Supervised low rank indefinite kernel approximation using minimum enclosing balls

Frank Michael Schleif*, Andrej Gisbrecht, Peter Tino

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)


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
Pages (from-to)213-226
Number of pages14
Publication statusPublished - 27 Nov 2018
MoE publication typeA1 Journal article-refereed


  • Classification
  • Indefinite kernel
  • Indefinite learning
  • Kernel fisher discriminant
  • Low rank approximation
  • Minimum enclosing ball
  • Nyström approximation


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