Adaptive variable-structure basis function expansions: Candidates for machine learning

This paper proposes a novel top-down approach to rule-based fuzzy systems, one that begins with the product—an equation—and then addresses the unique features of the product, without requiring the reader to know anything about fuzzy sets and systems. The "products" are adaptive variable-structure basis function expansions , where "adaptive variable-structure" means that different subsets of its basis functions are active (non-zero) in different regions of the state space, something that occurs automatically by virtue of the structure of the basis functions, so that the products can be said to "adapt" to locations in the state space. These products are novel candidates for machine learning . Unique features of all products are: (1) Number of basis functions is no longer a variable and is established locally through type-1 or type-2 uncertainty partitioning of each variable; (2) Both coarse and fine sculpting of the state space are achieved, and are described in terms of first- and second-order partitions of the state space, respectively; and (3) Linguistic interpretability is obtained, which may be of value to an end-user. Learning about rule-based fuzzy systems can be greatly compressed by using the top-down approach that is described in this paper.