Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Artificial Intelligence and Soft Computing Research

The Journal of Polish Neural Network Society, the University of Social Sciences in Lodz & Czestochowa University of Technology

4 Issues per year

Open Access
See all formats and pricing
More options …

Kernel Analysis for Estimating the Connectivity of a Network with Event Sequences

Taro Tezuka / Christophe Claramunt
Published Online: 2016-12-17 | DOI: https://doi.org/10.1515/jaiscr-2017-0002


Estimating the connectivity of a network from events observed at each node has many applications. One prominent example is found in neuroscience, where spike trains (sequences of action potentials) are observed at each neuron, but the way in which these neurons are connected is unknown. This paper introduces a novel method for estimating connections between nodes using a similarity measure between sequences of event times. Specifically, a normalized positive definite kernel defined on spike trains was used. The proposed method was evaluated using synthetic and real data, by comparing with methods using transfer entropy and the Victor-Purpura distance. Synthetic data was generated using CERM (Coupled Escape-Rate Model), a model that generates various spike trains. Real data recorded from the visual cortex of an anaesthetized cat was analyzed as well. The results showed that the proposed method provides an effective way of estimating the connectivity of a network when the time sequences of events are the only available information.

Keywords: connectivity estimation; neural network; kernel methods; spike train


  • [1] Alain Berlinet and Christine Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics, Kluwer Academic Publishers, 2001.Google Scholar

  • [2] Timothy J. Blanche, Martin A. Spacek, Jamille F. Hetke, and Nicholas V. Swindale, Polytrodes: high density silicon electrode arrays for large scale multiunit recording, Journal of Neurophysiology, Vol.93, No.5, pp.2987-3000, 2005.CrossrefGoogle Scholar

  • [3] Tim Blanche, Multi-neuron recordings in primary visual cortex. CRCNS.org. 2009. http://dx.doi.org/10.6080/K0MW2F2JCrossrefGoogle Scholar

  • [4] Zhiyi Chi, Wei Wu, Zach Haga, Nicholas G. Hatsopoulos, and Daniel Margoliash, Template-based spike pattern identification with linear convolution and dynamic time warping, Journal of Neurophysiology, Vol.97, pp.1221-1235, 2007.Web of ScienceGoogle Scholar

  • [5] Justin Dauwels, Franc¸ois Vialatte, Theophane Weber, and Andrzej Cichocki, On similarity measures for spike trains, in Proceeding of the 15th International Conference on Advances in Neuro- Information Processing, pp.177-185, 2009.Google Scholar

  • [6] Peter Dayan and L. F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, MIT Press, 2001.Google Scholar

  • [7] Alexander J. Dubbs, Brad A. Seiler, and Marcelo O. Magnasco, A fast Lp spike alignment metric, Neural Computation, Vol.22, pp.2785-2808, 2010.CrossrefGoogle Scholar

  • [8] Jan Eichhorn, Andreas Tolias, Alexander Zien, Malte Kuss, Carl Edward Rasmussen, JasonWeston, Nikos Logothetis, and Bernhard Sch¨olkopf, Prediction on spike data using kernel algorithms, Advances in Neural Information Processing Systems, Vol.16, pp.1367-1374, 2004.Google Scholar

  • [9] Nicholas Fisher and Arunava Banerjee, A novel kernel for learning a neuron model from spike train data, Advances in Neural Information Processing Systems, Vol.23, pp.595-603, 2010.Google Scholar

  • [10] K.J. Friston, L. Harrison, and W. Penny, Dynamic causal modeling, NeuroImage, Vol.19, no. 4, pg.1273-1302, 2003.CrossrefGoogle Scholar

  • [11] Matteo Garofalo, Thierry Nieus, Paolo Massobrio, and Sergio Martinoia, Evaluation of the performance of information theory-based methods and cross-correlation to estimate the functional connectivity in cortical networks, PLoS One, Vol.4, No.8, e6482, 2009.Google Scholar

  • [12] Wulfram Gerstner, Werner M. Kistler, Richard Naud, and Liam Paninski, Neuronal Dynamics, Cambridge University Press, 2014.Google Scholar

  • [13] C.W.J. Granger, Investigating causal relations by econometric models and cross-spectral methods, Econometrica, Vol.37, No.3, 424-438, 1969.CrossrefGoogle Scholar

