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标题：Uncovering and Displaying the Coherent Groups of Rank Data by Exploratory Riffle Shuffling
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作者：Vartan Choulakian ; Jacques Allard
期刊名称：Open Journal of Statistics
印刷版ISSN：2161-718X
电子版ISSN：2161-7198
出版年度：2021
卷号：11
期号：1
页码：178-212
DOI：10.4236/ojs.2021.111010
语种：English
出版社：Scientific Research Publishing
摘要：Let n respondents rank order d items, and suppose that . 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: 1) Voters have identical first TCA factor score, where TCA designates taxicab correspondence analysis, an L1 variant of correspondence analysis; 2) Any preference is easily interpreted as riffle shuffling of its items; 3) The nature of different riffle shuffling of items can be seen in the structure of the contingency table of the first-order marginals constructed from the Borda scorings of the voters; 4) The first TCA factor scores of the items of a coherent cluster are interpreted as Borda scale of the items. We also introduce a crossing index, which measures the extent of crossing of scores of voters between the two blocks seriation of the items. The novel approach is explained on the benchmarking SUSHI data set, where we show that this data set has a very simple structure, which can also be communicated in a tabular form.
关键词：Borda Score and Scale;Exploratory Riffle Shuffle;Coherent Group;Coherent Cluster;Crossing Index;Taxicab Correspondence Analysis