Geometric analysis of concept vectors based on similarity values

Abstract

In this paper, we offer a geometric framework for the computing of a concept's conceptual vector based on its similarity position with other concepts in a vector space called concept space, which is a set of concept vectors together with a distance function derived from a similarity model. We show that there exists an isometry to map a concept space to a Euclidean space. So, the concept vector can be mapped to a coordinate in a Euclidean space and vice versa. Therefore, given only the similarity position of a concept, we can locate its coordinate and its concept vector subsequently, using distance geometry methods. We prove that such mapping functions do exist under some conditions. We also discuss how to map non-numerical attributes. At last, we show some preliminary experimental results and thoughts in the implementation of an attribute mining task. This work will benefit attribute retrieval tasks.