BICO: BIRCH Meets Coresets for k-Means Clustering

  • Hendrik Fichtenberger
  • Marc Gillé
  • Melanie Schmidt
  • Chris Schwiegelshohn
  • Christian Sohler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)


We design a data stream algorithm for the k-means problem, called BICO, that combines the data structure of the SIGMOD Test of Time award winning algorithm BIRCH [27] with the theoretical concept of coresets for clustering problems. The k-means problem asks for a set C of k centers minimizing the sum of the squared distances from every point in a set P to its nearest center in C. In a data stream, the points arrive one by one in arbitrary order and there is limited storage space.

BICO computes high quality solutions in a time short in practice. First, BICO computes a summary S of the data with a provable quality guarantee: For every center set C, S has the same cost as P up to a (1 + ε)-factor, i. e., S is a coreset. Then, it runs k-means++ [5] on S.

We compare BICO experimentally with popular and very fast heuristics (BIRCH, MacQueen [24]) and with approximation algorithms (Stream-KM++ [2], StreamLS [16,26]) with the best known quality guarantees. We achieve the same quality as the approximation algorithms mentioned with a much shorter running time, and we get much better solutions than the heuristics at the cost of only a moderate increase in running time.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hendrik Fichtenberger
    • 1
  • Marc Gillé
    • 1
  • Melanie Schmidt
    • 1
  • Chris Schwiegelshohn
    • 1
  • Christian Sohler
    • 1
  1. 1.Efficient Algorithms and Complexity TheoryTU DortmundGermany

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