Data Depth and Classification
Data depth provides a center outward ordering of a multivariate observation w.r.t. a multivariate distribution or a data cloud.
Using various notions of data depth, a variety of depth based classifiers have been constructed.
They can be broadly classified into four categories.
Max Depth Generalized Classifiers Local Depth Depth and discriminating surfaces
Relevent papers are as follows.
Dutta, S. and Ghosh, A. K. (2012a) On robust classification using projection depth. Annals of the Institute of Statistical Mathematics, 64, 657-676.
Dutta, S. and Ghosh, A. K. (2012b) On classification based on Lp depth with an adaptive choice of p. Technical Report Number R5/2011, Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, India. (Submitted for publication)
Dutta, S., Chaudhuri, P. and Ghosh, A. K. (2012b) Classification using Localized Spatial Depth with Multiple Localization. (Ongoing Work)
Ghosh, A. K. and Chaudhuri, P. (2005a). On data depth and distribution free discriminant analysis using separating surfaces. Bernoulli, 11:1–27.
Ghosh, A. K. and Chaudhuri, P. (2005) On maximum depth and related classifiers. Scand. J. Statist., 32, 328-350.