Assessing the Effectiveness of Intrinsic Dimension Estimators for Uncovering the Phase Space Dimensionality of Dynamical Systems from State Observations - A Comparative Analysis.

Devising a model of a dynamical system from raw observations of its states and evolution requires characterising its phase space, which includes identifying its dimension and state variables. Recently, Boyuan Chen and his colleagues proposed a technique that uses intrinsic dimension estimators to discover the hidden variables in experimental data. The method uses estimators of the intrinsic dimension of the manifold of observations. We present the results of a comparative empirical performance evaluation of various candidate estimators. We expand the repertoire of estimators proposed by Chen et al. and find that several estimators not initially suggested by the authors outperforms the others.