Metric Methods for Analyzing Partially Ranked Data

@inproceedings{Critchlow1986MetricMF,
  title={Metric Methods for Analyzing Partially Ranked Data},
  author={Douglas E. Critchlow},
  year={1986}
}
  • D. Critchlow
  • Published 6 January 1986
  • Mathematics, Computer Science
I. Introduction and Outline.- II. Metrics on Fully Ranked Data.- A. Permutations: Some Important Conventions.- B. Metrics on Permutations: Discussion and Exampl es.- C. The Requirement of Right-Invariance.- III. Metrics on Partially Ranked Data: The Case where Each Judge Lists His k Favorite Items Out of n.- A. The Coset Space Sn/Sn-k.- B. The Hausdorff Metrics on Sn/Sn-k.- C. The Fixed Vector Metrics on Sn/Sn-k.- IV. Metrics on Other Types of Partially Ranked Data.- A. The Coset Space Sn/S… 
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271 Citations
Highly Influential Citations
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102
Methods Citations
61
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271 Citations

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Ranked data arise when some group of judges is asked to rank order a set of n items according to some preference function. A judge's ranking is denoted by a vector x = (x 1 ; : : : ; x n), where x i…
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This paper initializes a step of research toward a systematic study on distances on the symmetric groups Sn together with their applications in many contexts; for example: statistics, coding theory, computing, bell-ringing and so on, which were originally seen unrelated.
Understanding Local Structure in Ranked Datasets
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It is argued for the use of fundamental data management principles such as declarativeness and incremen- tal evaluation, in combination with state-of-the-art machine learn- ing and data mining techniques, for addressing the effectiveness and efficiency challenges of large ranked datasets.
On rank statistics : an approach via metrics on the permutation group
How to aggregate Top-lists: Approximation algorithms via scores and average ranks
TLDR
Using inspiration from approval voting, the score of an element is defined as the frequency with which it is ranked, i.e. appears in an input top-list, and the footrule algorithm for rank aggregation is generalized.
Probability models on rankings.
Graph-Based Tests for Two-Sample Comparisons of Categorical Data
TLDR
This work proposes a general non-parametric approach that utilizes similarity information on the space of all categories in two sample tests and explores different ways to extend graph-based tests to the categorical setting and found two types of statistics that are both powerful and fast to compute.
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References

The distribution of a linear combination of 2 random variables
pr(Q<c). (2) The algorithm is based on the method of Davis (1973) involving the numerical inversion of the characteristic function. It will yield results for most linear combinations that are likely…