Evolving Basis Function Networks for System Identification

Abstract

This paper is concerned with learning and optimization of different basis function networks in the aspect of structure adaptation and parameter tuning. Basis function networks include the Volterra polynomial, Gaussian radial, B-spline, fuzzy, recurrent fuzzy, and local Gaussian basis function networks. Based on creation and evolution of the type constrained sparse tree, a unified framework is constructed, in which structure adaptation and parameter adjustment of different basis function networks are addressed using a hybrid learning algorithm combining a modified probabilistic incremental program evolution (MPIPE) and random search algorithm. Simulation results for the identification of nonlinear systems show the feasibility and effectiveness of the proposed method.

Using Additive Expression Programming for Gene Regulatory Network Inference

“…I 1 is the operator set, where {*, /,sin,cos,exp, log} F r  and { , } T x R  are function and terminal sets. *, /, sin, cos, exp, rlog, x, and R denote the multiplication, protected division (  x, y  R : when y = 0, x/0 = 1), sine, cosine, exponent, protected logarithm (  x  R, x  0 : rlog(x) = log(abs(x)) and rlog(0) = 0), system inputs, and random constant number, taking 2, 2, 1, 1, 1, 1, 0 and 0 arguments respectively [18]. According to the specific problems, we could add some complex functions into operator set I 1 , for example 11 {*, /,sin, cos, log, tan, , , ,*3,*4, , } 111…”

“…We have proposed a new representation scheme of the additive tree models for the system identification especially identification of linear/nonlinear ODE system [13,18]. Compared with genetic programming (GP) and gene expression programming (GEP), this model was powerful than the GEP and GP models, both in the aspects of accuracy and runtime.…”

A Novel Hybrid Framework for Reconstructing Gene Regulatory Networks

“…The additive models resulted from our previously published work, are proposed for the system identification especially the reconstruction of polynomials and the identification of linear/nonlinear systems [10]. Thus we encode the right-hand side of linear and nonlinear mathematic models into a additive tree individual (Please refer to Figure. …”

Ensemble of Flexible Neural Tree and Ordinary Differential Equations for Small-time Scale Network Traffic Prediction

“…+N, *, /, sin, cos, exp, rlog, x, and R denote the addition, multiplication, protected division, sine, cosine, exponent, protected logarithm, system inputs, and random constant number, respectively, and take N, 2, 2, 1, 1, 1, 1, 0 and 0 arguments [24]. N is an integer number (the maximum number of an ODE terms), I 0 is the instruction set and the root node, and the instructions of other nodes are selected from the instruction set I 1 [20].…”

“…N is an integer number (the maximum number of an ODE terms), I 0 is the instruction set and the root node, and the instructions of other nodes are selected from the instruction set I 1 [20]. It is worth mentioning that if the right-hand side of ODEs is the polynomial, the instruction set I 1 can be defined as I 1 = {*2, *3, ..., *n, x 1 , x 2 , ..., x n , R} [24].…”