A kernel-based framework for learning graded relations from data

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are often expressed in a graded manner in real-world applications. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types of graded relations can be modeled, including symmetric and reciprocal relations. This framework establishes important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated through various experiments on synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

HIPAD - A Hybrid Interior-Point Alternating Direction algorithm for knowledge-based SVM and feature selection

We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net support vector machine (SVM) through an alternating direction method of multipliers in the first phase, followed by an interior-point method for the classical SVM in the second phase. Both SVM formulations are adapted to knowledge incorporation. Our proposed algorithm addresses the challenges of automatic feature selection, high optimization accuracy, and algorithmic flexibility for taking advantage of prior knowledge. We demonstrate the effectiveness and efficiency of our algorithm and compare it with existing methods on a collection of synthetic and real-world data.Comment: Proceedings of 8th Learning and Intelligent OptimizatioN (LION8) Conference, 201