Advertisement

Finding Ensembles of Neurons in Spike Trains by Non-linear Mapping and Statistical Testing

  • Christian Braune
  • Christian Borgelt
  • Sonja Grün
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7014)

Abstract

Finding ensembles in neural spike trains has been a vital task in neurobiology ever since D.O. Hebb’s work on synaptic plasticity [15]. However, with recent advancements in multi-electrode technology, which provides means to record 100 and more spike trains simultaneously, classical ensemble detection methods became infeasible due to a combinatorial explosion and a lack of reliable statistics. To overcome this problem we developed an approach that reorders the spike trains (neurons) based on pairwise distances and Sammon’s mapping to one dimension. Thus, potential ensemble neurons are placed close to each other. As a consequence we can reduce the number of statistical tests considerably over enumeration-based approaches (like e.g. [1]), since linear traversals of the neurons suffice, and thus can achieve much lower rates of false-positives. This approach is superior to classical frequent item set mining algorithms, especially if the data itself is imperfect, e.g. if only a fraction of the items in a considered set is part of a transaction.

Keywords

Spike Train Outlier Detection Method Copy Probability Fiedler Vector Synchronous Spike 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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 Ann. Computational Neuroscience Meeting (CNS*2009), Berlin, Germany (2009); BMC Neuroscience, vol. 10(suppl. 1) Google Scholar
  2. 2.
    Besson, J., Robardet, C., Boulicaut, J.-F.: Mining a New Fault-Tolerant Pattern Type as an Alternative to Formal Concept Discovery. In: Proc. Int. Conference on Computational Science (ICCS 2006), Reading, United Kingdom, pp. 144–157. Springer, Berlin (2006)Google Scholar
  3. 3.
    Borgelt, C., Wang, X.: SaM: A Split and Merge Algorithm for Fuzzy Frequent Item Set Mining. In: Proc. 13th Int. Fuzzy Systems Association World Congress and 6th Conf. of the European Society for Fuzzy Logic and Technology (IFSA/EUSFLAT 2009), Lisbon, Portugal, pp. 968–973. IFSA/EUSFLAT Organization Committee, Lisbon (2009)Google Scholar
  4. 4.
    Choi, S.-S., Cha, S.-H., Tappert, C.C.: A Survey of Binary Similarity and Distance Measures. Journal of Systemics, Cybernetics and Informatics 8(1), 43–48 (2010); Int. Inst. of Informatics and Systemics, Caracas, Venezuela Google Scholar
  5. 5.
    Davé, R.N.: Characterization and Detection of Noise in Clustering. Pattern Recognition Letters 12, 657–664 (1991)CrossRefGoogle Scholar
  6. 6.
    Dice, L.R.: Measures of the Amount of Ecologic Association between Species. Ecology 26, 297–302 (1945)CrossRefGoogle Scholar
  7. 7.
    Diesmann, M., Gewaltig, M.-O., Aertsen, A.: Conditions for Stable Propagation of Synchronous Spiking in Cortical Neural Networks. Nature 402, 529–533 (1999)CrossRefGoogle Scholar
  8. 8.
    Edwards, A.L.: The Correlation Coefficient. In: An Introduction to Linear Regression and Correlation, pp. 33–46. W.H. Freeman, San Francisco (1976)Google Scholar
  9. 9.
    Gerstein, G.L., Perkel, D.H., Subramanian, K.N.: Identification of Functionally Related Neural Assemblies. Brain Research 140(1), 43–62 (1978)CrossRefGoogle Scholar
  10. 10.
    Gionis, A., Mannila, H., Seppänen, J.K.: Geometric and Combinatorial Tiles in 0-1 Data. In: Boulicaut, J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) PKDD 2004. LNCS (LNAI), vol. 3202, pp. 173–184. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Grün, S., Diesmann, M., Aertsen, A.: ‘Unitary Events’ in Multiple Single-neuron Activity. I. Detection and Significance. Neural Computation 14(1), 43–80 (2002)CrossRefzbMATHGoogle 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 - from Neural Spikes to Behaviors. LNCS, vol. 5286, pp. 96–114. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Berger, D., Borgelt, C., Louis, S., Morrison, A., Grün, S.: Efficient Identification of Assembly Neurons within Massively Parallel Spike Trains. In: Computational Intelligence and Neuroscience, article ID 439648. Hindawi Publishing Corp., New York (2009/2010)Google Scholar
  14. 14.
    Hamming, R.V.: Error Detecting and Error Correcting Codes. Bell Systems Tech. Journal 29, 147–160 (1950)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Hebb, D.O.: The Organization of Behavior. J. Wiley & Sons, New York (1949)Google Scholar
  16. 16.
    Jaccard, P.: Étude comparative de la distribution florale dans une portion des Alpes et des Jura. Bulletin de la Société Vaudoise des Sciences Naturelles 37, 547–579 (1901)Google Scholar
  17. 17.
    Lewicki, M.S.: A Review of Methods for Spike Sorting: The Detection and Classification of Neural Action Potentials. Network: Computation in Neural Systems 9, R53–R78 (1998)CrossRefzbMATHGoogle Scholar
  18. 18.
    Rehm, F., Klawonn, F., Kruse, R.: A Novel Approach to Noise Clustering for Outlier Detection. Soft Computing — A Fusion of Foundations, Methodologies and Applications 11(5), 489–494 (2007)Google Scholar
  19. 19.
    Rogers, D.J., Tanimoto, T.T.: A Computer Program for Classifying Plants. Science 132, 1115–1118 (1960)CrossRefGoogle Scholar
  20. 20.
    Sammon, J.W.: A Nonlinear Mapping for Data Structure Analysis. IEEE Trans. Comput. 18(5), 401–409 (1969)CrossRefGoogle Scholar
  21. 21.
    Sørensen, T.: A Method of Establishing Groups of Equal Amplitude in Plant Sociology based on Similarity of Species and its Application to Analyses of the Vegetation on Danish Commons. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab 5(4), 1–34 (1948)Google Scholar
  22. 22.
    Tanimoto, T.T.: IBM Internal Report (November 17, 1957)Google Scholar
  23. 23.
    Wang, X., Borgelt, C., Kruse, R.: Mining Fuzzy Frequent Item Sets. In: Proc. 11th Int. Fuzzy Systems Association World Congress (IFSA 2005), Beijing, China, pp. 528–533. Tsinghua University Press and Springer, Beijing, and Heidelberg (2005)Google Scholar
  24. 24.
    Yule, G.U.: On the Association of Attributes in Statistics. Philosophical Transactions of the Royal Society of London, Series A 194, 257–319 (1900)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christian Braune
    • 1
    • 2
  • Christian Borgelt
    • 1
  • Sonja Grün
    • 3
    • 4
    • 5
  1. 1.European Centre for Soft ComputingMieresSpain
  2. 2.Otto-von-Guericke-University of MagdeburgMagdeburgGermany
  3. 3.RIKEN Brain Science InstituteWako-ShiJapan
  4. 4.Institute of Neuroscience and Medicine (INM-6)Research Center JülichGermany
  5. 5.Theoretical Systems NeurobiologyRWTH Aachen UniversityAachenGermany

Personalised recommendations