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Clustering and classification based on the L1 data depth

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  • Jörnsten, Rebecka

Abstract

Clustering and classification are important tasks for the analysis of microarray gene expression data. Classification of tissue samples can be a valuable diagnostic tool for diseases such as cancer. Clustering samples or experiments may lead to the discovery of subclasses of diseases. Clustering genes can help identify groups of genes that respond similarly to a set of experimental conditions. We also need validation tools for clustering and classification. Here, we focus on the identification of outliers--units that may have been misallocated, or mislabeled, or are not representative of the classes or clusters. We present two new methods: DDclust and DDclass, for clustering and classification. These non-parametric methods are based on the intuitively simple concept of data depth. We apply the methods to several gene expression and simulated data sets. We also discuss a convenient visualization and validation tool--the relative data depth plot.

Suggested Citation

  • Jörnsten, Rebecka, 2004. "Clustering and classification based on the L1 data depth," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 67-89, July.
    • Handle: RePEc:eee:jmvana:v:90:y:2004:i:1:p:67-89
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    References listed on IDEAS

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    1. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
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    1. Nedret Billor & Asheber Abebe & Asuman Turkmen & Sai Nudurupati, 2008. "Classification Based on Depth Transvariations," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 249-260, November.
    2. Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
    3. B. Karmakar & K. Dhara & K. Dey & A. Basu & A. Ghosh, 2015. "Tests for statistical significance of a treatment effect in the presence of hidden sub-populations," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 97-119, March.
    4. Subhajit Dutta & Anil Ghosh, 2012. "On robust classification using projection depth," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 657-676, June.
    5. Yonggang Hu & Yong Wang & Yi Wu & Qiang Li & Chenping Hou, 2011. "Generalized Mahalanobis depth in the reproducing kernel Hilbert space," Statistical Papers, Springer, vol. 52(3), pages 511-522, August.
    6. López Pintado, Sara, 2005. "Depth-based classification for functional data," DES - Working Papers. Statistics and Econometrics. WS ws055611, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Hennig, Christian, 2008. "Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1154-1176, July.

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