Abstract: Two-layered neural networks are well known as autoencoders (AEs) in order to reduce the dimensionality of data. AEs are successfully employed as pre-trained layers of neural networks for classification tasks. Most of the existing studies conceived real-valued AEs in real-valued neural networks. This study investigated complex- and quaternion-valued AEs for complex- and quaternion-valued neural networks. Inputs, weights, biases, and outputs in complex-valued AE (CAE) are complex variables, whereas those in quaternion-valued AE (QAE) are quaternions. In both methods, a split-type activation function is used in the hidden and output units. To deal with the images using the proposed methods, pairs of pixels are allotted to complex-valued inputs in the CAE and quartets of pixels are allotted to quaternion-valued inputs in the QAE. Proposed autoencoders are tested and performance compared with conventional AE for several tasks which are encoding/decoding, handwritten numeral recognition and large-scale multi-class classification. Proposed CAE and QAE revealed as good recognition methods for the tasks and outperformed conventional AE with significance performance in case of large-scale multi-class images recognition.

Ryusuke Hata, M. A. H. Akhand and Kazuyuki Murase, “Multi-Valued Autoencoders and Classification of Large-Scale Multi-Class Problem” International Journal of Advanced Computer Science and Applications(IJACSA), 8(11), 2017. http://dx.doi.org/10.14569/IJACSA.2017.081103

@article{Hata2017,
title = {Multi-Valued Autoencoders and Classification of Large-Scale Multi-Class Problem},
journal = {International Journal of Advanced Computer Science and Applications},
doi = {10.14569/IJACSA.2017.081103},
url = {http://dx.doi.org/10.14569/IJACSA.2017.081103},
year = {2017},
publisher = {The Science and Information Organization},
volume = {8},
number = {11},
author = {Ryusuke Hata and M. A. H. Akhand and Kazuyuki Murase}
}