Efficient and Scalable Nonlinear Multiple Kernel Aggregation Using the Choquet Integral

Previously, we investigated the definition and applicability of the fuzzy integral (FI) for nonlinear multiple kernel (MK) aggregation in pattern recognition. Kernel theory provides an elegant way to map multi-source heterogeneous data into a combined homogeneous (implicit) space in which aggregation can be carried out. The focus of our initial work was the Choquet FI, a per-matrix sorting based on the quality of a base learner and learning was restricted to the Sugeno lambda-fuzzy measure (FM). Herein, we investigate what representations of FMs and FIs are valid and ideal for nonlinear MK aggregation. We also discuss the benefit of our approach over the linear convex sum MK formulation in machine learning. Furthermore, we study the Mobius transform and k-additive integral for scalable MK learning (MKL). Last, we discuss an extension to our genetic algorithm (GA) based MKL algorithm, called FIGA, with respect to a combination of multiple light weight FMs and FIs.