New Fast ApEn and SampEn Entropy Algorithms Implementation and Their Application to Supercomputer Power Consumption

Area of Science:

• Complexity science
• Computational statistics
• Time series analysis

Background:

• Approximate Entropy (ApEn) and Sample Entropy (SampEn) are widely used for time series complexity.
• Accelerated versions, Fast Approximate Entropy (Fast ApEn) and Fast Sample Entropy (Fast SampEn), are less known.
• Efficient implementation of these algorithms is crucial for practical applications.

Purpose of the Study:

• Introduce and explain the algorithms for time series complexity: ApEn, SampEn, Fast ApEn, and Fast SampEn.
• Describe the TSEntropies R package, its functions, and parameters.
• Evaluate the performance and speed of the TSEntropies package compared to existing solutions.

Main Methods:

• Explanation of the theoretical principles behind ApEn, SampEn, and their accelerated versions.
• Implementation and description of the TSEntropies R package functions.
• Benchmarking TSEntropies against the R package 'pracma' using artificial and real-world time series data (supercomputer power consumption).

Main Results:

• The TSEntropies package provides efficient implementations of ApEn, SampEn, Fast ApEn, and Fast SampEn.
• TSEntropies demonstrates a speed improvement of up to 100 times compared to the 'pracma' R package.
• Fast ApEn and Fast SampEn algorithms achieve computational time reductions of up to 500 times over their original versions.

Conclusions:

• The TSEntropies R package offers a significant speed advantage for calculating time series complexity measures.
• The accelerated algorithms (Fast ApEn, Fast SampEn) provide substantial computational efficiency gains.
• TSEntropies is a valuable tool for researchers and practitioners dealing with complex time series analysis.