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Empirical intrinsic geometry for nonlinear modeling and time series filtering
Ronen Talmon1, Ronald R Coifman
1Department of Mathematics, Yale University, New Haven, CT 06520, USA. ronen.talmon@yale.edu
Summary
Empirical intrinsic geometry (EIG) offers a novel method for time series analysis, revealing underlying dynamics in complex data without prior models. This noise-resilient approach enhances nonlinear filtering and tracking applications.
Area of Science:
- Data Science
- Geometry
- Signal Processing
Background:
- High-dimensional time series analysis often relies on predefined statistical models.
- Existing geometric analysis tools have limitations in stochastic and empirical settings.
Purpose of the Study:
- To introduce Empirical Intrinsic Geometry (EIG) for time series analysis.
- To reveal low-dimensional manifolds and infer dynamics of high-dimensional time series.
- To extend geometric analysis to stochastic settings without requiring prior statistical models.
Main Methods:
- Utilizing concepts from information geometry to parametrize empirical distributions.
- Developing a noise-resilient and invariant inference model.
- Extending the method for sequential data acquisition.
Main Results:
- EIG successfully reveals underlying dynamics and low-dimensional structures in time series.
- The method demonstrates resilience to noise and invariance across different observation modalities.
- Sequential extension enables efficient incorporation of new measurements.
Conclusions:
- EIG provides a robust framework for analyzing complex time series data, particularly in the absence of definitive models.
- The integration of EIG into nonlinear filtering enhances tracking and localization capabilities.
- This approach broadens the applicability of geometric methods in data analysis and signal processing.
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