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A permutation test for determining significance of clusters with applications to spatial and gene expression data

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  • Park, P.J.
  • Manjourides, J.
  • Bonetti, M.
  • Pagano, M.

Abstract

Hierarchical clustering is a common procedure for identifying structure in a dataset, and this is frequently used for organizing genomic data. Although more advanced clustering algorithms are available, the simplicity and visual appeal of hierarchical clustering have made it ubiquitous in gene expression data analysis. Hence, even minor improvements in this framework would have significant impact. There is currently no simple and systematic way of assessing and displaying the significance of various clusters in a resulting dendrogram without making certain distributional assumptions or ignoring gene-specific variances. In this work, we introduce a permutation test based on comparing the within-cluster structure of the observed data with those of sample datasets obtained by permuting the cluster membership. We carry out this test at each node of the dendrogram using a statistic derived from the singular value decomposition of variance matrices. The p-values thus obtained provide insight into the significance of each cluster division. Given these values, one can also modify the dendrogram by combining non-significant branches. By adjusting the cut-off level of significance for branches, one can produce dendrograms with a desired level of detail for ease of interpretation. We demonstrate the usefulness of this approach by applying it to illustrative datasets.

Suggested Citation

  • Park, P.J. & Manjourides, J. & Bonetti, M. & Pagano, M., 2009. "A permutation test for determining significance of clusters with applications to spatial and gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4290-4300, October.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4290-4300
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    References listed on IDEAS

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    1. Gordon, A. D., 1994. "Identifying genuine clusters in a classification," Computational Statistics & Data Analysis, Elsevier, vol. 18(5), pages 561-581, December.
    2. Glenn Milligan & Richard Cheng, 1996. "Measuring the influence of individual data points in a cluster analysis," Journal of Classification, Springer;The Classification Society, vol. 13(2), pages 315-335, September.
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    Cited by:

    1. Dario Bruzzese & Domenico Vistocco, 2015. "DESPOTA: DEndrogram Slicing through a PemutatiOn Test Approach," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 285-304, July.
    2. Bongiorno, Christian & Miccichè, Salvatore & Mantegna, Rosario N., 2022. "Statistically validated hierarchical clustering: Nested partitions in hierarchical trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    3. Christian Haedo & Michel Mouchart, 2022. "Two-mode clustering through profiles of regions and sectors," Empirical Economics, Springer, vol. 63(4), pages 1971-1996, October.
    4. Christian Bongiorno & Salvatore Miccichè & Rosario N Mantegna, 2022. "Statistically validated hierarchical clustering: Nested partitions in hierarchical trees," Post-Print hal-02157744, HAL.

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