Metric Methods for Analyzing Partially Ranked Data
@inproceedings{Critchlow1986MetricMF, title={Metric Methods for Analyzing Partially Ranked Data}, author={Douglas E. Critchlow}, year={1986} }
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…
271 Citations
Visual estimation of structure in ranked data
- Mathematics
- 1995
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…
Graphical Techniques for Ranked Data
- Mathematics
- 1993
Exploratory graphical methods are critically needed for displaying ranked data. Fully and partially ranked data are functions on the symmetric group of n elements, S n , and on the related coset…
Visualizing and modeling partial incomplete ranking data
- Computer Science
- 2012
A distance measure for top-k rankings with the following three properties: metric, emphasis on top ranks, and computational efficiency and an efficient learning algorithm to construct a preference elicitation system from partial incomplete rankings, which can be used to solve the cold-start problems in ranking recommendations.
Comparing top k lists
- Computer Science, MathematicsSODA '03
- 2003
Besides the applications to the task of identifying good notions of (dis-)similarity between two top k lists, the results imply polynomial-time constant-factor approximation algorithms for the rank aggregation problem with respect to a large class of distance measures.
Metrics on Permutations, a Survey
- Mathematics
- 2004
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
- Computer ScienceCIDR
- 2013
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
- Mathematics, Computer Science
- 1992
How to aggregate Top-lists: Approximation algorithms via scores and average ranks
- Computer ScienceSODA
- 2020
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.
Graph-Based Tests for Two-Sample Comparisons of Categorical Data
- Mathematics, Computer Science
- 2012
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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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…