Multi-scale Classification using Localized Spatial Depth
Friday, September 15, 2017 - 3:30pm
In this talk, we will first discuss the notion of data depth for multivariate data and look into related inferential aspects. We shall then focus on depth based classification, and construct a classifier based on spatial depth. The construction of the proposed classifier is based on fitting a generalized additive model to the posterior probabilities corresponding to different classes. In order to cope with possible multi-modal, as well as non-elliptic nature of the population distributions, we develop a localized version of spatial depth and use that with varying degrees of localization to build a collection of classifiers. Final classification is done by aggregating over several posterior probability estimates, each of which is based on localized spatial depth with a fixed level of localization. The new classifier can be conveniently used for high-dimensional data, and its good discriminatory power for such data has been established using theoretical and some numerical results.
This is a joint work with Soham Sarkar and Anil K. Ghosh.
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