Abstract
The prevalence of imperfections in data, characterized by uncertainty and imprecision, prompts the need for effective modeling techniques. The theory of belief functions offers a mathematical framework to address this challenge. In this paper, we tackle the problem of calculating the mean distance between elements of the same class, especially when class membership is uncertain and imprecise. Leveraging belief functions and a notion of similarity between elements, we propose a solution and validate its efficacy through experimental evaluations. The proposed method proves effective when labels exhibit low imprecision, whereas unsupervised methods may be more effective for labels closer to complete ignorance.
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Notes
- 1.
Homogeneity is represented by the mean distance between students of the same class.
- 2.
Grades are: \(A, A^-, B^+, B, B^-, C^+, C, C^-, D^+, D, D^-, F\).
- 3.
For the class that maximizes the pignistic probability, the mean distances are 9.3 for class 1 and 7.8 for class 2.
- 4.
The first class present in each dataset is always depicted.
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Hoarau, A., Thierry, C., Dubois, JC., Le Gall, Y. (2024). A Mean Distance Between Elements of Same Class for Rich Labels. In: Bi, Y., Jousselme, AL., Denoeux, T. (eds) Belief Functions: Theory and Applications. BELIEF 2024. Lecture Notes in Computer Science(), vol 14909. Springer, Cham. https://doi.org/10.1007/978-3-031-67977-3_22
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DOI: https://doi.org/10.1007/978-3-031-67977-3_22
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