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Brain Sci. 2016, 6(4), 44; doi:10.3390/brainsci6040044

The Cluster Variation Method: A Primer for Neuroscientists

Northwestern University School of Professional Studies, Master of Science in Predictive Analytics Program, 405 Church St, Evanston, IL 60201, USA
Academic Editor: Vaibhav Gandhi
Received: 27 July 2016 / Revised: 14 September 2016 / Accepted: 15 September 2016 / Published: 30 September 2016
(This article belongs to the Special Issue Brain-Computer Interfaces: Current Trends and Novel Applications)
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Abstract

Effective Brain–Computer Interfaces (BCIs) require that the time-varying activation patterns of 2-D neural ensembles be modelled. The cluster variation method (CVM) offers a means for the characterization of 2-D local pattern distributions. This paper provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 2-D pattern distributions expressing structural and functional dynamics in the brain. The premise is that local-in-time free energy minimization works alongside neural connectivity adaptation, supporting the development and stabilization of consistent stimulus-specific responsive activation patterns. The equilibrium distribution of local patterns, or configuration variables, is defined in terms of a single interaction enthalpy parameter (h) for the case of an equiprobable distribution of bistate (neural/neural ensemble) units. Thus, either one enthalpy parameter (or two, for the case of non-equiprobable distribution) yields equilibrium configuration variable values. Modeling 2-D neural activation distribution patterns with the representational layer of a computational engine, we can thus correlate variational free energy minimization with specific configuration variable distributions. The CVM triplet configuration variables also map well to the notion of a M = 3 functional motif. This paper addresses the special case of an equiprobable unit distribution, for which an analytic solution can be found. View Full-Text
Keywords: brain–computer interfaces; pattern recognition; statistical thermodynamics; Cluster Variation Method; entropy; brain networks; functional motifs; variational free energy; neural activation patterns; deep learning brain–computer interfaces; pattern recognition; statistical thermodynamics; Cluster Variation Method; entropy; brain networks; functional motifs; variational free energy; neural activation patterns; deep learning
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Maren, A.J. The Cluster Variation Method: A Primer for Neuroscientists. Brain Sci. 2016, 6, 44.

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