Extreme Learning Machines on Cayley-Dickson Algebra Applied for Color Image Auto-Encoding
| Autor: | Marcos Eduardo Valle, Guilherme Henrique Alves Vieira |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Artificial neural network
Mathematics::General Mathematics Color image Mathematics::Rings and Algebras 020206 networking & telecommunications 02 engineering and technology Mathematics::Algebraic Topology Least squares Matrix multiplication Algebra Mathematics::Group Theory Encoding (memory) Linear algebra 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Quaternion Complex number Mathematics |
| Zdroj: | IJCNN |
| DOI: | 10.1109/ijcnn48605.2020.9207495 |
| Popis: | This paper aims to provide a useful framework for extreme learning machines (ELMs) on Cayley-Dickson algebras. Cayley-Dickson algebras, which include complex numbers, quaternions, and octonions as particular instances, are hyper-complex algebras defined using a recursive procedure. Firstly, we review some basic concepts on Cayley-Dickson algebras and formulate Cayley-Dickson matrix product using real-valued linear algebra. Then, we propose the Cayley-Dickson ELMs and derive their learning using Cayley-Dickson least squares problem. Lastly, we compare the performance of real-valued and four-dimensional Cayley-Dickson ELM models, including quaternion-valued ELM, in an experiment on color image auto-encoding using the well-known CIFAR dataset. |
| Databáze: | OpenAIRE |
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