A sliding window-based algorithm for faster transformation of time series into complex networks

Area of Science:

• Complex systems analysis
• Time series analysis
• Network science

Background:

• Visibility Graphs (VG) are used for time series analysis.
• Traditional VG methods have quadratic time complexity, limiting their use with large datasets.
• Most nodes in a VG are not connected to distant nodes, suggesting potential for optimization.

Purpose of the Study:

• Introduce a new, efficient approximation method for Visibility Graphs.
• Evaluate the time efficiency and accuracy of the proposed method.
• Assess the applicability of the method for real-time time series analysis.

Main Methods:

• Developed the Sliding Visibility Graph (SVG) method, which leverages the sparse nature of VG adjacency matrices.
• Performed numerical tests on various time series using SVG.
• Compared SVG results with exact VG values.

Main Results:

• SVG exhibits linear time complexity (O(N)), a significant improvement over VG's quadratic complexity (O(N^2)).
• SVG results rapidly converge to exact VG values, particularly for random and stochastic time series.
• The method is adaptable for real-time analysis using fixed-length data segments.

Conclusions:

• SVG provides a computationally efficient and accurate approximation for Visibility Graph analysis.
• The linear time complexity makes SVG suitable for analyzing very large time series.
• SVG's adaptability to real-time data streams opens new avenues for dynamic time series analysis.