Learning Operator-Valued Kernels From Multilabel Datesets With Fuzzy Rough Sets

Abstract

In multilabel learning, the precise mining and appropriate application of label correlation can improve the effectiveness and generalization of prediction models. In order to characterize label correlation more carefully, the concept of operator-valued kernel is introduced. The value of operator-valued kernel is an operator on Hilbert space, and when applied to a practical problem, the function-valued operator degenerates into a positive-definite matrix, which aims to describe the label correlation. However, existing works focus on the basic theory of operator-valued kernel, and lack way to learn specific kernel from specific datasets, thus the application of operator-valued kernel in practical problem is greatly hindered. In this article, we focus on learning operator-valued kernels with fuzzy rough sets from multilabel datasets and designing learning algorithm for multilabel classification. First, the importance distribution of feature set to different labels at each sample is measured by using kernelized fuzzy rough sets. For a single sample, label correlation matrix is constructed based on the consistency of the importance distribution of features to labels, so as to characterize the correlation information between different labels. By considering the interaction information between two label correlation matrices, the label incidence matrix between two samples is obtained. Therefore, a new operator-valued kernel is defined by using label incidence matrices as elements. This operator-valued kernel is further proved to be an entangled and transformable kernel. On the basis, the proposed operator-valued kernel is applied to develop an efficient learning algorithm for multilabel classification. The generalization error bound of the prediction function is measured by Rademacher complexity. In order to illustrate the effectiveness of our algorithm, the classification experiments and statistical analysis results on twelve multilabel datasets are provided, which are compared with seven high performance algorithms.