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Entropy 2013, 15(10), 4540-4552; doi:10.3390/e15104540
Article

A Kernel-Based Calculation of Information on a Metric Space

1
 and
2,*
1 School of Mathematics, Trinity College Dublin, Dublin 2, Ireland 2 Department of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK
* Author to whom correspondence should be addressed.
Received: 24 July 2013 / Revised: 14 October 2013 / Accepted: 14 October 2013 / Published: 22 October 2013
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Abstract

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual information between stimuli and spiking responses; the space of these responses is a metric space. It is shown that kernel density estimation on a metric space resembles the k-nearest-neighbor approach. This approach is applied to a toy dataset designed to mimic electrophysiological data.
Keywords: mutual information; neuroscience; electrophysiology; metric spaces; kernel density estimation mutual information; neuroscience; electrophysiology; metric spaces; kernel density estimation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Tobin, R.J.; Houghton, C.J. A Kernel-Based Calculation of Information on a Metric Space. Entropy 2013, 15, 4540-4552.

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