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Comparing distance metrics for rotation using the k-nearest neighbors algorithm for entropy estimation.

David J Huggins1

  • 1Theory 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.

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Summary

Quaternion metrics outperform Euler angle metrics for molecular orientation analysis and entropy estimation using the k-nearest neighbors (KNN) algorithm. Independent samples are crucial for KNN accuracy in molecular dynamics simulations.

Keywords:
distance metricentropyk-nearest neighborsmolecular dynamicssolvationstatistical mechanics

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Area of Science:

  • Statistical mechanics
  • Computational chemistry
  • Data analysis

Background:

  • Distance metrics are essential for statistical analysis, particularly for calculating molecular orientation differences in statistical mechanics.
  • Various distance metrics exist for rotations, including those based on Euler angles and quaternions.
  • Entropy estimation is a key task in analyzing molecular configurations.

Purpose of the Study:

  • To evaluate the utility of different distance metrics for entropy estimation using the k-nearest neighbors (KNN) algorithm.
  • To compare the performance of quaternion-based metrics against Euler angle-based metrics.
  • To assess the impact of data characteristics, such as random and molecular dynamics simulation data, on the chosen methods.

Main Methods:

  • Utilized the k-nearest neighbors (KNN) algorithm for entropy estimation.
  • Compared distance metrics based on quaternion representation and Euler angles.
  • Assessed methods using uniformly random, biased random, and molecular dynamics simulation data of bulk water.

Main Results:

  • Quaternion metrics demonstrated superior performance compared to Euler angle metrics for entropy estimation.
  • The KNN algorithm offers advantages over traditional histogram-based entropy estimation methods.
  • Independence of samples is critical for the effective application of the KNN algorithm, especially with molecular dynamics data.

Conclusions:

  • Quaternion metrics are recommended over Euler angle metrics for analyzing molecular orientations and estimating entropy.
  • The k-nearest neighbors algorithm is a powerful tool for entropy estimation, provided data independence is ensured.
  • Findings have significant implications for applying KNN to time-series data from molecular dynamics simulations.