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Title
Abstract
Introduction
Analysis of Cross-Intensity Kernels 4.1 Properties
Conclusion
References
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Mathematics
Functional Analysis

A Reproducing Kernel Hilbert Space Framework for ITL

Profile image of Antonio PaivaAntonio Paiva

2010, Information Science and Statistics

https://doi.org/10.1162/NECO.2008.09-07-614
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27 pages

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Abstract

This paper presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical description as point processes. Moreover, because many inner products can be formulated, a particular definition can be crafted to best fit an application. These ideas are illustrated by the definition of a number of spike train inner products. To further elicit the advantages of the RKHS framework, a family of these inner products, called the cross-intensity (CI) kernels, is further analyzed in detail. This particular inner product family encapsulates the statistical description from conditional intensity functions of spike trains. The problem of their estimation is also addressed. The simplest of the spike train kernels in this family provides an interesting perspective to other works presented in the literature, as will be illustrated in terms of spike train distance measures. Finally, as an application example, the presented RKHS framework is used to derive from simple principles a clustering algorithm for spike trains.

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Related topics

  • Functional Analysis
  • Algorithms
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