Supervised low rank indefinite kernel approximation using minimum enclosing balls

Research output: Contribution to journalArticle


Colleges, School and Institutes

External organisations

  • University of Appl. Sc. Wuerzburg-Schweinfurt, Wuerzburg, 97074 Germany
  • Helsinki Institute for Information Technology, Department of Computer Science, Aalto University, Finland


Indefinite similarity measures can be frequently found in bio-informatics by means of alignment scores, but are also common in other fields like shape measures in image retrieval. Lacking an underlying vector space, the data are given as pairwise similarities only. The few algorithms available for such data do not scale to larger datasets. Focusing on probabilistic batch classifiers, the Indefinite Kernel Fisher Discriminant (iKFD) and the Probabilistic Classification Vector Machine (PCVM) are both effective algorithms for this type of data but, with cubic complexity. Here we propose an extension of iKFD and PCVM such that linear runtime and memory complexity is achieved for low rank indefinite kernels. Employing the Nyström approximation for indefinite kernels, we also propose a new almost parameter free approach to identify the landmarks, restricted to a supervised learning problem. Evaluations at several larger similarity data from various domains show that the proposed methods provides similar generalization capabilities while being easier to parametrize and substantially faster for large scale data.


Original languageEnglish
Number of pages43
Early online date3 Sep 2018
Publication statusE-pub ahead of print - 3 Sep 2018


  • indefinite kernel, kernel fisher discriminant, minimum enclosing ball, Nyström approximation, low rank approximation, classification, indefinite learning