2008•Journal of Yanshan UniversityRequires access

Geometric algebra representation principle of multivariate data dimension-increasing transformation

XU Yong-hong

Abstract

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.

About this research paper

What this paper is about

Why it matters

OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Geometric algebra, Conformal geometric algebra, Universal geometric algebra, Mathematics, Algebra over a field, Geometric transformation, Multivector, Dimension (graph theory)