Topology Structure Optimization of Reservoirs Using GLMY Homology
This work addresses the problem of optimizing reservoir computing networks for researchers and practitioners in time series analysis, representing an incremental advancement by applying a novel mathematical tool to a known bottleneck.
The paper tackled the challenge of analyzing and optimizing reservoir network topology for time series processing by applying persistent GLMY homology theory, resulting in a method that improves performance by modifying one-dimensional GLMY homology groups, with experiments validating the influence of reservoir structure and dataset periodicity.
Reservoir is an efficient network for time series processing. It is well known that network structure is one of the determinants of its performance. However, the topology structure of reservoirs, as well as their performance, is hard to analyzed, due to the lack of suitable mathematical tools. In this paper, we study the topology structure of reservoirs using persistent GLMY homology theory, and develop a method to improve its performance. Specifically, it is found that the reservoir performance is closely related to the one-dimensional GLMY homology groups. Then, we develop a reservoir structure optimization method by modifying the minimal representative cycles of one-dimensional GLMY homology groups. Finally, by experiments, it is validated that the performance of reservoirs is jointly influenced by the reservoir structure and the periodicity of the dataset.