Weighted Bonferroni mean-based classifiers with factorization machines for binary classification

Feature interaction plays a very significant role in binary classification. In this paper, we study binary classification with weighted feature interactions by means of weighted Bonferroni mean (WBM) operators. After analyzing the characteristics of interactions in the (dependently weighted) Bonferroni mean (BM) operators, the quadratic-polynomial (POLY2)-based classifier, and the factorization-machine (FM)-based classifier, we introduce the WBM operators to capture the independent importance of weighted feature interactions among input arguments. These operators are a general generalization of the existing BM operators and the crossover parts of the POLY2-based and FM-based classifiers. Then, the WBM-based classifiers and their special cases, namely the WBM-based classifiers based on the factorization machines (abbreiated as FM <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="normal">_</mml:mi> </mml:math> WBM-based classifiers), are constructed to handle the (in)dependent importance of weighted feature interactions. Extensive experimental results on the synthetic datasets and four UCI machine-learning datasets verify the effectiveness of these proposed classifiers.