Rebecka Jornsten
Department of Statistics, Rutgers University

TITLE: 
Cluster Validation using the Relative Data Depth.

ABSTRACT:
Gene and sample clustering are important tasks in the analysis of gene  
expression data. Gene clustering can suggest candidate gene pathways, and 
provide a method for dimension reduction. Sample clustering can be used for
class discovery, or validation. We present a fast and robust k-median 
clustering method based on a modified Weiszfeld algorithm for the multivariate 
median. The multivariate medians are used to represent the clusters, while the 
associated data depths are used to identify the nuclei of clusters, and 
outliers. 
We introduce a new cluster validation and visualization tool based on the 
within cluster data depths, and the data depths with respect to competing 
clusters. We demonstrate on several gene expression data sets, and simulated 
data sets that this Relative Data Depth outperforms the silhouette width and 
the gap statistic for estimating the number of clusters, and identifying 
outliers. 

References:
[1] S. Dudoit, J. Fridlyand. Application of resampling methods to estimate the 
number of clusters and to improve the accuracy of a clustering method. 
Technical report 600, Department of Statistics, UC Berkeley (2001). 
[2] R. Tibshirani, G. Walther, T. Hastie. Estimating the number of clusters in 
a data set via the gap statistic. Technical report, Department of Statistics, 
Stanford university (2000).
[3] Y. Vardi, C. Zhang. The multivariate L1 median and associated data depth. 
PNAS 97: 1423-1426 (2000).