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BETULA: Numerically Stable CF-Trees for BIRCH Clustering

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Similarity Search and Applications (SISAP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12440))

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Abstract

BIRCH clustering is a widely known approach for clustering, that has influenced much subsequent research and commercial products. The key contribution of BIRCH is the Clustering Feature tree (CF-Tree), which is a compressed representation of the input data. As new data arrives, the tree is eventually rebuilt to increase the compression. Afterward, the leaves of the tree are used for clustering. Because of the data compression, this method is very scalable. The idea has been adopted for example for k-means, data stream, and density-based clustering.

Clustering features used by BIRCH are simple summary statistics that can easily be updated with new data: the number of points, the linear sums, and the sum of squared values. Unfortunately, how the sum of squares is then used in BIRCH is prone to catastrophic cancellation.

We introduce a replacement cluster feature that does not have this numeric problem, that is not much more expensive to maintain, and which makes many computations simpler and hence more efficient. These cluster features can also easily be used in other work derived from BIRCH, such as algorithms for streaming data. In the experiments, we demonstrate the numerical problem and compare the performance of the original algorithm compared to the improved cluster features.

Part of the work on this paper has been supported by Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center SFB 876 “Providing Information by Resource-Constrained Analysis”, project A2. https://sfb876.tu-dortmund.de/.

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Notes

  1. 1.

    https://data.gov.uk/dataset/cb7ae6f0-4be6-4935-9277-47e5ce24a11f.

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Authors and Affiliations

  1. TU Dortmund University, Dortmund, Germany

    Andreas Lang & Erich Schubert

Authors
  1. Andreas Lang
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  2. Erich Schubert
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Correspondence to Erich Schubert .

Editor information

Editors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Shin'ichi Satoh

  2. ISTI-CNR, Pisa, Italy

    Lucia Vadicamo

  3. University of Southern Denmark, Odense M, Denmark

    Arthur Zimek

  4. ISTI-CNR, Pisa, Italy

    Fabio Carrara

  5. University of Bologna, Bologna, Italy

    Ilaria Bartolini

  6. IT University of Copenhagen, Copenhagen, Denmark

    Martin Aumüller

  7. IT University of Copenhagen, Copenhagen, Denmark

    Björn Þór Jónsson

  8. IT University of Copenhagen, Copenhagen, Denmark

    Rasmus Pagh

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Lang, A., Schubert, E. (2020). BETULA: Numerically Stable CF-Trees for BIRCH Clustering. In: Satoh, S., et al. Similarity Search and Applications. SISAP 2020. Lecture Notes in Computer Science(), vol 12440. Springer, Cham. https://doi.org/10.1007/978-3-030-60936-8_22

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  • DOI: https://doi.org/10.1007/978-3-030-60936-8_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-60935-1

  • Online ISBN: 978-3-030-60936-8

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