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Machine learning of time series data using persistent homology.

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Area of Science:

  • Complex Systems Analysis
  • Topological Data Analysis
  • Biomedical Signal Processing

Background:

  • Traditional persistent homology for time-series analysis faces high computational costs.
  • Recurrence plots offer a computationally efficient way to visualize dynamical systems.

Purpose of the Study:

  • To develop a novel, computationally efficient method for time-series analysis.
  • To extract meaningful topological features from time-series data.
  • To demonstrate the method's effectiveness in identifying system dynamics and classifying biological signals.

Main Methods:

  • Generate recurrence plots from time-series datasets.
  • Extract topological features using persistent homology.
  • Vectorize topological data using persistence images and reduce dimensionality with non-negative matrix factorization.

Main Results:

  • Successfully identified periodic-to-chaotic and chaotic-to-chaotic transitions in Chua's system.
  • Distinguished between healthy, neuropathic, and myopathic individuals using electromyogram data.
  • Achieved accurate classification of electrocardiogram data based on extracted features.

Conclusions:

  • The proposed method efficiently captures essential information from time-series data.
  • This approach offers a powerful tool for analyzing complex dynamical systems and biomedical signals.
  • The extracted topological features are distinctive and useful for various classification tasks.