title: Comparing distance metrics for rotation using the k-nearest neighbors algorithm for entropy estimation.
abstract: Distance metrics facilitate a number of methods for statistical analysis. For statistical mechanical applications, it is useful to be able to compute the distance between two different orientations of a molecule. However, a number of distance metrics for rotation have been employed, and in this study, we consider different distance metrics and their utility in entropy estimation using the k-nearest neighbors (KNN) algorithm. This approach shows a number of advantages over entropy estimation using a histogram method, and the different approaches are assessed using uniform randomly generated data, biased randomly generated data, and data from a molecular dynamics (MD) simulation of bulk water. The results identify quaternion metrics as superior to a metric based on the Euler angles. However, it is demonstrated that samples from MD simulation must be independent for effective use of the KNN algorithm and this finding impacts any application to time series data.
authors: Theory of Condensed Matter Group, University of Cambridge, Cavendish Laboratory, 19 J J Thomson Avenue, Cambridge, CB3 0HE, United Kingdom; Cambridge Molecular Therapeutics Programme, University of Cambridge, Hutchison/MRC Research Centre, Hills Road, Cambridge, CB2 0XZ, United Kingdom; Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, UK CB2 1EW, United Kingdom.
authors: David J
authors: DJ
authors: Huggins
mesh_terms: D000465:Algorithms; D019277:Entropy; D056004:Molecular Dynamics Simulation; D012399:Rotation; D014867:Water / Q000737:chemistry
chemical_list: D014867:Water
keywords: distance metric; entropy; k-nearest neighbors; molecular dynamics; solvation; statistical mechanics