An approximated decision-theoretic algorithm for minimization of the Tversky loss under the multi-label framework

In this paper, we addressed the problem of building a decision-theoretic classifier tailored for minimizing the Tversky loss under the framework of multi-label classification. The proposed approach is a generalization of the Dembczyński Fβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{\beta }$$\end{document} measure optimization algorithm. The introduced technique is based on a series of discrete linear approximations of the Tversky measure. The approximated criterion is then optimized using original optimization algorithm. To assess quality of classification results produced by the designed strategy and compare its outcome with the results obtained by the state-of-the-art approaches, we conducted an experimental study on 24 benchmark datasets. The investigated methods were compared with respect to eleven different quality criteria. We considered quality criteria belonging to three main groups, i.e., example-based, micro-averaged and macro-averaged. During the experimental study, we considered four testing scenarios. Two of them deal with a symmetric variant of the Tversky loss. Remaining scenarios examine asymmetric Tversky loss. The study shows that, in general, the proposed method is comparable to the Dembczyński approach. However, for both symmetric scenarios and one asymmetric scenario, the average ranks suggest that the proposed approach achieves better classification quality in terms of the example-based Tversky measure. This is an important result because the proposed method was designed to optimize the above-mentioned quality indicator. Additionally, the introduced procedure can outperform the reference methods with respect to the zero-one loss under all testing scenarios.