Estimate the Intrinsic Dimension of a Metric Space Using the Eigenvalues of the Pair-wise Distance Matrix


Xi Liu,Houjun Tang,Zhao Jiang,Pang Yue,Ye Cai,Haijun Lei,Hong Zhou,Rui Mao * National High Performance Computing Center at Shenzhen College of Computer Science and Software Engineering,Shenzhen University 3688 Nanhai Road,Shenzhen,518060,China


One of the important properties of a metric space is the intrinsic dimension,which relies solely on the given space.The intrinsic dimension is a key factor in metric space indexing for nearest-neighbor search and range search.Therefore,there has been several studies of how to estimate it accurately and effectively.In this paper,we propose a simple and effective method to estimate the intrinsic dimension of a metric space,using the eigenvalues of the pair-wise distance matrix of the metric space.Three criteria are compared to find the best one that can most accurately determine the intrinsic dimension.Empirical results and comparison with other method show that this method can be used to reliably measure the intrinsic dimension of a metric space.


Similarity search,metric space indexing,intrinsic dimension,eigenvalue,pair-wise matrix


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Total: 11 articles

  • [1] Edgar Chávez;;Gonzalo Navarro;;Ricardo Baeza-Yates;;José Luis Marroquín, Searching in metric spaces, ACM Computing Surveys (CSUR),
  • [2] Gene H. Golub;;Henk A. van der Vorst, Eigenvalue computation in the 20th century, Journal of Computational and Applied Mathematics,
  • [3] Benjamin Bustos;;Gonzalo Navarro;;Edgar Chávez, Pivot selection techniques for proximity searching in metric spaces, Pattern Recognition Letters,
  • [4] R. Mao;W. Xu;S. Ramakrishnan;G. Nuckolls;D.P. Miranker, On Optimizing Distance-Based Similarity Search for Biological Databases, Proceedings of the 2005 IEEE Computational Systems Bioinformatics Conference,


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