  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.
