New Applications of Clifford’s Geometric Algebra

International audienceThe new applications of Clifford's geometric algebra surveyed in this paper include kinematics and robotics, computer graphics and animation, neural networks and pattern recognition, signal and image processing, applications of versors and orthogonal transformations, spinors and matrices, applied geometric calculus, physics, geometric algebra software and implementations, applications to discrete mathematics and topology, geometry and geographic information systems, encryption, and the representation of higher order curves and surfaces

A Clustering Method for Geometric Data based on Approximation using Conformal Geometric Algebra

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 uses conformal GA (CGA), which is a part of GA, to transform a vector in a real vector space into a vector in a CGA space and presents a proposed 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.2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), June 27-30, 2011, Grand Hyatt Taipei, Taipei, Taiwa

幾何データからのGeometric Algebraを用いた特徴抽出

要旨ありデータマイニングと統計数理研究ノー