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A class of monotone kernelized classifiers on the basis of the Choquet integral
Author(s) -
Fallah Tehrani Ali,
Strickert Marc,
Ahrens Diane
Publication year - 2020
Publication title -
expert systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 38
eISSN - 1468-0394
pISSN - 0266-4720
DOI - 10.1111/exsy.12506
Subject(s) - monotone polygon , computer science , monotonic function , quadratic equation , classifier (uml) , choquet integral , mathematical optimization , support vector machine , kernel (algebra) , artificial intelligence , property (philosophy) , class (philosophy) , mathematics , discrete mathematics , fuzzy logic , geometry , mathematical analysis , philosophy , epistemology
The key property of monotone classifiers is that increasing (decreasing) input values lead to increasing (decreasing) the output value. Preserving monotonicity for a classifier typically requires many constraints to be respected by modelling approaches such as artificial intelligence techniques. The type of constraints strongly depends on the modelling assumptions. Of course, for sophisticated models, such conditions might be very complex. In this study, we present a new family of kernels that we call it Choquet kernels. Henceforth, it allows for employing popular kernel‐based methods, such as support vector machines. Instead of a naïve approach with exponential computational complexity, we propose an equivalent formulation with quadratic time in the number of attributes. Furthermore, because coefficients derived from kernel solutions are not necessarily monotone in the dual form, different approaches are proposed to monotonize coefficients. Finally, experiments illustrate beneficial properties of the Choquet kernels.