Article by Siva Kakula, Tim Havens Published in IEEE Transactions on Fuzzy Systems

Timothy Havens

An article by Dr. Siva Krishna Kakula (’00 CS) and Dr. Timothy Havens (CS, ICC-Data S) has been published in the October 2021 issue of the journal, IEEE Transactions on Fuzzy Systems. The article, “Novel Regularization for Learning the Fuzzy Choquet Integral With Limited Training Data,” is available on IEEE Xplore,

Kakula’s and Havens’s co-authors are Michigan Tech faculty member Dr. Anthony Pinar (ECE, ICC-DataS), and Muhammad Aminul Islam and Derek T. Anderson of the Department of Electrical Engineering and Computer Science at University of Missouri, Columbia.

Abstract. Fuzzy integrals (FIs) are powerful aggregation operators that fuse information from multiple sources. The aggregation is parameterized using a fuzzy measure (FM), which encodes the worths of all subsets of sources. Since the FI is defined with respect to an FM, much consideration must be given to defining the FM. However, in practice this is a difficult task—the number of values in an FM scales as 2n , where n is the number of input sources, thus manually specifying an FM quickly becomes tedious. In this article, we review an automatic, data-supported method of learning the FM by minimizing a sum-of-squared error objective function in the context of decision-level fusion of classifiers using the Choquet FI. While this solves the specification problem, we illuminate an issue encountered with many real-world data sets; i.e., if the training data do not contain a significant number of all possible sort orders, many of the FM values are not supported by the data. We propose various regularization strategies to alleviate this issue by pushing the learned FM toward a predefined structure; these regularizers allow the user to encode knowledge of the underlying FM to the learning problem. Furthermore, we propose another regularization strategy that constrains the learned FM’s structure to be a linear order statistic. Finally, we perform several experiments using synthetic and real-world data sets and show that our proposed extensions can improve the learned FM behavior and classification accuracy. A previously proposed visualization technique is employed to simultaneously quantitatively illustrate the FM as well as the FI.

Citation. S. K. Kakula, A. J. Pinar, M. A. Islam, D. T. Anderson and T. C. Havens, “Novel Regularization for Learning the Fuzzy Choquet Integral With Limited Training Data,” in IEEE Transactions on Fuzzy Systems, vol. 29, no. 10, pp. 2890-2901, Oct. 2021, doi: 10.1109/TFUZZ.2020.3009722.

The IEEE Transactions on Fuzzy Systems publishes high quality technical papers in the theory, design, and application of fuzzy systems.