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Fuzzy models describe nonlinear input-output relationships with linguistic fuzzy rules. A hierarchical fuzzy modeling is promising for identification of fuzzy models of target systems that have many input variables. In the identification, (1) determination of a hierarchical structure of submodels, (2) selection of input variables of each submodel, (3)… (More)

Neural computation in Clifford algebras, which include familiar complex numbers and quaternions as special cases, has recently become an active research field. As always, neurons are the atoms of computation. The paper provides a general notion for the Hessian matrix of Clifford neurons of an arbitrary algebra. This new result on the dynamics of Clifford… (More)

—We study the optimization of neural networks with Clifford geometric algebra versor and spinor nodes. For that purpose important multivector calculus results are introduced. Such nodes are generalizations of real, complex and quaternion spinor nodes. In particular we consider nodes that can learn all proper and improper Euclidean transformations with… (More)

Most conventional methods of feature extraction do not pay much attention to the geometric properties of data, even in cases where the data have spatial features. In this study we introduce geometric algebra to undertake various kinds of feature extraction from spatial data. Geometric algebra is a generalization of complex numbers and of quaternions, and it… (More)

This paper discusses feature extraction methods. The feature extraction methods such principal component analysis and multiple discriminant analysis are very important techniques in machine learning research areas. The characteristic of feature extraction is to transform the data from a difficultly classified space to a easily classified space. There are… (More)

This paper discusses acquisition of cooperative behaviour among heterogeneous agents and proposes two methods to promote cooperative behaviour: phased learning and selective recognition. For complicated scenarios such as multi-agent tasks, we propose phased learning, in which agents first learn in a simpler environment before learning in the target… (More)

—Clustering is one of the most useful methods for understanding similarity among data. However, most conventional clustering methods do not pay sufficient attention to the geometric properties of data. Geometric algebra (GA) is a generalization of complex numbers and quaternions able to describe spatial objects and the relations between them. This paper… (More)