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Entropy 2013, 15(5), 1690-1704; doi:10.3390/e15051690

An Estimate of Mutual Information that Permits Closed-Form Optimisation

Department of Computing, Imperial College, London SW7 2RH, UK
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Received: 1 February 2013 / Revised: 18 April 2013 / Accepted: 28 April 2013 / Published: 8 May 2013
(This article belongs to the Special Issue Estimating Information-Theoretic Quantities from Data)
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Abstract

We introduce a new estimate of mutual information between a dataset and a target variable that can be maximised analytically and has broad applicability in the field of machine learning and statistical pattern recognition. This estimate has previously been employed implicitly as an approximation to quadratic mutual information. In this paper we will study the properties of these estimates of mutual information in more detail, and provide a derivation from a perspective of pairwise interactions. From this perspective, we will show a connection between our proposed estimate and Laplacian eigenmaps, which so far has not been shown to be related to mutual information. Compared with other popular measures of mutual information, which can only be maximised through an iterative process, ours can be maximised much more efficiently and reliably via closed-form eigendecomposition.
Keywords: mutual information; dimensionality reduction; feature extraction; pattern recognition; machine learning mutual information; dimensionality reduction; feature extraction; pattern recognition; machine learning
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Liu, R.; Gillies, D.F. An Estimate of Mutual Information that Permits Closed-Form Optimisation. Entropy 2013, 15, 1690-1704.

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