Temporal Self-Organization: A Reaction-Diffusion Framework for Spatiotemporal Memories

Gowgi, P and Garani, SS (2019) Temporal Self-Organization: A Reaction-Diffusion Framework for Spatiotemporal Memories. In: IEEE Transactions on Neural Networks and Learning Systems, 30 (2). pp. 427-448.

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Abstract

Self-organizing maps (SOMs) find numerous applications in learning, clustering, and recalling spatial input patterns. The traditional approach in learning spatiotemporal patterns is to incorporate time on the output space of a SOM along with heuristic update rules that work well in practice. Inspired by the pioneering work of Alan Turing, who used reaction-diffusion equations to explain spatial pattern formation, we develop an analogous theoretical model for a spatiotemporal memory to learn and recall temporal patterns. The contribution of the paper is threefold: 1) using coupled reaction-diffusion equations, we develop a theory from first principles for constructing a spatiotemporal SOM and derive an update rule for learning based on the gradient of a potential function; 2) we analyze the dynamics of our algorithm and derive conditions for optimally setting the model parameters; and 3) we mathematically quantify the temporal plasticity effect observed during recall in response to the input dynamics. The simulation results show that the proposed algorithm outperforms the SOM with temporal activity diffusion, neural gas with temporal activity diffusion and spatiotemporal map formation based on a potential function in the presence of correlated noise for the same data set and similar training conditions.

Item Type:	Journal Article
Publication:	IEEE Transactions on Neural Networks and Learning Systems
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Bioinformatics; Biological systems; Conformal mapping; Diffusion in liquids; Heuristic algorithms; Linear equations; Mathematical models; Models; Neural networks; Neurons; Partial differential equations, Biological system modeling; Reaction diffusion equations; Self organizations; Self organizing maps(soms); Spatiotemporal phenomena, Self organizing maps
Department/Centre:	Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Date Deposited:	29 Nov 2022 06:21
Last Modified:	29 Nov 2022 06:21
URI:	https://eprints.iisc.ac.in/id/eprint/78076

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