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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)

—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)

—Most conventional methods of feature extraction for pattern recognition do not pay sufficient attention to inherent geometric properties of data, even in the case where the data have spatial features. This paper introduces geometric algebra to extract invariant geometric features from spatial data given in a vector space. Geometric algebra is a… (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… (More)