Topological time-series analysis with delay-variant embedding.

Area of Science:

• Complex Systems Analysis
• Topological Data Analysis
• Time Series Analysis

Background:

• Qualitative changes in time-series data reveal underlying dynamics.
• Topological approaches using time-delay embedding can detect these changes.
• Single time-delay methods often yield insufficient topological features.

Purpose of the Study:

• To propose a delay-variant embedding method for enhanced topological feature extraction.
• To reveal multiple-timescale patterns in time-series data.
• To improve the classification accuracy of time-series data.

Main Methods:

• Constructing extended topological features by treating time delay as a variable parameter.
• Utilizing the delay-variant embedding to create an additional dimension in the topological feature space.
• Combining the novel features with kernel machine learning for classification.

Main Results:

• Theoretically proven robustness of topological features against noise.
• Demonstrated effectiveness in classifying synthetic noisy biological and real time-series data.
• Achieved higher classification accuracy compared to single time-delay methods and other standard techniques.

Conclusions:

• The delay-variant embedding method offers a more comprehensive analysis of time-series dynamics.
• This approach effectively captures multiple-timescale patterns and improves data classification.
• The method shows significant potential for various time-series analysis applications.