Optimal piecewise locally linear modeling
Harris, C. J., Hong, X. and Feng, M. (1999) Optimal piecewise locally linear modeling. In: SPIE AeroSense'99, Applications and Science of Computational Intelligence II, 5th April 1999, Orlando, Florida, USA, p. 486.
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To link to this article DOI: 10.1117/12.342906
Associative memory networks such as Radial Basis Functions, Neurofuzzy and Fuzzy Logic used for modelling nonlinear processes suffer from the curse of dimensionality (COD), in that as the input dimension increases the parameterization, computation cost, training data requirements, etc. increase exponentially. Here a new algorithm is introduced for the construction of a Delaunay input space partitioned optimal piecewise locally linear models to overcome the COD as well as generate locally linear models directly amenable to linear control and estimation algorithms. The training of the model is configured as a new mixture of experts network with a new fast decision rule derived using convex set theory. A very fast simulated reannealing (VFSR) algorithm is utilized to search a global optimal solution of the Delaunay input space partition. A benchmark non-linear time series is used to demonstrate the new approach.