There have been several attempts to extend the parameters (weights and
thresholds) of the usual real-valued neural networks to higher dimensions
(complex numbers, 3-dimensional vectors, quaterninons, etc.). We call such neural networks with high-dimensional parameters high-dimensional neural networks. High-dimensional neural networks can deal with a cluster of something
(for example, 4-dimensional vector consisting of height, width, breadth
and time, and a N-dimensional vector consisting of N particles and so on)
and will extend the applicable domains of artificial neural networks.
We already proposed the following high-dimensional neural networks:
Related papers：
1. Kobayashi, M., Muramatsu, J. and Yamazaki, H., "High Dimensional Neural Network by Linear Connections of Matrix"，IEICE Trans. Fundamentals, Vol.J85-A, No.7, pp.763-770, 2002 (in Japanese).
Content: The authors discussed high-dimensional neural networks from the point of
view of the vector representation.
2. Kobayashi, M.., "Three-Dimensional Associative Memory Using Exterior Product"，IEE Trans. EIS, Vol.124, No.1, pp.150-156, 2004 (in Japanese).
Content: The author proposed a mutually connected three-dimensional neural network
model with exterior product calculations and investigated its performance.
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