Learning Valued Relations from Data Willem Waegeman Tapio Pahikkala Antti Airola Tapio Salakoski Bernard De Baets Abstract Driven by a large number of potential applications in areas like bioin- formatics, 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 typ- ically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are in many real-world applications often expressed in a graded man- ner. A general kernel-based framework for learning relations from data is intro- duced here. It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric and reciprocal relations. This frame- work establishes in this way important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated on a case study in document retrieval. 1 Introduction Relational data can be observed in many predictive modeling tasks, such as forecast- ing the winner in two-player computer games [1], predicting proteins that interact with other proteins in bioinformatics [2], retrieving documents that are similar to a target document in text mining [3], investigating the persons that are friends of each other on social network sites [4], etc. All these examples represent fields of applica- Willem Waegeman, Bernard De Baets Ghent University, KERMIT, Department of Applied Mathematics, Biometrics and Process Control, Coupure links 653, B-9000 Ghent, e-mail: forname.surname@ugent.be Tapio Pahikkala, Antti Airola, Tapio Salakoski University of Turku, Department of Information Technology and the Turku Centre for Computer Science, Joukahaisenkatu 3-5 B 20520 Turku, e-mail: forname.surname@utu.fi 1