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M-ary Rank Classifier Combination: A Binary Linear Programming Problem

Informatique, Bio-informatique et Systèmes Complexes (IBISC) EA 4526, univ Evry, Université Paris-Saclay, 40 rue du Pelvoux, 91020 Evry, France
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Entropy 2019, 21(5), 440; https://doi.org/10.3390/e21050440
Received: 16 January 2019 / Revised: 11 April 2019 / Accepted: 18 April 2019 / Published: 26 April 2019
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Abstract

The goal of classifier combination can be briefly stated as combining the decisions of individual classifiers to obtain a better classifier. In this paper, we propose a method based on the combination of weak rank classifiers because rankings contain more information than unique choices for a many-class problem. The problem of combining the decisions of more than one classifier with raw outputs in the form of candidate class rankings is considered and formulated as a general discrete optimization problem with an objective function based on the distance between the data and the consensus decision. This formulation uses certain performance statistics about the joint behavior of the ensemble of classifiers. Assuming that each classifier produces a ranking list of classes, an initial approach leads to a binary linear programming problem with a simple and global optimum solution. The consensus function can be considered as a mapping from a set of individual rankings to a combined ranking, leading to the most relevant decision. We also propose an information measure that quantifies the degree of consensus between the classifiers to assess the strength of the combination rule that is used. It is easy to implement and does not require any training. The main conclusion is that the classification rate is strongly improved by combining rank classifiers globally. The proposed algorithm is tested on real cytology image data to detect cervical cancer. View Full-Text
Keywords: classifier combination; rank; aggregation; total order; independence; data fusion; mutual information; plurality voting; binary linear programming; cervical cancer; HPV classifier combination; rank; aggregation; total order; independence; data fusion; mutual information; plurality voting; binary linear programming; cervical cancer; HPV
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Vigneron, V.; Maaref, H. M-ary Rank Classifier Combination: A Binary Linear Programming Problem. Entropy 2019, 21, 440.

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