A clustering method for geometric data based on approximation using conformal geometric algebra
A clustering method for geometric data based on approximation using conformal geometric algebra
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DOI：
10.1109/fuzzy.2011.6007574
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
M. Pham;K. Tachibana;T. Yoshikawa;T. Furuhashi
中科院分区：
文献类型：
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作者：
M. Pham;K. Tachibana;T. Yoshikawa;T. Furuhashi
聚类是理解数据之间相似性的最有用的方法之一。然而，大多数传统的聚类方法没有充分注意到数据的几何属性。几何代数（GA）是复数和四元数的推广，能够描述空间对象及其之间的关系。本文利用遗传算法中的保角遗传算法（CGA）将真实的向量空间中的向量转换为CGA空间中的向量，提出了一种新的基于保角向量的聚类方法。特别是，本文表明，所提出的方法是能够提取的几何簇，不能检测到的常规方法。
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.