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Multivariate Data Analysis Using Persistence-Based Filtering and Topological Signatures.

B Rieck1, H Mara, H Leitte

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This study introduces a novel topological data analysis pipeline using persistent homology to extract significant structures from high-dimensional, noisy datasets. The method effectively identifies data features and similarities, offering a unique topological signature for analysis.

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Area of Science:

  • Computational Topology
  • Data Science
  • Scientific Visualization

Background:

  • High-dimensional data analysis presents challenges in structure extraction and noise identification.
  • Existing clustering methods often lack relational insights and require predefined parameters.
  • Topological Data Analysis (TDA) offers advanced methods for understanding complex datasets.

Purpose of the Study:

  • To present a visualization pipeline for extracting significant structures from arbitrary high-dimensional datasets.
  • To address the inherent noise and dimensionality challenges in data analysis.
  • To introduce novel visualization techniques for enhanced data interpretation.

Main Methods:

  • Utilizing persistent homology for topological data analysis on high-dimensional datasets.
  • Employing a theoretically-founded persistence-based filtering algorithm for hierarchical structure extraction.
  • Introducing persistence rings as a novel visualization technique for topological features (persistence intervals).

Main Results:

  • The pipeline inherently handles noisy data and arbitrary dimensions.
  • Central data structures are extracted hierarchically using a robust filtering algorithm.
  • Persistence rings provide a unique topological signature for recognizing data similarities.
  • Interactive visualization aids in parameter space evaluation for structure extraction.

Conclusions:

  • The developed pipeline effectively extracts significant structures from complex, high-dimensional datasets.
  • Persistent homology and novel visualization techniques like persistence rings offer powerful tools for data analysis.
  • The method demonstrates utility in both synthetic and real-world applications, including cultural heritage research.