This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 532
Type: Contributed
Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #308528
Title: Fast Euclidean Embedding of Ordinal Nearest Neighbor Graphs
Author(s): Brent Shannon Castle*+ and Faming Liang and Michael Trosset
Companies: Indiana University and Texas A&M University and Indiana University
Address: 5347 N. College Ave. #315, Indianapolis, IN, 46220,
Keywords: nonmetric multidimensional scaling ; nearest neighbor graphs ; raw stress criterion ; partial ordering ; isotonic regression
Abstract:

A number of interesting data sets provide information about the nearest neighbors of a set of objects. For example, each book sold by Amazon.com is accompanied by a list of its most similar neighbors, measured by the proportion of viewers who ultimately buy the other book. These data can be conceived as a directed graph in which vertices represent objects and edges identify nearest neighbor structure. For Amazon.com, the edges are weighted by a quantitative measure of proximity; in other applications, the edge weights may be ordinal, i.e., the ranks of the nearest neighbors may be provided without a corresponding quantitative measure of proximity. We develop methods for mapping such data sets, i.e., for embedding ordinal nearest neighbor graphs in low-dimensional Euclidean spaces.


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