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It has become common to perform kinetic analysis using approximate Koopmanoperators that transforms high-dimensional time series of observables intoranked dynamical modes. Key to a practical success of the approach is theidentification of a set of observables which form a good basis in which toexpand the slow relaxation modes. Good observables are, however, difficult toidentify {\em a priori} and sub-optimal choices can lead to significantunderestimations of characteristic timescales. Leveraging the representation ofslow dynamics in terms of Hidden Markov Model (HMM), we propose a simple andcomputationally efficient clustering procedure to infer surrogate observablesthat form a good basis for slow modes. We apply the approach to an analyticallysolvable model system, as well as on three protein systems of differentcomplexities. We consistently demonstrate that the inferred indicator functionscan significantly improve the estimation of the leading eigenvalues of theKoopman operators and correctly identify key states and transition timescalesof stochastic systems, even when good observables are not known {\em a priori}.

Improving Estimation of the Koopman Operator with Kolmogorov-Smirnov Indicator Functions