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Edit distance for marked point processes revisited: An implementation by binary integer programming.

Yoshito Hirata1, Kazuyuki Aihara1

  • 1Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.

Chaos (Woodbury, N.Y.)
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Summary
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We present a new binary integer programming method for calculating the edit distance for marked point processes. This approach enhances computational flexibility and improves performance, especially for large event count differences.

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Area of Science:

  • Computational Mathematics
  • Data Science
  • Applied Physics

Background:

  • Marked point processes (MPPs) are crucial for modeling event data over time.
  • Calculating the edit distance between MPPs is essential for comparing temporal patterns.
  • Existing methods, like minimum cost perfect matching, have limitations in flexibility and speed.

Purpose of the Study:

  • To implement the edit distance for marked point processes (MPPs) using a binary integer programming (BIP) approach.
  • To compare the BIP implementation against the minimum cost perfect matching (MCPM) method.
  • To highlight the advantages of the novel BIP implementation for MPP analysis.

Main Methods:

  • Formulated the edit distance for MPPs as a binary integer program.
  • Leveraged existing BIP solvers and hardware (e.g., spin glasses, coherent Ising machines) for computation.
  • Compared computational performance against the MCPM-based implementation.

Main Results:

  • The BIP implementation allows for broader hardware and software applicability, including specialized computing architectures.
  • The proposed method demonstrates superior speed compared to MCPM when the number of events in the time windows differs significantly.
  • Successfully adapted a complex computational task (edit distance for MPPs) to a versatile BIP framework.

Conclusions:

  • The BIP implementation offers a more flexible and potentially faster alternative for calculating MPP edit distances.
  • This work opens avenues for utilizing diverse computational resources for analyzing marked point processes.
  • The findings are relevant for fields relying on the comparison of time-stamped event data.