Maximum margin clustering for state decomposition of metastable systems

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.

Maximum Margin Clustering for State Decomposition of Metastable Systems

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“…In this section, we apply the framework of large margin learning to metastability analysis. Suppose that we have L trajectories {x 1 1 , . .…”

“…x x (1) x (2) (b) Trajectory data, where dotted lines represent trajectories of xt and circles denote data points sampled from trajectories. global optima of the MMC problem.…”

“…x (1) x (2) x (1) x x (1) x (2) Model II due to the large difference between the empirical data distribution and the equilibrium distribution. It is interesting to see from Fig.…”

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