Adaptive Fuzzy Mixture of Local Feature Models

Abstract

This paper addresses an important issue in model combination, that is, model locality. Since usually a global linear model is unable to reflect nonlinearity and to characterize local features, especially in a complex system, we propose a mixture of local feature models in order to overcome these weaknesses. The basic idea is to split the entire input space into operating domains, and a recently developed feature-based model combination method is applied to build local models for each region. In order to realize this idea, three steps are required, which include clustering, local modeling and model combination, governed by a single objective function. An adaptive fuzzy parametric clustering algorithm is proposed in order to divide the whole input space into operating regimes, create local feature models in each individual region by applying a recently developed feature-based model combination method, and finally the local feature models are combined into a single mixture model. Correspondingly, a three-stage optimization procedure is designed to optimize the complete objective function, which is actually a hybrid Genetic Algorithm (GA). Our simulation results show that the adaptive fuzzy mixture of local feature models turns out to be superior to global models.

Keywords: Adaptive fuzzy mixture, local feature model, PCA, ICA, phase transition, fuzzy parametric clustering, Real-coded Genetic Algorithm

JEL Classification: C13, C14, C51, C52, C61