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Connectivity of the mutual k-nearest-neighbor graph in clustering and outlier detection

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  • Brito, M. R.
  • Chávez, E. L.
  • Quiroz, A. J.
  • Yukich, J. E.

Abstract

For multivariate data sets, we study the relationship between the connectivity of a mutual k-nearest-neighbor graph, and the presence of clustering structure and outliers in the data. A test for detection of clustering structure and outliers is proposed and its performance is evaluated in simulated data.

Suggested Citation

  • Brito, M. R. & Chávez, E. L. & Quiroz, A. J. & Yukich, J. E., 1997. "Connectivity of the mutual k-nearest-neighbor graph in clustering and outlier detection," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 33-42, August.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:1:p:33-42
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    References listed on IDEAS

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    1. Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 159-179, June.
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    1. S. Camelo & M. González-Lima & A. Quiroz, 2015. "Nearest neighbors methods for support vector machines," Annals of Operations Research, Springer, vol. 235(1), pages 85-101, December.
    2. Nie, Chun-Xiao, 2022. "Analysis of critical events in the correlation dynamics of cryptocurrency market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    3. Brito, María R. & Quiroz, Adolfo J. & Yukich, J. E., 2002. "Graph-Theoretic Procedures for Dimension Identification," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 67-84, April.
    4. Yong-Jing Hao & Ying-Lian Gao & Mi-Xiao Hou & Ling-Yun Dai & Jin-Xing Liu, 2019. "Hypergraph Regularized Discriminative Nonnegative Matrix Factorization on Sample Classification and Co-Differentially Expressed Gene Selection," Complexity, Hindawi, vol. 2019, pages 1-12, August.
    5. Shemendyuk, Aleksandr & Wagner, Joël, 2024. "On the factors determining the health profiles and care needs of institutionalized elders," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 223-241.
    6. Nie, Chun-Xiao, 2020. "Correlation dynamics in the cryptocurrency market based on dimensionality reduction analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    7. Ahmed Shamsul Arefin & Carlos Riveros & Regina Berretta & Pablo Moscato, 2012. "GPU-FS-kNN: A Software Tool for Fast and Scalable kNN Computation Using GPUs," PLOS ONE, Public Library of Science, vol. 7(8), pages 1-13, August.
    8. Nie, Chun-Xiao & Song, Fu-Tie, 2023. "Stable versus fragile community structures in the correlation dynamics of Chinese industry indices," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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