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

We implement the edit distance for marked point processes [Suzuki et al., Int. J. Bifurcation Chaos 20, 3699-3708 (2010)] as a binary integer program. Compared with the previous implementation using minimum cost perfect matching, the proposed implementation has two advantages: first, by using the proposed implementation, we can apply a wide variety of software and hardware, even spin glasses and coherent ising machines, to calculate the edit distance for marked point processes; second, the proposed implementation runs faster than the previous implementation when the difference between the numbers of events in two time windows for a marked point process is large.

[1]  Kazuyuki Aihara,et al.  Definition of Distance for Marked Point Process Data and its Application to Recurrence Plot-Based Analysis of Exchange Tick Data of Foreign Currencies , 2010, Int. J. Bifurc. Chaos.

[2]  Alistair I. Mees,et al.  Convergence of an annealing algorithm , 1986, Math. Program..

[3]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[4]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[5]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[6]  Kazuyuki Aihara,et al.  Timing matters in foreign exchange markets , 2012 .

[7]  Jonathan D. Victor,et al.  Metric-space analysis of spike trains: theory, algorithms and application , 1998, q-bio/0309031.

[8]  Kazuyuki Aihara,et al.  Identifying hidden common causes from bivariate time series: a method using recurrence plots. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Thomas Kreuz,et al.  Characterizing unidirectional couplings between point processes and flows , 2011 .

[10]  K. Aihara,et al.  Intra-day response of foreign exchange markets after the Tohoku-Oki earthquake , 2015 .

[11]  H. Kantz.  A robust method to estimate the maximal Lyapunov exponent of a time series , 1994 .

[12]  R. Byer,et al.  Coherent Ising machine based on degenerate optical parametric oscillators , 2013, 1311.2696.

[13]  F. Schoenberg,et al.  Description of earthquake aftershock sequences using prototype point patterns , 2007 .

[14]  Jürgen Kurths,et al.  Estimation of the direction of the coupling by conditional probabilities of recurrence. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.