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Reconstruction of network structures from marked point processes using multi-dimensional scaling

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  • Kuroda, Kaori
  • Hashiguchi, Hiroki
  • Fujiwara, Kantaro
  • Ikeguchi, Tohru

Abstract

We propose a method of estimating network structures only from observed marked point processes using the multi-dimensional scaling. In this method, first, we calculate a spike time metric which quantifies a metric distance between the observed marked point processes. Next, to represent a relationship among point processes in the Euclidean space, we apply the multi-dimensional scaling to the metric distance between point processes. Then we apply the partialization analysis to the obtained coordinate vectors by the multi-dimensional scaling. As a result, we can estimate the network structures from multiple point processes even though the elements have many common spurious inputs from the other elements.

Suggested Citation

  • Kuroda, Kaori & Hashiguchi, Hiroki & Fujiwara, Kantaro & Ikeguchi, Tohru, 2014. "Reconstruction of network structures from marked point processes using multi-dimensional scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 194-204.
    • Handle: RePEc:eee:phsmap:v:415:y:2014:i:c:p:194-204
    DOI: 10.1016/j.physa.2014.08.001
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    References listed on IDEAS

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    1. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    2. Gale Young & A. Householder, 1938. "Discussion of a set of points in terms of their mutual distances," Psychometrika, Springer;The Psychometric Society, vol. 3(1), pages 19-22, March.
    3. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    4. Kuroda, Kaori & Ashizawa, Tohru & Ikeguchi, Tohru, 2011. "Estimation of network structures only from spike sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 4002-4011.
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