Generalizing the Mean and Variance to Categorical Data Using Metrics

• Activity Number: 655
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Roger Bilisoly*+
• Companies: Central Connecticut State University
• Keywords: Categorical Data ; Edit Distance ; Group Theory ; Word Metric ; Riemannian Manifolds

Abstract

Researchers have developed ways to generalize the mean and variance to situations in which a data metric is available. We apply the tools developed in Pennec (2006) to categorical data, and show the generality of this approach by considering two quite different applications. First, spelling variability in Middle English is quantified. Second, variability of a finite group (in the sense of group theory) is defined and applied to an example.