Clustering of Questionnaire Based on Feature Extracted by Geometric Algebra

Abstract

Clustering is one of the most useful methods to understand similarity among data. However, most conventional clustering methods do not pay sufficient attention to geometric properties of data. Geometric algebra (GA) is a generalization of complex numbers and of quaternions, and it is able to describe spatial objects and relations between them. In this study we introduce GA to systematically extract geometric features from data. We propose a new clustering method by using various geometric features extracted with GA. We apply the proposed method to clarification of human impressions of a product. In the field of marketing, companies often carry out a questionnaire on consumers for grasping their impressions. Analyzing consumers through the obtained evaluation data enables us to know the tendency of the market and to find problems and/or to make hypotheses that are useful for the development of products. Finally, we discuss clustering results of a questionnaire with/without GA.