#### Filter Results:

#### Publication Year

1998

2016

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

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)

- Sven Buchholz, Eckhard Hitzer, Kanta Tachibana
- 2008

—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)

- Minh Tuan Pham, Phuc Hao Do, Kanta Tachibana
- IJCNN
- 2016

—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)

- Minh Tuan Pham, Kanta Tachibana, Tomohiro Yoshikawa, Takeshi Furuhashi
- 2010

—One of the most important designs for a lot of machine learning methods is the determination of the similarity between instances. Especially the kernel matrix, which is also known as the Gram matrix, plays a central role in the kernel machines such as support vector machine. The simplest design of similarity function is to use the distances between… (More)