., 2022-01-01. (22/01831-2)

VIEIRA, GUILHERME; VALLE, MARCOS EDUARDO; LOPES, WILDER. Clifford Convolutional Neural Networks for Lymphoblast Image Classification. ADVANCED COMPUTATIONAL APPLICATIONS OF GEOMETRIC ALGEBRA, ICACGA 2022, v. 13771, p. 13-pg., 2024-01-01. (22/01831-2)

VALLE, MARCOS EDUARDO; VITAL, WINGTON L.; VIEIRA, GUILHERME. Universal approximation theorem for vector- and hypercomplex-valued neural networks. NEURAL NETWORKS, v. 180, p. 14-pg., 2024-08-21. (22/01831-2)

VITAL, WINGTON L.; VIEIRA, GUILHERME; VALLE, MARCOS EDUARDO; XAVIER-JUNIOR, JC; RIOS, RA. Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks. INTELLIGENT SYSTEMS, PT II, v. 13654, p. 15-pg., 2022-01-01. (22/01831-2)

VALLE, MARCOS EDUARDO. Understanding Vector-Valued Neural Networks and Their Relationship With Real and Hypercomplex-Valued Neural Networks: Incorporating intercorrelation between features into neural networks. IEEE SIGNAL PROCESSING MAGAZINE, v. 41, n. 3, p. 10-pg., 2024-05-01. (22/01831-2)

DOS SANTOS, ALEX SANTANA; VALLE, MARCOS EDUARDO. Max-C and Min-D Projection Auto-Associative Fuzzy Morphological Memories: Theory and an Application for Face Recognition. APPLIEDMATH, v. 3, n. 4, p. 30-pg., 2023-12-01. (22/01831-2, 19/02278-2)