  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.
