L1-norm regularization based nonlinear integrals

Abstract

Since Nonlinear Integrals, such as the Choquet Integral and Sugeno Integrals, were proposed, how to get the Fuzzy Measure and confirm the unique solution became the hard problems. Some researchers can obtain the optimal solution for Fuzzy Measure using soft computing tools. When the Nonlinear Integrals can be transformed to a linear equation with regards to Fuzzy Measure by Prof. Wang, we can apply the L1-norm regularization method to solve the linear equation system for one dataset and find a solution with the fewest nonzero values. The solution with the fewest nonzero can show the degree of contribution of some features or their combinations for decision. The experimental results show that the L1-norm regularization is helpful to the classifier based on Nonlinear Integrals. It can not only reduce the complexity of Nonlinear Integral but also keep the good performance of the model based on Nonlinear Integral. Meanwhile, we can dig out and understand the affection and meaning of the Fuzzy Measure better. © 2009 Springer Berlin Heidelberg.