  • [14] Conor Houghton and Thomas Kreuz, Measures of spike train synchrony: From single neurons to populations, in Misha Meyer Pesenson (Ed.), Multiscale Analysis and Nonlinear Dynamics: From Genes to the Brain, John Wiley & Sons, Inc., 2013.Google Scholar

  • [15] Conor Houghton and Jonathan Victor, Measuring representational distances - the spike-train metrics approach, in Nikolaus Kriegeskorte and Gabriel Kreiman (Eds.), Understanding Visual Population Codes: Towards a Common Multivariate Framework for Cell Recording and Functional Imaging, MIT Press, 2011.Google Scholar

  • [16] Don H. Johnson, Charlotte M. Gruner, Keith Baggerly, and Chandran Seshagiri, Informationtheoretic analysis of neural coding, Journal of Computational Neuroscience, Vol.10, pp.47-69, 2001.CrossrefGoogle Scholar

  • [17] Maciej Kaminski and Katarzyna J. Blinowska, A new method of the description of the information flow in the brain structures, Biological Cybernetics, Vol. 65, No.3, pp.203-210, 1991.CrossrefGoogle Scholar

  • [18] Maciej Kaminski, Mingzhou Ding, Wilson A. Truccolo, and Steven L. Bressler, Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance, Biological Cybernetics, Vol. 85, No.2, pp.145-157, 2001.CrossrefGoogle Scholar

  • [19] Ryota Kobayashi and Katsunori Kitano, Impact of network topology on inference of synaptic connectivity from multi-neuronal spike data simulated by a large-scale cortical network model, Journal of Computational Neuroscience, Vol.35, pp.109-124, 2013.CrossrefWeb of ScienceGoogle Scholar

  • [20] Thomas Kreuz, Daniel Chicharro, Conor Houghton, Ralph G. Andrzejak, and Florian Mormann, Monitoring spike train synchrony, Journal of Neurophysiology, Vol.109, pp.1457-1472, 2012.CrossrefGoogle Scholar

  • [21] Lin Li, Austin J. Brockmeier, John S. Choi, Joseph T. Francis, Justin C. Sanchez, and Jose C. Principe, A tensor-product-kernel framework for multiscale neural activity decoding and control, Computational Intelligence and Neuroscience, 2014.Web of ScienceGoogle Scholar

  • [22] Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar, Foundations of Machine Learning, MIT Press, 2012.Google Scholar

  • [23] Richard Naud, Felipe Gerhard, Skander Mensi, and Wulfram Gerstner, Improved similarity measures for small sets of spike trains, Neural Computation, Vol.23, pp.3016-3069, 2011.CrossrefGoogle Scholar

  • [24] Murat Okatan, Mathew A. Wilson, and Emery N. Brown, Analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity, Neural Computation, Vol.17, pp.1927-1961, 2005.CrossrefGoogle Scholar

  • [25] Antonio R.C. Paiva, Il Park, and Jose C. Principe, A reproducing kernel Hilbert space framework for spike train signal processing, Neural Computation, Vol.21, No.2, pp.424-449, 2009.CrossrefGoogle Scholar

  • [26] Antonio R.C. Paiva, Il Park, and Jose C. Principe, Inner products for representation and learning in the spike train domain, in Karim G. Oweiss (Ed.), Statistical Signal Processing for Neuroscience and Neurotechnology, Academic Press, 2010.Google Scholar

  • [27] Stefano Panzeri and Alessandro Treves, Analytical estimates of limited sampling in different information measures, Network: Computation in Neural Systems, 7, pp.87-107, 1996.Google Scholar

  • [28] Il Memming Park, Sohan Seth, Murali Rao, and Jose C. Principe, Strictly positive definite spike train kernels for point process divergences, Neural Computation, Vol.24, pp.2223-2250, 2012.CrossrefGoogle Scholar

  • [29] Il Memming Park, Sohan Seth, Antonio R.C. Paiva, Lin Li, and Jose C. Principe, Kernel methods on spike train space for neuroscience: a tutorial, Signal Processing Magazine, Vol.30, No.4, pp.149-160, 2013.Google Scholar

