Tessarine and Quaternion-Valued Deep Neural Networks for Image Classification

Abstract

Many image processing and analysis tasks are performed with deep neural networks. Although the vast majority of advances have been made with real numbers, recent works have shown that complex and hypercomplex-valued networks may achieve better results. In this paper, we address quaternion-valued and introduce tessarine-valued deep neural networks, including tessarine-valued 2D convolutions. We also address initialization schemes and hypercomplex batch normalization. Finally, a tessarine-valued ResNet model with hypercomplex batch normalization outperformed the corresponding real and quaternion-valued networks on the CIFAR dataset.

Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks

“…However, besides the quaternions, many other hypercomplex-valued algebras exist, including the coquaternions, the tessarines, Clifford algebras, and Cayley-Dickson algebras. The tessarines, introduced by Cockle a few years after the introduction of quaternions, is a commutative hypercomplex algebra that has been effectively used for signal processing and the development of neural networks [17], [18], [19], [20], [21]. The Clifford algebras comprise a broad family of associative hypercomplex algebras with interesting geometrical properties [22], [23], [24].…”