Growing Self-Organizing Maps for Nonlinear Time-Varying Function Approximation

Function approximation may be described as the task of modeling the input-output relation and therefore yielding an estimation of the real output function value. In many domains, an ideal learning algorithm needs to approximate nonlinear time-varying functions from a high-dimensional input space and...

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Bibliographic Details
Published in:Neural processing letters 2020-04, Vol.51 (2), p.1689-1714
Main Authors: Ferreira, Paulo H. M., Araújo, Aluízio F. R.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Architecture
Artificial Intelligence
Complex Systems
Computational efficiency
Computational Intelligence
Computer Science
Computing costs
Interpolation
Machine learning
Mapping
Mathematical analysis
Methods
Neural networks
Self organizing maps
Support vector machines
Topology
Unsupervised learning
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Summary:Function approximation may be described as the task of modeling the input-output relation and therefore yielding an estimation of the real output function value. In many domains, an ideal learning algorithm needs to approximate nonlinear time-varying functions from a high-dimensional input space and avoid problems from irrelevant or redundant input data. Therefore, the method has to meet three requirements, namely, it must: allow incremental learning to deal with changing functions and changing input distributions; keep the computational cost low; and achieve accurate estimations. In this paper, we explore different approaches to perform function approximation based on the Local Adaptive Receptive Fields Self-Organizing Map (LARFSOM). Local models are built by calculating between the output associated with the winning node and the difference vector between the input vector and the weight vector. These models are combined by using a weighted sum to yield the final approximate value. The topology is adapted in a self-organizing way, and the weight vectors are adjusted in a modified unsupervised learning algorithm for supervised problems. Experiments were carried out on synthetic and real-world datasets. Experimental results indicate that the proposed approaches perform competitively against Support Vector Regression (SVR) and can improve function approximation accuracy and computational cost against the locally weighted interpolation (LWI), a state-of-the-art interpolating algorithm for self-organizing maps.
ISSN:1370-4621
1573-773X
DOI:10.1007/s11063-019-10168-9