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dc.contributor.authorParker, Albert E.
dc.contributor.authorDimitrov, Alexander G.
dc.contributor.authorGedeon, Tomas
dc.identifier.citationParker, A., Dimitrov, A., and Gedeon, T., "Symmetry breaking clusters in soft clustering decoding of neural codes," IEEE Transactions on Information Theory: Special Issue on Molecular Biology and Neuroscience 2010; 56(2):901-927en_US
dc.description.abstractInformation-based distortion methods have been used successfully in the analysis of neural coding problems. These approaches allow the discovery of neural symbols and the corresponding stimulus space of a neuron or neural ensemble quantitatively, while making few assumptions about the nature of either the code or of relevant stimulus features. The neural codebook is derived by quantizing sensory stimuli and neural responses into a small set of clusters, and optimizing the quantization to minimize an information distortion function. The method of annealing has been used to solve the corresponding high-dimensional nonlinear optimization problem. The annealing solutions undergo a series of bifurcations, which we study using bifurcation theory in the presence of symmetries. In this contribution we describe these symmetry breaking bifurcations in detail, and indicate some of the consequences of the form of the bifurcations. In particular, we show that the annealing solutions break symmetry at pitchfork bifurcations, and that subcritical branches can exist. Thus, at a subcritical bifurcation, there are local information distortion solutions which are not found by the method of annealing. Since the annealing procedure is guaranteed to converge to a local solution eventually, the subcritical branch must turn and become optimal at some later saddle-node bifurcation, which we have shown occur generically for this class of problems. This implies that the rate distortion curve, while convex for noninformation-based distortion measures, is not convex for information-based distortion methods.en_US
dc.titleSymmetry breaking clusters in soft clustering decoding of neural codesen_US
mus.citation.journaltitleIEEE Transactions on Information Theory: Special Issue on Molecular Biology and Neuroscienceen_US
mus.identifier.categoryChemical & Material Sciencesen_US
mus.identifier.categoryEngineering & Computer Scienceen_US
mus.identifier.categoryLife Sciences & Earth Sciencesen_US
mus.relation.collegeCollege of Agricultureen_US
mus.relation.collegeCollege of Engineeringen_US
mus.relation.collegeCollege of Letters & Scienceen_US
mus.relation.departmentCell Biology & Neuroscience.en_US
mus.relation.departmentCenter for Biofilm Engineering.en_US
mus.relation.departmentChemical & Biological Engineering.en_US
mus.relation.departmentChemical Engineering.en_US
mus.relation.departmentChemistry & Biochemistry.en_US
mus.relation.departmentMicrobiology & Immunology.en_US
mus.relation.universityMontana State University - Bozemanen_US
mus.relation.researchgroupCenter for Biofilm Engineering.en_US
mus.contributor.orcidGedeon, Tomas|0000-0001-5555-6741en_US

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