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On K-means algorithm with the use of Mahalanobis distances

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  • Melnykov, Igor
  • Melnykov, Volodymyr

Abstract

The K-means algorithm is commonly used with the Euclidean metric. While the use of Mahalanobis distances seems to be a straightforward extension of the algorithm, the initial estimation of covariance matrices can be complicated. We propose a novel approach for initializing covariance matrices.

Suggested Citation

  • Melnykov, Igor & Melnykov, Volodymyr, 2014. "On K-means algorithm with the use of Mahalanobis distances," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 88-95.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:88-95
    DOI: 10.1016/j.spl.2013.09.026
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    References listed on IDEAS

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    1. Melnykov, Volodymyr & Chen, Wei-Chen & Maitra, Ranjan, 2012. "MixSim: An R Package for Simulating Data to Study Performance of Clustering Algorithms," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i12).
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
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    Citations

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    Cited by:

    1. Volodymyr Melnykov & Xuwen Zhu, 2019. "An extension of the K-means algorithm to clustering skewed data," Computational Statistics, Springer, vol. 34(1), pages 373-394, March.
    2. Chun-Wei Chen & Chun-Chang Li & Chen-Yu Lin, 2020. "Combine Clustering and Machine Learning for Enhancing the Efficiency of Energy Baseline of Chiller System," Energies, MDPI, vol. 13(17), pages 1-20, August.
    3. Volodymyr Melnykov & Semhar Michael, 2020. "Clustering Large Datasets by Merging K-Means Solutions," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 97-123, April.
    4. Andrea Martino & Andrea Ghiglietti & Francesca Ieva & Anna Maria Paganoni, 2019. "A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 301-322, June.
    5. Yanpeng Hao & Jie Wei & Xiaolan Jiang & Lin Yang & Licheng Li & Junke Wang & Hao Li & Ruihai Li, 2018. "Icing Condition Assessment of In-Service Glass Insulators Based on Graphical Shed Spacing and Graphical Shed Overhang," Energies, MDPI, vol. 11(2), pages 1-12, February.
    6. Amirfakhrian, Majid & Samavati, Faramarz, 2021. "Weather daily data approximation using point adaptive ellipsoidal neighborhood in scattered data interpolation methods," Applied Mathematics and Computation, Elsevier, vol. 392(C).

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