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

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.