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Smoothing method for unit quaternion time series in a classification problem: an application to motion data.

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This study introduces a new logarithm-based method for smoothing quaternion time series, improving classification performance. The novel approach demonstrates superior effectiveness compared to traditional angular velocity transformations on real and noisy datasets.

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Area of Science:

  • Mathematics
  • Computer Science
  • Engineering

Background:

  • Smoothing orientation data is crucial across various research fields.
  • Existing methods for smoothing quaternion time series have limitations in practical application.
  • Quaternion time series smoothing is essential for accurate data analysis and classification.

Purpose of the Study:

  • To develop an effective smoothing approach for quaternion time series.
  • To enhance the performance of classification problems using smoothed quaternion data.
  • To propose a novel method utilizing the logarithm function for quaternion time series transformation.

Main Methods:

  • A new method transforms unit quaternion time series into real three-dimensional time series using the logarithm function.
  • The proposed method is compared against a classical approach based on angular velocity transformation.
  • Empirical validation is performed on both real and artificially noisy datasets.

Main Results:

  • The proposed logarithm-based smoothing method shows significant effectiveness.
  • The new approach outperforms the classical angular velocity transformation method.
  • Empirical evidence confirms the method's robustness on diverse datasets.

Conclusions:

  • The logarithm-based transformation provides a superior method for smoothing quaternion time series.
  • This technique enhances the performance of classification tasks.
  • The developed R functions will be made available, facilitating broader adoption and research.