Classifying with Uncertain Data Envelopment Analysis

• URL: http://arxiv.org/abs/2209.01052v1
• Date: Fri, 2 Sep 2022 13:41:19 GMT
• Title: Classifying with Uncertain Data Envelopment Analysis
• Authors: Casey Garner and Allen Holder
• Abstract summary: We propose a new classification scheme premised on the reality of imperfect data. Our model uses uncertain data envelopment analysis to define a classification's proximity to equitable efficiency. We conclude by classifying the thirty stocks in the Dow Jones Industrial average into performant tiers and by classifying prostate treatments into clinically effectual categories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classifications organize entities into categories that identify similarities within a category and discern dissimilarities among categories, and they powerfully classify information in support of analysis. We propose a new classification scheme premised on the reality of imperfect data. Our computational model uses uncertain data envelopment analysis to define a classification's proximity to equitable efficiency, which is an aggregate measure of intra-similarity within a classification's categories. Our classification process has two overriding computational challenges, those being a loss of convexity and a combinatorially explosive search space. We overcome the first by establishing lower and upper bounds on the proximity value, and then by searching this range with a first-order algorithm. We overcome the second by adapting the p-median problem to initiate our exploration, and by then employing an iterative neighborhood search to finalize a classification. We conclude by classifying the thirty stocks in the Dow Jones Industrial average into performant tiers and by classifying prostate treatments into clinically effectual categories.

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