多元数据升维变换的几何代数表示原理

Geometric algebra representation principle of multivariate data dimension-increasing transformation

传统多元数据分析和模式识别领域一般采用向量空间模型。本文提出将多元数据从维向量空间映射到其生成的几何代数空间的升维变换方法,给出了多元数据在几何代数空间的多向量表示,并且证明了该多向量表示的完备性。最后展望了将几何代数应用于可视化模式识别的前景。

The vector space model is generally adopted in the multivariate data analysis and pattern recognition domain. In this paper, a dimension increasing transformation method, which mapping the vector space to the generated geometric algebra space, is proposed. The multi-vector representation of multivariate data in the geometric algebra space is presented and the completeness of this representation is proved. In the end, the prospect of geometric algebra applying to visual pattern recognition is outlined.