Uncovering and Displaying the Coherent Groups of Rank Data by Exploratory Riffle Shuffling
Vartan Choulakian, Jacques Allard (Universit\'e de Moncton, Canada)

TL;DR
This paper introduces an exploratory riffle shuffling method to uncover and visualize the structure of rank data, identifying coherent groups and outliers through a novel analysis involving taxicab correspondence analysis and seriation techniques.
Contribution
It presents a new approach combining riffle shuffling, seriation, and taxicab correspondence analysis to reveal the structure of rank data and identify coherent groups and outliers.
Findings
The method effectively uncovers simple structures in rank data.
It distinguishes coherent groups from noisy outliers.
The approach provides interpretable visualizations of ranking patterns.
Abstract
Let n respondents rank order d items, and suppose that d << n. Our main task is to uncover and display the structure of the observed rank data by an exploratory riffle shuffling procedure which sequentially decomposes the n voters into a finite number of coherent groups plus a noisy group : where the noisy group represents the outlier voters and each coherent group is composed of a finite number of coherent clusters. We consider exploratory riffle shuffling of a set of items to be equivalent to optimal two blocks seriation of the items with crossing of some scores between the two blocks. A riffle shuffled coherent cluster of voters within its coherent group is essentially characterized by the following facts : a) Voters have identical first TCA factor score, where TCA designates taxicab correspondence analysis, an L1 variant of correspondence analysis ; b) Any preference is easily…
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