Support Vector Data Descriptions and k-Means Clustering: One Class?

Nico Gornitz, Luiz Alberto Lima, Klaus Robert Muller, Marius Kloft, Shinichi Nakajima

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


We present ClusterSVDD, a methodology that unifies support vector data descriptions (SVDDs) and k-means clustering into a single formulation. This allows both methods to benefit from one another, i.e., by adding flexibility using multiple spheres for SVDDs and increasing anomaly resistance and flexibility through kernels to k-means. In particular, our approach leads to a new interpretation of k-means as a regularized mode seeking algorithm. The unifying formulation further allows for deriving new algorithms by transferring knowledge from one-class learning settings to clustering settings and vice versa. As a showcase, we derive a clustering method for structured data based on a one-class learning scenario. Additionally, our formulation can be solved via a particularly simple optimization scheme. We evaluate our approach empirically to highlight some of the proposed benefits on artificially generated data, as well as on real-world problems, and provide a Python software package comprising various implementations of primal and dual SVDD as well as our proposed ClusterSVDD.

Original languageEnglish
Article number8052229
Pages (from-to)3994-4006
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number9
Publication statusPublished - 2018 Sept

Bibliographical note

Funding Information:
Manuscript received August 7, 2016; revised December 8, 2016 and May 4, 2017; accepted August 1, 2017. Date of publication September 27, 2017; date of current version August 20, 2018. This work was supported by the German Research Foundation under Grant DFG MU 987/6-1 and Grant RA 1894/1-1. The work of N. Görnitz was supported by BMBF ALICE II under Grant 01IB15001B. The work of L. A. Lima was supported by Petrobras. The work of K.-R. Müller was supported by the National Research Foundation of Korea, Ministry of Education, Science, and Technology, through the BK21 Program. The work of M. Kloft was supported by the German Research Foundation under Grant KL 2698/1-1 and Grant KL 2698/2-1. The work of S. Nakajima was supported by the German Ministry for Education and Research as Berlin Big Data Center under Grant 01IS14013A. (Corresponding author: Nico Görnitz; Klaus-Robert Müller.) N. Görnitz and S. Nakajima are with the Machine Learning Group, Berlin Institute of Technology, 10587 Berlin, Germany (e-mail: [email protected]).

Publisher Copyright:
© 2012 IEEE.


  • Anomaly detection
  • clustering
  • k-means
  • one-class classification
  • support vector data description (SVDD)

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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