A Conformal Geometric Algebra Based Clustering Method and Its Applications
| Autor: | Kanta Tachibana, Minh Tuan Pham |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Applied Mathematics
Universal geometric algebra Correlation clustering Geometric transformation Conformal geometric algebra 020206 networking & telecommunications 02 engineering and technology Topology 01 natural sciences Geometric algebra 0103 physical sciences 0202 electrical engineering electronic engineering information engineering 010307 mathematical physics Quaternion Cluster analysis Algorithm Euclidean vector Mathematics |
| Zdroj: | Advances in Applied Clifford Algebras. 26:1013-1032 |
| ISSN: | 1661-4909 0188-7009 |
| DOI: | 10.1007/s00006-015-0548-7 |
| Popis: | 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 distributions of data. Geometric algebra (GA) is a generalization of complex numbers and quaternions able to describe spatial objects and the geometric relations between them. This paper uses conformal GA (CGA), which is a part of GA. This paper transforms data from a real Euclidean vector space into a CGA space and presents a new clustering method using conformal vectors. In particular, this paper shows that the proposed method was able to extract the geometric clusters which could not be detected by conventional methods. |
| Databáze: | OpenAIRE |
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