Behavioral Clustering for Point Processes

  • Christian Braune
  • Christian Borgelt
  • Rudolf Kruse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8207)

Abstract

Groups of (parallel) point processes may be analyzed with a variety of different goals. Here we consider the case in which one has a special interest in finding subgroups of processes showing a behavior that differs significantly from the other processes. In particular, we are interested in finding subgroups that exhibit an increased synchrony. Finding such groups of processes poses a difficult problem as its naïve solution requires enumerating the power set of all processes involved, which is a costly procedure. In this paper we propose a method that allows us to efficiently filter the process set for candidate subgroups. We pay special attention to the possibilities of temporal imprecision, meaning that the synchrony is not exact, and selective participation, meaning that only a subset of the related processes participates in each synchronous event.

Keywords

point processes clustering spike train analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berger, D., Borgelt, C., Diesmann, M., Gerstein, G., Grün, S.: An Accretion based Data Mining Algorithm for Identification of Sets of Correlated Neurons. In: 18th Annual Computational Neuroscience Meeting, CNS 2009, vol. 10(suppl. 1) (2009), doi:10.1186/1471-2202-10-S1-P254Google Scholar
  2. 2.
    Borgelt, C., Kötter, T.: Mining Fault-tolerant Item Sets using Subset Size Occurrence Distributions. In: Gama, J., Bradley, E., Hollmén, J. (eds.) IDA 2011. LNCS, vol. 7014, pp. 43–54. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Berger, D., Borgelt, C., Louis, S., Morrison, A., Grün, S.: Efficient Identification of Assembly Neurons within Massively Parallel Spike Trains. Computational Intelligence and Neuroscience, Article ID 439648 (2010), doi:10.1155/2010Google Scholar
  4. 4.
    Braune, C., Borgelt, C., Grün, S.: Finding Ensembles of Neurons in Spike Trains by Non-linear Mapping and Statistical Testing. In: Gama, J., Bradley, E., Hollmén, J. (eds.) IDA 2011. LNCS, vol. 7014, pp. 55–66. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Braune, C., Borgelt, C., Grün, S.: Assembly Detection in Continuous Neural Spike Train Data. In: Hollmén, J., Klawonn, F., Tucker, A. (eds.) IDA 2012. LNCS, vol. 7619, pp. 78–89. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  6. 6.
    Braune, C., Borgelt, C.: Prototype Construction for Clustering of Point Processes based on Imprecise Synchrony. In: 8th Conf. of the European Society for Fuzzy Logic and Technology, EUSFLAT 2013 (submitted, under review, 2013)Google Scholar
  7. 7.
    Brown, E.N., Kass, R.E., Mitra, P.P.: Multiple Neural Spike Train Data Analysis: State-of-the-art and Future Challenges. Nature Neuroscience 7(5), 456–461 (2004), doi:10.1038/nn1228Google Scholar
  8. 8.
    Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes. Springer, New York (1988), doi:10.1007/978-0-387-49835-5Google Scholar
  9. 9.
    Ester, M., Kriegel, H.-P., Sander, J., Xu, X.: A Density-based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. In: Proc. 2nd Int. Conf. on Knowledge Discovery and Data Mining (KDD 1996), Portland, Oregon, pp. 226–231. AAAI Press, Menlo Park (1996)Google Scholar
  10. 10.
    Feldt, S., Waddell, J., Hetrick, V.L., Berke, J.D., Ochowski, M.: Functional Clustering Algorithm for the Analysis of Dynamic Network Data. Physical Review E 79, 056104 (2009), doi:10.1103/PhysRevE.79.056104Google Scholar
  11. 11.
    Gerstein, G.L., Perkel, D.H., Subramanian, K.N.: Identification of Functionally Related Neural Assemblies. Brain Research 140(1), 43–62 (1978), doi:10.1016/0006-8993(78)90237-8CrossRefGoogle Scholar
  12. 12.
    Grün, S., Abeles, M., Diesmann, M.: Impact of Higher-Order Correlations on Coincidence Distributions of Massively Parallel Data. In: Marinaro, M., Scarpetta, S., Yamaguchi, Y. (eds.) Dynamic Brain. LNCS, vol. 5286, pp. 96–114. Springer, Heidelberg (2008), doi:10.1007/978-3-540-88853-6_8)Google Scholar
  13. 13.
    Grün, S., Diesmann, M., Aertsen, A.M.: ‘Unitary Events’ in Multiple Single-neuron Spiking Activity. I. Detection and Significance. Neural Computation 14(1), 43–80 (2002), doi:10.1162/089976602753284455CrossRefMATHGoogle Scholar
  14. 14.
    Grün, S., Rotter, S. (eds.): Analysis of Parallel Spike Trains. Springer, Berlin (2010), doi:10.1007/978-1-4419-5675-0_10Google Scholar
  15. 15.
    Hebb, D.O.: The Organization of Behavior. J. Wiley & Sons, New York (1949)Google Scholar
  16. 16.
    Kruse, R., Borgelt, C., Klawonn, F., Moewes, C., Steinbrecher, M., Held, P.: Computational Intelligence. Springer, London (2013), doi:10.1007/978-1-4471-5013-8CrossRefMATHGoogle Scholar
  17. 17.
    Lewicki, M.: A Review of Methods for Spike Sorting: The Detection and Classification of Neural Action Potentials. Network 9(4), R53–R78 (1998), doi:10.1088/0954-898X_9_4_001Google Scholar
  18. 18.
    Louis, S., Borgelt, C., Grün, S.: Complexity Distribution as a Measure for Assembly Size and Temporal Precision. Neural Networks 23(6), 705–712 (2010), doi:10.1016/j.neunet.2010.05.004Google Scholar
  19. 19.
    Picado-Muino, D., Borgelt, C.: Characterization of Spike Synchrony without Discretization of Time. Neuroinformatics (submitted)Google Scholar
  20. 20.
    Rand, W.: Objective Criteria for the Evaluation of Clustering Methods. Journal of the American Statistical Association 336(66), 846–850 (1971), doi:10.2307/2284239CrossRefGoogle Scholar
  21. 21.
    Staude, B., Grün, S., Rotter, S.: Higher-order Correlations in Non-stationary Parallel Spike Trains: Statistical Modeling and Inference. Frontiers in Computational Neuroscience 4, 16 (2010), doi:10.3389/fncom.2010.00016Google Scholar
  22. 22.
    Staude, B., Rotter, S., Grün, S.: CuBIC: Cumulant Based Inference of Higher-order Correlations in Massively Parallel Spike Trains. Journal of Computational Neuroscience 29(1-2), 327–350 (2010), doi:10.1007/s10827-009-0195-xGoogle Scholar
  23. 23.
    Wells III, W.M., Viola, P., Atsumi, H., Nakajima, S., Kikinis, R.: Multi-modal Volume Registration by Maximization of Mutual Information. Medical Image Analysis 1(1), 35–51 (1996), doi:10.1016/S1361-8415(01)80004-9Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christian Braune
    • 1
  • Christian Borgelt
    • 2
  • Rudolf Kruse
    • 1
  1. 1.Otto-von-Guericke-University of MagdeburgMagdeburgGermany
  2. 2.European Centre for Soft ComputingMieres (Asturias)Spain

Personalised recommendations