Proceedings of International Joint Conference on Neural Networks, Montreal, Canada, July 31 - August 4, 2005 On the Design of an Ellipsoid ARTMAP Classifier within the Fuzzy Adaptive System ART Framework Ross Peralta Electrical & Computer Eng. ' rperalta@fit.edu Georgios C. Anagnostopoulos Electrical & Computer Eng. l georgio@fit.edu Eduardo Gomez-Sanchez Comm. & Telematics2 edugom@tel.uva.es Samuel Richie Electrical Eng.3 richie@mail.ucf.edu 'Florida Institute of Technology, Melbourne, FL 32901 2University of Valladolid, Valladolid, Spain 47011 3University of Central Florida, Orlando, FL 32816 Abstract - In this paper we present the design of Fuzzy Adaptive System Ellipsoid ARTMAP (FASEAM), a novel neural architecture based on Ellipsoid ARTMAP (EAM) that is equipped with concepts utilized in the Fuzzy Adaptive System ART (FASART) architecture. More specifically, we derive a new category choice function appropriate for EAM categories that is non-constant in a category's representation region. Additionally, we augment the EAM category description with a centroid vector, whose learning rate is inversely proportional to the number of training patterns accessing the category. Finally, we demonstrate the merits of our design choices by comparing FASART, EAM and FASEAM in terms of generalization performance and final structural complexity on a set of classification problems. I. INTRODUCTION Adaptive resonance theory (ART) based neural networks constitute a large family of neural architectures that have been used in a plethora of applications ranging from data clustering, classification and function approximation tasks. They are all based on the ART paradigm first introduced in [1] and feature a variety of highly desirable properties, like the ability of incremental (online) learning, network response transparency and fast training phase. A characteristic of these networks is that they summarize the input data into clusters via the use of prototypes called categories, whose geometrical representation may vary (depending on the particular architecture) from being hyper-rectangles, hyper-spheres or hyper-ellipsoids embedded in the input space. A member of the ART-based family is the Fuzzy Adaptive System ART (FASART) architecture, which was first presented in [2] as an enhancement to the standard Fuzzy ARTMAP (FAM) network [3]. FASART networks have also been successfully used for function approximation, data clustering, as well as classification tasks; see for example [4] and [5]. Both FAM and FASART employ categories, whose geometric representations are hyper-rectangles. However, FASART extends FAM by equipping categories with an additional centroid element and by introducing a new, parameterized category choice function (CCF). In FAM, the CCF value is constant within a category's representation region (see [6] for related definitions), while in FASART it monotonically decreases from 1 (at the centroid) to 0 beyond the boundaries of the category's representation region. Furthermore, while FAM's CCF depends on the category's size and the distance of the pattern from the category's representation region, in FASART the CCF depends on the distance of the pattern from the centroid and, implicitly, on the size of the category in a component-wise fashion. In this manner, FASART categories are appropriately defined as fuzzy sets and the CCF's value with respect to a pattern can be interpreted as its normalized, fuzzy membership in that fuzzy set. This permits the dual interpretation of FASART as a neural model as well as a formal fuzzy logic inference system, which is not the case for FAM according to [7]. Yet another ART-based architecture is Ellipsoid ARTMAP (EAM) [8]. The network shares almost all structural and behavioral features, as well as properties of learning with FAM. While FAM and FASART categories are represented as hyper-rectangles, EAM categories are of hyper-ellipsoid shape, which may be more suitable for certain learning problems. Like in the case of FAM, in EAM the CCF is of constant value within a category's representation region. In certain classification problem domains this CCF constancy may lead to unsatisfactory classification performance. More specifically, it is a known fact that patterns located inside the representation regions of two or more categories will access the category of the smallest size. This effect may potentially lead to poor approximation of the decision boundaries and could be avoided by using a CCF that is not constant within the representation region. This paper focuses on the design of a variant of EAM, which we named FASEAM classifier. The relationship of FASEAM to EAM is the same as the one of FASART to FAM. We equip EAM categories with a centroid vector that is adjusted according to patterns accessing the categories. Furthermore, we derive a new CCF that is reminiscent (with 0-7803-9048-2/05/$20.00 ©2005 IEEE 469