Skip to main content
  • Poster presentation
  • Open access
  • Published:

Parallel spike trains analysis using positive definite kernels

Since spikes are considered to be the fundamental element in neural systems, there has been a significant amount of work that analyzes the sequence of spike timings, or spike trains [1, 2]. One important research question is to know how information is encoded in a spike train. There is an approach to construct a feature space that captures characteristics of spike trains, as is usually done in the field of pattern recognition. Another approach, which is increasingly becoming popular in recent years, is to find an appropriate similarity measure between spike trains [3, 4]. This corresponds to constructing a model of information decoding done by the postsynaptic neurons.

One promising way to define such similarity measures is to use positive definite kernels [5–7]. Since positive definite kernels are generalizations of inner products, they enable application of various linear methods used in machine learning (including regression, classification, and dimension reduction) to spike trains. Positive definite kernels are extensively used in kernel methods.

While positive definite kernels on spike trains obtained from a single neuron have already been proposed [5–7], the extension of this to parallel spike trains obtained from multiple neurons has not been explored yet. Therefore, we defined such a kernel by extending the memoryless cross intensity kernel (mCI kernel) proposed by Paiva et al. [5]. To make the extension as natural as possible, we used a linear combination of cross-neuron interactions. We name the new kernel the linear combination of interactions kernel (LCIK) [9]. The parameters of the kernel can be set to make it positive definite.

We applied this kernel to publicly available in vivo recordings taken from the primary visual field in macaque monkey brains [8]. The LCIK performed better than other possible kernels defined on a set of spike trains. When the parameters of the kernel were estimated using spike trains obtained from real neurons, we obtained biologically plausible values. For example, the estimated time constant was near the value commonly used in neural modeling. This indicates the possibility of using such kernels to look for an appropriate model of neurons based on observed spike recordings.

We also simulated a simple neural network and generated spike trains to see the effect on the estimated values of the kernel parameters by changing the synaptic connection parameters. The result indicated that the kernel indirectly represents some of the internal parameters of the neural networks.

References

  1. Gerstner W, Kistler W: Spiking Neuron Models. 2002, Cambridge: Cambridge University Press

    Chapter  Google Scholar 

  2. Rieke F, Warland D, de Ruyter van Steveninck R, Bialek W: Spikes: Exploring the Neural Code. 1997, Cambridge, MA: MIT Press

    Google Scholar 

  3. Victor JD: Spike train metrics. Current Opinion in Neurobiology. 2005, 15: 585-592. 10.1016/j.conb.2005.08.002.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  4. Houghton C, Sen K: A new multi-neuron spike-train metric. Neural Computation. 2008, 20: 1495-1511. 10.1162/neco.2007.10-06-350.

    Article  PubMed Central  PubMed  Google Scholar 

  5. Paiva ARC, Park I, Principe JC: Inner products for representation and learning in the spike train domain. Statistical Signal Processing for Neuroscience and Neurotechnology. 2010, Academic Press

    Google Scholar 

  6. Park I, Seth S, Rao M, Principe JC: Strictly positive definite spike train kernels for point process divergences. Neural Computation. 2012, 24: 2223-2250. 10.1162/NECO_a_00309.

    Article  PubMed  Google Scholar 

  7. Fisher NK, Banerjee A: A novel kernel for learning a neuron model from spike train data. Advances in Neural Information Processing Systems. 2010, 23: 595-603.

    Google Scholar 

  8. Aronov D, Reich DS, Mechler F, Victor JD: Neural coding of spatial phase in V1 of the macaque monkey. J Neurophysiology. 2003, 89: 3304-3327. 10.1152/jn.00826.2002.

    Article  PubMed  Google Scholar 

  9. Tezuka T: Spike train kernels for multiple neuron recordings. Proceedings of the 39th International Conference on Acoustics, Speech and Signal Processing. 2014, (to appear)

    Google Scholar 

Download references

Acknowledgement

This work was supported in part by JSPS KAKENHI Grant Numbers 21700121, 25280110, and 25540159.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Taro Tezuka.

Rights and permissions

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tezuka, T. Parallel spike trains analysis using positive definite kernels. BMC Neurosci 15 (Suppl 1), P29 (2014). https://doi.org/10.1186/1471-2202-15-S1-P29

Download citation

  • Published:

  • DOI: https://doi.org/10.1186/1471-2202-15-S1-P29

Keywords