Abstract

This paper poses and solves a new problem, the rankability problem, which refers to a dataset's inherent ability to produce a meaningful ranking of its items. Ranking is a fundamental data science task. Its applications are numerous and include web search, data mining, cybersecurity, machine learning, and statistical learning theory. Yet little attention has been paid to the question of whether a dataset is suitable for ranking. As a result, when a ranking method is applied to an unrankable dataset, the resulting ranking may not be reliable. The rankability problem asks the following: How can rankability be quantified? At what point is a dynamic, time-evolving graph rankable? If a dataset has low rankability, can modifications be made and which most improve the graph's rankability? We present a combinatorial approach to a rankability measure and then compare several algorithms for computing this new measure. Finally, we apply our new measure to several datasets.

Keywords

  1. ranking
  2. rankability
  3. linear program
  4. integer program
  5. combinatorial optimization
  6. relaxation

MSC codes

  1. 90C08
  2. 90C10
  3. 52B12
  4. 90C35

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Supplementary Material


PLEASE NOTE: These supplementary files have not been peer-reviewed.


Index of Supplementary Materials

Title of paper: The Rankability of Data

Authors: Paul E. Anderson, Timothy P. Chartier, and Amy N. Langville

File: Supplementary_Materials_1.pdf

Type: PDF

Contents: An example using real data from the 2009 ACC college basketball season of games between n = 12 teams.

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Information & Authors

Information

Published In

cover image SIAM Journal on Mathematics of Data Science
SIAM Journal on Mathematics of Data Science
Pages: 121 - 143
ISSN (online): 2577-0187

History

Submitted: 26 April 2018
Accepted: 11 January 2019
Published online: 12 February 2019

Keywords

  1. ranking
  2. rankability
  3. linear program
  4. integer program
  5. combinatorial optimization
  6. relaxation

MSC codes

  1. 90C08
  2. 90C10
  3. 52B12
  4. 90C35

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