Hierarchical data fusion processes involving the Möbius representation of capacities

Beliakov, Gleb, Gagolewski, Marek and James, Simon 2021, Hierarchical data fusion processes involving the Möbius representation of capacities, Fuzzy Sets and Systems, pp. 1-21, doi: 10.1016/j.fss.2021.02.006.

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Title Hierarchical data fusion processes involving the Möbius representation of capacities
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Gagolewski, MarekORCID iD for Gagolewski, Marek orcid.org/0000-0003-0637-6028
James, SimonORCID iD for James, Simon orcid.org/0000-0003-1150-0628
Journal name Fuzzy Sets and Systems
Start page 1
End page 21
Total pages 21
Publisher Elsevier
Place of publication Amsterdam, The Netherlands
Publication date 2021-02-10
ISSN 0165-0114
Keyword(s) Non-additive measures
Capacities
Fuzzy measures
2-step Choquet integral
Aggregation operators
High dimensional data
Summary 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.
Notes In Press
Language eng
DOI 10.1016/j.fss.2021.02.006
Indigenous content off
Field of Research 0101 Pure Mathematics
0801 Artificial Intelligence and Image Processing
HERDC Research category C1 Refereed article in a scholarly journal
Persistent URL http://hdl.handle.net/10536/DRO/DU:30148104

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