Maximum Margin Clustering for State Decomposition of Metastable Systems

TL;DR

This paper introduces a novel maximum margin clustering method for decomposing metastable states in dynamical systems, avoiding the need for phase space discretization and broadening applicability beyond equilibrium data.

Contribution

It formulates metastable state decomposition as a semi-supervised learning problem, enabling large margin techniques to identify states without phase space discretization.

Findings

Effective in simulation examples

Does not require phase space discretization

Applicable to non-equilibrium data

Abstract

When studying a metastable dynamical system, a prime concern is how to decompose the phase space into a set of metastable states. Unfortunately, the metastable state decomposition based on simulation or experimental data is still a challenge. The most popular and simplest approach is geometric clustering which is developed based on the classical clustering technique. However, the prerequisites of this approach are: (1) data are obtained from simulations or experiments which are in global equilibrium and (2) the coordinate system is appropriately selected. Recently, the kinetic clustering approach based on phase space discretization and transition probability estimation has drawn much attention due to its applicability to more general cases, but the choice of discretization policy is a difficult task. In this paper, a new decomposition method designated as maximum margin metastable clustering is proposed, which converts the problem of metastable state decomposition to a semi-supervised learning problem so that the large margin technique can be utilized to search for the optimal decomposition without phase space discretization. Moreover, several simulation examples are given to illustrate the effectiveness of the proposed method.