## Finite Metric Spaces and Data Analysis

(Abstract)

### Michael D. Rice

Department of Mathematics & Computer Science

Wesleyan University

Middletown, CT 06459

*mrice@wesleyan.edu*
For the last few years, I have been studying current and potential uses of distance functions in a variety of areas that involve the presentation and analysis of data. These areas include cluster analysis, multi-dimensional scaling, concept analysis, computational biology, and the theory of relational databases.

The aim of the current paper is to

- present ideas from several of these fields that involve finite metric spaces

- suggest how the study of finite metric spaces can advance ideas in these fields.

Much of the presentation is simply a restatement of ideas and results from the literature in the various fields. However, I believe that the "repackaging" may be of some interest. I will also present a new result (obtained with Alex Russell of the University of Connecticut) that the distances of any finite metric space can be uniformly lengthened to obtain a space that is isometric to a subspace of an *n*-dimensional Euclidean space.