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Hierarchical data fusion processes involving the Möbius representation of capacities

Version 2 2024-06-04, 03:30
Version 1 2021-02-17, 09:31
journal contribution
posted on 2024-06-04, 03:30 authored by Gleb BeliakovGleb Beliakov, M Gagolewski, Simon JamesSimon James
The use of the Choquet integral in data fusion processes allows for the effective modelling of interactions and dependencies between data features or criteria. Its application requires identification of the defining capacity (also known as fuzzy measure) values. The main limiting factor is the complexity of the underlying parameter learning problem, which grows exponentially in the number of variables. However, in practice we may have expert knowledge regarding which of the subsets of criteria interact with each other, and which groups are independent. In this paper we study hierarchical aggregation processes, architecturally similar to feed-forward neural networks, but which allow for the simplification of the fitting problem both in terms of the number of variables and monotonicity constraints. We note that the Möbius representation lets us identify a number of relationships between the overall fuzzy measure and the data pipeline structure. Included in our findings are simplified fuzzy measures that generalise both k-intolerant and k-interactive capacities.

History

Journal

Fuzzy Sets and Systems

Volume

433

Pagination

1-21

Location

Amsterdam, The Netherlands

ISSN

0165-0114

Language

en

Notes

In Press

Publication classification

C1 Refereed article in a scholarly journal

Publisher

Elsevier BV