Feature and decision level fusion using multiple kernel learning and fuzzy integrals

Abstract

Kernel methods for classification is a well-studied area in which data are implicitly mapped from a lower-dimensional space to a higher-dimensional space to improve classification accuracy. However, for most kernel methods, one must still choose a kernel to use for the problem. Since there is, in general, no way of knowing which kernel is the best, multiple kernel learning (MKL) is a technique used to learn the aggregation of a set of valid kernels into a single (ideally) superior kernel. The aggregation can be done using weighted sums of the pre-computed kernels, but determining the summation weights is not a trivial task. A popular and successful approach to this problem is MKL-group lasso (MKLGL), where the weights and classification surface are simultaneously solved by iteratively optimizing a min-max optimization until convergence. In this work, we propose an ℓp-normed genetic algorithm MKL (GAMKLp), which uses a genetic algorithm to learn the weights of a set of pre-computed kernel matrices for use with MKL classification. We prove that this approach is equivalent to a previously proposed fuzzy integral aggregation of multiple kernels called fuzzy integral: genetic algorithm (FIGA). A second algorithm, which we call decision-level fuzzy integral MKL (DeFIMKL), is also proposed, where a fuzzy measure with respect to the fuzzy Choquet integral is learned via quadratic programming, and the decision value-viz., the class label-is computed using the fuzzy Choquet integral aggregation. Experiments on several benchmark data sets show that our proposed algorithms can outperform MKLGL when applied to support vector machine (SVM)-based classification.