JSM 2004 - Toronto

Abstract #301477

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Activity Number: 187
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract - #301477
Title: Multivariate Rankings of Outlier Groupings Using Minimal Spanning Trees and Convex Hull-peeling
Author(s): Mark W. Lukens*+ and James E. Gentle
Companies: George Mason University and George Mason University
Address: 4061 Cardinal Crest Dr., Woodbridge, VA, 22193,
Keywords: outliers ; multivariate ranking ; convex hull ; minimal spanning trees
Abstract:

Order statistics and the ranking of data are important techniques in data analysis. Ranking is unambiguous in one dimension where a simple sorting from lowest to highest will order the data. In the multivariate case, however, this natural concept of ordering is not so clearly defined. Ordering multivariate data and the concept of multivariate rankings become complicated in higher dimensions, and do not necessarily correspond to other characteristics of data, such as clusters. This paper will examine two techniques for ranking multivariate data, minimal spanning trees and convex hull peeling, in the context of data groupings. Both of these methods yield potentially undesirable results when data clusters are present. The rankings tend to bounce back and forth between the various groupings. It desirable to have similar rankings for groups of data that are otherwise similar. This grouping of the ranks could then assist in analysis of the data. This paper introduces changes to the multivariate ranking algorithms for both the minimal spanning tree and the convex hull-peeling so the multivariate rankings are grouped analogous to the data.

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