Skip to main content

Research Repository

Advanced Search

Efficient binary fuzzy measure representation and Choquet integral learning

Islam, Muhammad Aminul; Anderson, Derek T.; Du, Xiaoxiao; Havens, Timothy C.; Wagner, Christian

Authors

Muhammad Aminul Islam

Derek T. Anderson

Xiaoxiao Du

Timothy C. Havens



Abstract

The Choquet integral (ChI), a parametric function for information aggregation, is parameterized by the fuzzy measure (FM), which has 2N real-valued variables for N inputs. However, the ChI incurs huge storage and computational burden due to its exponential complexity relative to N and, as a result, its calculation, storage, and learning becomes intractable for even modest sizes (e.g., N= 15). Inspired by empirical observations in multi-sensor fusion and the more general need to mitigate the storage, computational, and learning limitations, we previously explored the binary ChI (BChI) relative to the binary fuzzy measure (BFM). The BChI is a natural fit for many applications and can be used to approximate others. Previously, we investigated different properties of the BChI and we provided an initial representation. In this article, we propose a new efficient learning algorithm for the BChI, called EBChI, by utilizing the BFM properties that add at most one variable per training instance. Furthermore, we provide an efficient representation of the BFM (EBFM) scheme that further reduces the number of variables required for storage and computation, thus enabling the use of the BChI for “big N”. Finally, we conduct experiments on synthetic data that demonstrate the efficiency of our proposed techniques.

Citation

Islam, M. A., Anderson, D. T., Du, X., Havens, T. C., & Wagner, C. (2018). Efficient binary fuzzy measure representation and Choquet integral learning. In Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (115-126). https://doi.org/10.1007/978-3-319-91473-2_10

Conference Name 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2018
Conference Location Cádiz, Spain
Start Date Jun 11, 2018
End Date Jun 15, 2018
Acceptance Date Feb 3, 2018
Online Publication Date May 30, 2018
Publication Date May 18, 2018
Deposit Date Jun 25, 2018
Publicly Available Date Mar 28, 2024
Electronic ISSN 1865-0929
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 853
Pages 115-126
Series ISSN 1865-0937
Book Title Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations
ISBN 9783319914725
DOI https://doi.org/10.1007/978-3-319-91473-2_10
Public URL https://nottingham-repository.worktribe.com/output/937306
Publisher URL http://dx.doi.org/10.1007/978-3-319-91473-2_10
Additional Information Communications in Computer and Information Science book series, vol. 853