Multi-Column RBF Neural Network Using Adaptive and Non-Adaptive Particle Swarm Optimization
2026-06-03 • Neural and Evolutionary Computing
Neural and Evolutionary ComputingArtificial Intelligence
AI summaryⓘ
The authors study ways to improve a type of neural network called radial basis function neural networks (RBFN), which can learn from data but slow down with large datasets. They build on a recent method that uses multiple small RBFNs working in parallel to handle data subsets separately. The authors propose two new versions combining this multi-column idea with advanced swarm-based training algorithms (PSO and its adaptive variant APSO). Their methods train specialized RBFNs on parts of the data, which speeds up training and testing and improves accuracy compared to previous methods.
Radial Basis Function Neural NetworkGradient DescentParticle Swarm OptimizationAdaptive Particle Swarm OptimizationMulti-column RBFNParallel ComputingKernel FunctionsEvolutionary AlgorithmsScalabilityBenchmark Datasets
Authors
Ammar Hoori, Yuichi Motai
Abstract
The radial basis function neural network (RBFN) trained with a gradient descending algorithm provides an effective fully connected structure in both shallow and deep networks. The error correction (ErrCor), a state-of-the-art gradient-based training method, selects optimal hidden units to improve accuracy. Alternatively, as a population-based algorithm, the particle swarm optimization algorithm (PSO) uses the swarm experience to optimize RBFN parameters, offering global search and robustness to local minima. Adaptive PSO (APSO) has emerged as an improved variant of PSO. APSO algorithm improves convergence speed by dynamically adjusting swarm parameters during optimization. Both ErrCor and PSO demonstrate improved results and competitive convergence. However, with large datasets, these methods face scalability challenges such as excessive kernel computations and large hidden layer structures. A recent multi-column RBFN approach (MCRN) improves ErrCor performance by deploying small RBFNs in a parallel system. Inspired by MCRN's success, we propose two novel approaches to improve PSO performance: the multi-column RBFN with PSO (MC-PSO) and the multi-column RBFN with APSO (MC-APSO). These methods introduce parallel RBFN structures trained using evolutionary swarm methods. Each RBFN is independently trained on a specific spatial subset of the dataset using either PSO or APSO algorithms. These resulting specialist-trained RBFNs are tailored to their respective subsets. During testing, only selected RBFNs, where the test instance neighbors are located, contribute to the multi-column output. This specialization improves accuracy, while parallelism enhances speed. We evaluate the proposed methods on various benchmark datasets. The MC-PSO and MC-APSO outperform ErrCor, PSO, APSO, and MCRN in terms of accuracy and recall. They also demonstrate faster training and testing times in most experiments.