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Fast agglomerative hierarchical clustering algorithm using Locality-Sensitive Hashing

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Abstract

The single linkage method is a fundamental agglomerative hierarchical clustering algorithm. This algorithm regards each point as a single cluster initially. In the agglomeration step, it connects a pair of clusters such that the distance between the nearest members is the shortest. This step is repeated until only one cluster remains. The single linkage method can efficiently detect clusters in arbitrary shapes. However, a drawback of this method is a large time complexity of O(n 2), where n represents the number of data points. This time complexity makes this method infeasible for large data. This paper proposes a fast approximation algorithm for the single linkage method. Our algorithm reduces the time complexity to O(nB) by rapidly finding the near clusters to be connected by Locality-Sensitive Hashing, a fast algorithm for the approximate nearest neighbor search. Here, B represents the maximum number of points going into a single hash entry and it practically diminishes to a small constant as compared to n for sufficiently large hash tables. Experimentally, we show that (1) the proposed algorithm obtains clustering results similar to those obtained by the single linkage method and (2) it runs faster for large data than the single linkage method.

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Authors and Affiliations

  1. Graduate School of Information Systems, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-si, Tokyo, 182-8585, Japan

    Hisashi Koga, Tetsuo Ishibashi & Toshinori Watanabe

Authors
  1. Hisashi Koga
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  2. Tetsuo Ishibashi
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  3. Toshinori Watanabe
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Correspondence to Hisashi Koga.

Additional information

Hisashi Koga received the M.S. and Ph.D. degree in information science in 1995 and 2002, respectively, from the University of Tokyo. From 1995 to 2003, he worked as a researcher at Fujitsu Laboratories Ltd. Since 2003, he has been a faculty member at the University of Electro-Communications, Tokyo (Japan). Currently, he is an associate professor at the Graduate School of Information Systems, University of Electro-Communications. His research interest includes various kinds of algorithms such as clustering algorithms, on-line algorithms, and algorithms in network communications.

Tetsuo Ishibashi received the M.E. degree in information systems design from the Graduate School of Information Systems at the University of Electro-Communications in 2004. Presently, he is a system engineer at Fujitsu Broad Solution & Consulting Inc.

Toshinori Watanabe received the B.E. degree in aeronautical engineering in 1971 and the D.E. degree in 1985, both from the University of Tokyo. In 1971, he worked at Hitachi as a researcher in the field of information systems design. His experience includes demand forecasting, inventory and production management, VLSI design automation, knowledge-based nonlinear optimizer, and a case-based evolutionary learning system nicknamed TAMPOPO. He also engaged in FGCS (Fifth Generation Computer System) project of Japan and developed a new hierarchical message-passing parallel cooperative VLSI layout problem solver that ran on PIM (Parallel Inference Machine) in 1991. Since 1992, he has been a professor at the Graduate School of Information Systems, University of Electro-Communications, Tokyo, Japan. His areas of interest include media analysis, learning intelligence, and the semantics of information systems. He is a member of the IEEE.

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Koga, H., Ishibashi, T. & Watanabe, T. Fast agglomerative hierarchical clustering algorithm using Locality-Sensitive Hashing. Knowl Inf Syst 12, 25–53 (2007). https://doi.org/10.1007/s10115-006-0027-5

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  • DOI: https://doi.org/10.1007/s10115-006-0027-5

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