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On the classification problem for Poisson point processes

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  • Cholaquidis, Alejandro
  • Forzani, Liliana
  • Llop, Pamela
  • Moreno, Leonardo

Abstract

For Poisson processes taking values in a general metric space, we tackle the problem of supervised classification in two different ways: via the classical k-nearest neighbor rule, by introducing suitable distances between patterns of points; and via the Bayes rule, by nonparametrically estimating the intensity function of the process. In the first approach we prove that under the separability of the space, the rule turns out to be consistent. In the second case, we prove the consistency of the rule by proving the consistency of the estimated intensities. Both classifiers are shown to behave well under departures from the Poisson distribution.

Suggested Citation

  • Cholaquidis, Alejandro & Forzani, Liliana & Llop, Pamela & Moreno, Leonardo, 2017. "On the classification problem for Poisson point processes," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 1-15.
    • Handle: RePEc:eee:jmvana:v:153:y:2017:i:c:p:1-15
    DOI: 10.1016/j.jmva.2016.09.002
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    References listed on IDEAS

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    1. Marie-Colette N. M. Lieshout, 2012. "On Estimation of the Intensity Function of a Point Process," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 567-578, September.
    2. Kang, Jian & Johnson, Timothy D. & Nichols, Thomas E. & Wager, Tor D., 2011. "Meta Analysis of Functional Neuroimaging Data via Bayesian Spatial Point Processes," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 124-134.
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    Cited by:

    1. Kateřina Pawlasová & Iva Karafiátová & Jiří Dvořák, 2024. "Neural networks with functional inputs for multi-class supervised classification of replicated point patterns," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(3), pages 705-721, September.
    2. Abdollah Jalilian & Jorge Mateu, 2023. "Assessing similarities between spatial point patterns with a Siamese neural network discriminant model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 21-42, March.

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