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Cross-Modal Multivariate Pattern Analysis
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Harmonic cross-correlation decomposition for multivariate time series.

Tanja Zerenner1, Marc Goodfellow1, Peter Ashwin1

  • 1EPSRC Centre for Predictive Modeling in Healthcare, University of Exeter, Exeter EX4 4PY, United Kingdom and College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4PY, United Kingdom.

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Summary
This summary is machine-generated.

We developed harmonic cross-correlation decomposition (HCD) to analyze complex data patterns. This method visualizes dominant oscillations in multivariate time series, offering a new way to understand frequency structures.

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Area of Science:

  • Time Series Analysis
  • Signal Processing
  • Complex Systems

Background:

  • Analyzing multivariate time series requires methods to capture complex oscillatory patterns.
  • Existing techniques like data-adaptive harmonic decomposition (DAHD) and multivariate singular spectrum analysis (MSSA) have limitations.

Purpose of the Study:

  • Introduce harmonic cross-correlation decomposition (HCD) for detecting and visualizing frequency structures in multivariate time series.
  • Compare HCD with DAHD and MSSA, highlighting its advantages.

Main Methods:

  • HCD decomposes time series into spatiotemporal harmonic modes via eigendecomposition of a cross-correlation matrix.
  • Each mode is linked to a specific Fourier frequency, enabling multidimensional spectra analysis.
  • Unlike DAHD, HCD is independent of channel ordering.

Main Results:

  • HCD effectively identifies dominant oscillatory patterns.
  • HCD provides intuitive phase spectra related to data phase relations.
  • Demonstrated HCD's utility on traveling waves, coupled oscillators, and human EEG data.

Conclusions:

  • HCD is a robust tool for analyzing frequency structures in multivariate time series.
  • HCD offers advantages over existing methods in terms of channel independence and intuitive phase interpretation.
  • HCD has broad applicability in various scientific fields analyzing time-dependent data.