  • [30] Christopher J. Quinn, Todd P. Coleman, Negar Kiyavash, and Nicholas G. Hatsopoulos, Estimating the directed information to infer causal relationships in ensemble neural spike train recordings, Journal of Computational Neuroscience, 2010.Google Scholar

  • [31] Carl Edward Rasmussen and Christopher K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006.Google Scholar

  • [32] Fred Rieke, David Warland, Rob de Ruyter van Steveninck, and William Bialek, Spikes: Exploring the Neural Code, MIT Press, 1997.Google Scholar

  • [33] Catalin V. Rusu and Razvan V. Florian, A new class of metrics for spike trains, Neural Computation, Vol.26, No.2, pp.306-348, 2014.CrossrefWeb of ScienceGoogle Scholar

  • [34] Gerard M. Salton, Andrew Wong, and Chungshu Yang, A vector space model for automatic indexing, Communications of the ACM, Vol.18, No.11, pp.613-620, 1975.CrossrefGoogle Scholar

  • [35] Thomas Schreiber, Measuring information transfer, Physical Review Letters, Vol.85, No.2, 2000.Google Scholar

  • [36] John Shawe-Taylor and Nello Cristianini, Kernel Methods for Pattern Analysis, Cambridge University Press, 2004.Google Scholar

  • [37] Lavi Shpigelman, Yoram Singer, Rony Paz, and Eilon Vaadia, Spikernels: embedding spiking neurons in inner product spaces, Advances in Neural Information Processing Systems, Vol.15, pp.125-132, 2003.Google Scholar

  • [38] Lavi Shpigelman, Yoram Singer, Rony Paz, and Eilon Vaadia, Spikernels: predicting arm movements by embedding population spike rate patterns in inner-product spaces, Neural Computation, Vol.17, pp.671-690, 2005.CrossrefGoogle Scholar

  • [39] Lavi Shpigelman, Hagai Lalazar, and Eilon Vaadia, Kernel-ARMA for hand tracking and brainmachine interfacing during 3D motor control, Advances in neural information processing systems, Vol.21, 1489-1496, 2008.Google Scholar

  • [40] Taro Tezuka, Spike train kernels for multiple neuron recordings, Proceedings of the 39th International Conference on Acoustics, Speech and Signal Processing, pp.6035-6039, 2014.Google Scholar

  • [41] Taro Tezuka and Christophe Claramunt, Connectivity estimation of neural networks using a spike train kernel, Proceedings of the 2015 International Joint Conference on Neural Networks, pp.1-7, Killarney, Ireland, July 12-17, 2015.Google Scholar

  • [42] M.C.W. van Rossum, A novel spike distance, Neural Computation, Vol.13, pp.751-763, 2001. CrossrefGoogle Scholar

  • [43] Raul Vicente, Michael Wibral, Michael Lindner, and Gordon Pipa, Transfer entropy - a model-free measure of effective connectivity for the neurosciences. Journal of Computational Neuroscience, Vol.30, No.1, pp.45-67, 2011.CrossrefGoogle Scholar

  • [44] Jonathan D. Victor, Spike train metrics, Current Opinion in Neurobiology, Vol.15, pp.585-592, 2005.CrossrefGoogle Scholar

  • [45] Jonathan D. Victor and Keith P. Purpura, Nature and precision of temporal coding in visual cortex: a metric-space analysis, Journal of Neurophysiology, Vol.76, pp.1310-1326, 1996.Google Scholar

  • [46] Jonathan D. Victor and Keith P. Purpura, Spike metrics, in Nikolaus Kriegeskorte and Gabriel Kreiman (Eds.), Understanding Visual Population Codes: Towards a Common Multivariate Framework for Cell Recording and Functional Imaging, MIT Press, 2011.Google Scholar

  • [47] Wei Wu and Anuj Srivastava, An informationgeometric framework for statistical inferences in the neural spike train space, Journal of Computational Neuroscience, Vol.31, No.3, pp.725-48, 2011.CrossrefGoogle Scholar

About the article

Published Online: 2016-12-17

Published in Print: 2017-01-01

Citation Information: Journal of Artificial Intelligence and Soft Computing Research, ISSN (Online) 2083-2567, DOI: https://doi.org/10.1515/jaiscr-2017-0002.

Export Citation

© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Comments (0)

Please log in or register to comment.
Log in