Genetic evolution of radial basis function coverage using orthogonal niches

Abstract

A well-performing set of radial basis functions (RBFs) can emerge from genetic competition among individual RBFs. Genetic selection of the individual RBFs is based on credit sharing which localizes competition within orthogonal niches. These orthogonal niches are derived using singular value decomposition and are used to apportion credit for the overall performance of the RBF network among individual nonorthogonal RBFs. Niche-based credit apportionment facilitates competition to fill each niche and hence to cover the training data. The resulting genetic algorithm yields RBF networks with better prediction performance on the Mackey-Glass chaotic time series than RBF networks produced by the orthogonal least squares method and by k-means clustering.

Credit Assignment Among Neurons in Co-evolving Populations

“…where α = 0.2, β = −0.1, τ = 17 as used in [7,8,[13][14][15]. Each network receives four past data points x(t), x(t − 6), x(t − 12) and x(t − 18) as inputs and predicts 6 time steps ahead (x(t + 6)).…”

“…u m , Σ is a diagonal matrix with positive or zero elements (the singular values), and V an orthogonal matrix with entries v ij . Credit available to each basis function φ i is given by (for details refer to [8])…”

“…Here a credit apportionment strategy (proposed in [8]) is used to split the credit for the overall performance of the RBF network, first, into orthogonal niches and then the credit available for each individual niche is apportioned among individual RBGFs depending on how much they contribute to that niche. In an RBF Network for a set of (say) m basis functions φ i s, singular value decomposition (SVD) of transformed training data matrix A, whose elements are a ki = φ i (x k ), gives A = UΣV T , where U has orthogonal columns u 1 , .…”

“…It does not hold for MLPs, where the effect of all hidden neurons should be taken into account at each point of the input space. Locality in RBF Networks has been exploited [7,8] to solve the aforementioned credit assignment problem.…”

A pareto archive evolutionary strategy based radial basis function neural network training algorithm for failure rate prediction in overhead feeders

“…As these networks make use of units having highly localized responses, called kernels, many methods exist to train such networks that use clustering [4]. Evolutionary algorithms [7] have also been a popular choice amongst researchers [8,9,10,11,12,13].…”