428
Views
0
CrossRef citations to date
0
Altmetric
Statistical Learning

Statistical Significance of Clustering with Multidimensional Scaling

, & ORCID Icon
Pages 219-230 | Received 24 May 2022, Accepted 19 May 2023, Published online: 20 Jul 2023

References

  • Abbe, E., Fan, J., Wang, K., and Zhong, Y. (2020), “Entrywise Eigenvector Analysis of Random Matrices with Low Expected Rank,” Annals of Statistics, 48, 1452–1474.
  • Agrawal, N., Akbani, R., Aksoy, B. A., Ally, A., Arachchi, H., Asa, S. L., Auman, J. T., Balasundaram, M., Balu, S., Baylin, S. B. et al. (2014), “Integrated Genomic Characterization of Papillary Thyroid Carcinoma,” Cell, 159, 676–690. DOI: 10.1016/j.cell.2014.09.050.
  • Ben-Hur, A., Horn, D., Siegelmann, H. T., and Vapnik, V. (2001), “Support Vector Clustering,” Journal of Machine Learning Research, 2, 125–137.
  • Borg, I., and Groenen, P. J. F. (2005), Modern Multidimensional Scaling Theory and Applications, New York: Springer.
  • Chakravarti, P., Balakrishnan, S., and Wasserman, L. (2019), “Gaussian Mixture Clustering Using Relative Tests of Fit,” arXiv preprint arXiv:1910.02566.
  • Fraley, C., and Raftery, A. E. (2002), “Model-based Clustering, Discriminant Analysis, and Density Estimation,” Journal of the American Statistical Association, 97, 611–631. DOI: 10.1198/016214502760047131.
  • Fred, A. L., and Jain, A. K. (2005), “Combining Multiple Clusterings Using Evidence Accumulation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 835–850. DOI: 10.1109/TPAMI.2005.113.
  • Holm, S. (1979), “A Simple Sequentially Rejective Multiple Test Procedure,” Scandinavian Journal of Statistics, 6, 65–70.
  • Huang, H., Liu, Y., Yuan, M., and Marron, J. (2015), “Statistical Significance of Clustering Using Soft Thresholding,” Journal of Computational and Graphical Statistics, 24, 975–993. DOI: 10.1080/10618600.2014.948179.
  • Kimes, P. K., Liu, Y., Neil Hayes, D., and Marron, J. S. (2017), “Statistical Significance for Hierarchical Clustering,” Biometrics, 73, 811–821. DOI: 10.1111/biom.12647.
  • Little, A., Xie, Y., and Sun, Q. (2022), “An Analysis of Classical Multidimensional Scaling with Applications to Clustering,” Information and Inference: A Journal of the IMA, 12, 72–112. DOI: 10.1093/imaiai/iaac004.
  • Liu, Y., Hayes, D. N., Nobel, A., and Marron, J. S. (2008), “Statistical Significance of Clustering for High-Dimension, Low–Sample Size Data,” Journal of the American Statistical Association, 103, 1281–1293. DOI: 10.1198/016214508000000454.
  • Löffler, M., Zhang, A. Y., and Zhou, H. H. (2021), “Optimality of Spectral Clustering in the Gaussian Mixture Model,” Annals of Statistics, 49, 2506–2530.
  • MacQueen, J. et al. (1967), “Some Methods for Classification and Analysis of Multivariate Observations,” in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Oakland, CA, USA (Vol. 1), pp. 281–297.
  • Maitra, R., Melnykov, V., and Lahiri, S. N. (2012), “Bootstrapping for Significance of Compact Clusters in Multidimensional Datasets,” Journal of the American Statistical Association, 107, 378–392. DOI: 10.1080/01621459.2011.646935.
  • McLachlan, G., and Peel, D. (2000), Finite Mixture Models, Wiley Series in Probability and Statistics, pp. 420–427, New York: Wiley.
  • McShane, L. M., Radmacher, M. D., Freidlin, B., Yu, R., Li, M.-C., and Simon, R. (2002), “Methods for Assessing Reproducibility of Clustering Patterns Observed in Analyses of Microarray Data,” Bioinformatics, 18, 1462–1469. DOI: 10.1093/bioinformatics/18.11.1462.
  • Nakamura, A. (2006), “Laboratory for Algorithmics: Datasets,” available at https://www-alg.ist.hokudai.ac.jp/datasets.html.
  • Poland, J., and Zeugmann, T. (2006), “Clustering Pairwise Distances with Missing Data: Maximum Cuts Versus Normalized Cuts,” in International Conference on Discovery Science, pp. 197–208, Springer.
  • Pollard, D. (1982), “A Central Limit Theorem for k-means Clustering,” Annals of Probability, 10, 919–926.
  • Prat, A., Parker, J. S., Karginova, O., Fan, C., Livasy, C., Herschkowitz, J. I., He, X., and Perou, C. M. (2010), “Phenotypic and Molecular Characterization of the Claudin-Low Intrinsic Subtype of Breast Cancer,” Breast Cancer Research, 12, R68. DOI: 10.1186/bcr2635.
  • TCGA (2012), “Comprehensive Genomic Characterization of Squamous Cell Lung Cancers,” Nature, 489, 519–525.
  • Von Luxburg, U. (2007), “A Tutorial on Spectral Clustering,” Statistics and Computing, 17, 395–416. DOI: 10.1007/s11222-007-9033-z.
  • Xu, D., and Tian, Y. (2015), “A Comprehensive Survey of Clustering Algorithms,” Annals of Data Science, 2, 165–193. DOI: 10.1007/s40745-015-0040-1.
  • Yersal, O., and Barutca, S. (2014), “Biological Subtypes of Breast Cancer: Prognostic and Therapeutic Implications,” World Journal of Clinical Oncology, 5, 412–24. DOI: 10.5306/wjco.v5.i3.412.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.