Evolving Systems

, Volume 3, Issue 3, pp 135–151

A dynamic split-and-merge approach for evolving cluster models

Original Paper

DOI: 10.1007/s12530-012-9046-5

Cite this article as:
Lughofer, E. Evolving Systems (2012) 3: 135. doi:10.1007/s12530-012-9046-5


This paper describes new dynamic split-and-merge operations for evolving cluster models, which are learned incrementally and expanded on-the-fly from data streams. These operations are necessary to resolve the effects of cluster fusion and cluster delamination, which may appear over time in data stream learning. We propose two new criteria for cluster merging: a touching and a homogeneity criterion for two ellipsoidal clusters. The splitting criterion for an updated cluster applies a 2-means algorithm to its sub-samples and compares the quality of the split cluster with that of the original cluster by using a penalized Bayesian information criterion; the cluster partition of higher quality is retained for the next incremental update cycle. This new approach is evaluated using two-dimensional and high-dimensional streaming clustering data sets, where feature ranges are extended and clusters evolve over time—and on two large streams of classification data, each containing around 500K samples. The results show that the new split-and-merge approach (a) produces more reliable cluster partitions than conventional evolving clustering techniques and (b) reduces impurity and entropy of cluster partitions evolved on the classification data sets.


Evolving cluster models Cluster fusion and delamination Dynamic split-and-merge Touching and homogeneity criteria Penalized Bayesian information criterion 

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Knowledge-based Mathematical SystemsJohannes Kepler University of LinzLinzAustria

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