Goulermas John Y, Zeng Xiao-Jun, Liatsis Panos, Ralph Jason F
Department of Electrical Engineering and Electronics, University of Liverpool, L69 3GJ Liverpool, UK.
IEEE Trans Syst Man Cybern B Cybern. 2007 Dec;37(6):1434-45. doi: 10.1109/tsmcb.2007.904541.
This paper proposes a novel algorithm for function approximation that extends the standard generalized regression neural network. Instead of a single bandwidth for all the kernels, we employ a multiple-bandwidth configuration. However, unlike previous works that use clustering of the training data for the reduction of the number of bandwidths, we propose a distinct scheme that manages a dramatic bandwidth reduction while preserving the required model complexity. In this scheme, the algorithm partitions the training patterns to groups, where all patterns within each group share the same bandwidth. Grouping relies on the analysis of the local nearest neighbor distance information around the patterns and the principal component analysis with fuzzy clustering. Furthermore, we use a hybrid optimization procedure combining a very efficient variant of the particle swarm optimizer and a quasi-Newton method for global optimization and locally optimal fine-tuning of the network bandwidths. Training is based on the minimization of a flexible adaptation of the leave-one-out validation error that enhances the network generalization. We test the proposed algorithm with real and synthetic datasets, and results show that it exhibits competitive regression performance compared to other techniques.
本文提出了一种新颖的函数逼近算法，该算法扩展了标准的广义回归神经网络。我们采用多带宽配置，而不是为所有核使用单个带宽。然而，与以往使用训练数据聚类来减少带宽数量的工作不同，我们提出了一种独特的方案，该方案在保持所需模型复杂度的同时，大幅减少了带宽。在该方案中，算法将训练模式划分为若干组，每组内的所有模式共享相同的带宽。分组依赖于对模式周围局部最近邻距离信息的分析以及基于模糊聚类的主成分分析。此外，我们使用一种混合优化过程，该过程结合了粒子群优化器的一种非常高效的变体和拟牛顿法，用于网络带宽的全局优化和局部最优微调。训练基于对留一法验证误差的灵活调整的最小化，这增强了网络的泛化能力。我们用真实和合成数据集测试了所提出的算法，结果表明与其他技术相比，它具有有竞争力的回归性能。
