Criticality Analysis for Non-linear Data Representation

Video recording:

Speaker: Tjeerd V. olde Scheper (School of Engineering, Computing and Mathematics, Oxford Brookes University, UK)
Title: Criticality Analysis for Non-linear Data Representation
Time: Wednesday, 2022.01.12, 10:00 a.m. (CET)
Place: fully virtual (contact Jakub Lengiewicz to register)
Format: 30 min. presentation + 30 min. discussion

Abstract: Within this seminar, I will provide a short introduction to the concept of Criticality Analysis and expand on the application and relevance of this method to generate nonlinear representation spaces. These can be used for deterministic representation of multimodal data for categorisation, as a regularisation method, or for controllable self-organised reservoir computing.
 Criticality Analysis is based on the concept of a Self-Organised Critical (SOC) system. Such a system is in an apparent stable state, but can change rapidly to another critical state when perturbed. They are commonly observed within large aggregates of nonlinear smaller systems, such as sand particles or snow flakes, forming SOC piles. They seem to have a specific affinity with scale-free power law relations, and have been proposed to underpin biological systems.

To generate a deterministic SOC, a network of controlled nonlinear oscillators is used which shares key properties with SOC systems, namely non-trivial scaling due to the external perturbation, spatiotemporal power-law correlation in respect to the total behaviour of the network, and self-tuning to the critical point where the network self-selects the periodic orbit. The underlying control is based on the method of Rate Control of Chaos, which is a nonlinear control method that can stabilise chaotic systems.

Because these networks are in a critical state and deterministic, they can be used to create stable global states when perturbed with data, and this property is exploited to allow readily classification of the data, irrespective of its modality. It has been used to classify gait patterns, and seems especially useful for categorisation of dynamic biological data.