Adv Data Anal Classif (2017) 11:493–518
Constrained clustering with a complex cluster structure
· Magdalena Wiercioch
Received: 9 May 2014 / Revised: 6 May 2016 / Accepted: 10 May 2016 /
Published online: 24 May 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract In this contribution we present a novel constrained clustering method,
Constrained clustering with a complex cluster structure (C4s), which incorporates
equivalence constraints, both positive and negative, as the background information.
C4s is capable of discovering groups of arbitrary structure, e.g. with multi-modal dis-
tribution, since at the initial stage the equivalence classes of elements generated by the
positive constraints are split into smaller parts. This provides a detailed description of
elements, which are in positive equivalence relation. In order to enable an automatic
detection of the number of groups, the cross-entropy clustering is applied for each par-
titioning process. Experiments show that the proposed method achieves signiﬁcantly
better results than previous constrained clustering approaches. The advantage of our
algorithm increases when we are focusing on ﬁnding partitions with complex structure
Keywords Constrained clustering · Model-based clustering · Mixture of models ·
Pairwise equivalence constraints · Semi-supervised learning · Cross-entropy clustering
Mathematics Subject Classiﬁcation Primary 68T Computer Science; Secondary
The work of the M.
Smieja was supported by the National Science Centre (Poland) Grant No.
2014/13/N/ST6/01832, while the work of the M. Wiercioch was supported by the National Science Centre
(Poland) Grant No. 2014/13/B/ST6/01792.
Faculty of Mathematics and Computer Science, Jagiellonian University,
Łojasiewicza 6, 30-348 Kraków, Poland