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Neural Computation, Vol 9, 1601-1622, Copyright © 1997 by The MIT Press

LETTERS

Online Learning in Radial Basis Function Networks

Jason A. S. Freeman and David Saad

An analytic investigation of the average case learning and generalization properties of radial basis function (RBFs) networks is presented, utilizing online gradient descent as the learning rule. The analytic method employed allows both the calculation of generalization error and the examination of the internal dynamics of the network. The generalization error and internal dynamics are then used to examine the role of the learning rate and the specialization of the hidden units, which gives insight into decreasing the time required for training. The realizable and some over-realizable cases are studied in detail: the phase of learning in which the hidden units are unspecialized (symmetric phase) and the phase in which asymptotic convergence occurs are analyzed, and their typical properties found. Finally, simulations are performed that strongly confirm the analytic results.


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H. Wei, J. Zhang, F. Cousseau, T. Ozeki, and S.-i. Amari
Dynamics of learning near singularities in layered networks.
Neural Comput., March 1, 2008; 20(3): 813 - 843.
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Copyright © 1997 by The MIT Press.