A General Framework for Hypercomplex-valued Extreme Learning Machines

• URL: http://arxiv.org/abs/2101.06166v1
• Date: Fri, 15 Jan 2021 15:22:05 GMT
• Title: A General Framework for Hypercomplex-valued Extreme Learning Machines
• Authors: Guilherme Vieira and Marcos Eduardo Valle
• Abstract summary: This paper aims to establish a framework for extreme learning machines (ELMs) on general hypercomplex algebras. We show a framework to operate in these algebras through real-valued linear algebra operations. Experiments highlight the excellent performance of hypercomplex-valued ELMs to treat high-dimensional data.
• Score: 2.055949720959582
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper aims to establish a framework for extreme learning machines (ELMs) on general hypercomplex algebras. Hypercomplex neural networks are machine learning models that feature higher-dimension numbers as parameters, inputs, and outputs. Firstly, we review broad hypercomplex algebras and show a framework to operate in these algebras through real-valued linear algebra operations in a robust manner. We proceed to explore a handful of well-known four-dimensional examples. Then, we propose the hypercomplex-valued ELMs and derive their learning using a hypercomplex-valued least-squares problem. Finally, we compare real and hypercomplex-valued ELM models' performance in an experiment on time-series prediction and another on color image auto-encoding. The computational experiments highlight the excellent performance of hypercomplex-valued ELMs to treat high-dimensional data, including models based on unusual hypercomplex algebras.

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