Extended Linear Order Statistic (ELOS) Aggregation and Regression

Document Type

Conference Proceeding

Publication Date



Department of Electrical and Computer Engineering; College of Computing


The ordered weighted average (OWA) operator is a well-known aggregation tool that is primarily used for decisionlevel fusion. However, the OWA is a convex sum, i.e., its learned coefficients are constrained to sum to one, and thus the output is restricted to lie between the maximum and minimum values of the inputs. Relaxing this constraint on the sum of weights transforms the OWA into a linear order statistic (LOS), which allows the aggregation operation to map the input to any value on the set of reals, thus behaving more like a regression operator. The LOS parameterizes the regression operation of d-features using just d parameters, which helps with the model's interpretability. However, learning just d parameters limits the amount of nonlinear space explored for an optimal solution, and thus reduces the expressibility of the LOS algorithm. We propose a novel aggregation method called the extended linear order statistic (ELOS), where for each position in the sorted input vector we have d parameters, one for each input feature, thus learning a total of d2 weights for the aggregation of d features. The increased number of parameters helps the algorithm improve its expressibility while maintaining interpretability. In our experiments on real-world benchmark data sets, ELOS has outperformed both linear regression and LOS in 8 out of 10 experiments.

Publisher's Statement

© 2020 IEEE. Publisher’s version of record: https://doi.org/10.1109/FUZZ48607.2020.9177595

Publication Title

IEEE International Conference on Fuzzy Systems