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Data depth is a powerful tool for multivariate data analysis. It has widespread applications in different areas of statistics including supervised and unsupervised classification. In this talk, we shall propose and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to posterior probabilities of different competing classes. To cope with possible multi-modal as well as non-elliptic nature of the population distribution, we shall also develop a localized version of spatial depth and use that with varying degrees of localization to build the classifier. The final classification is
done by aggregating several posterior probability estimates, each of which is obtained using this localized spatial depth with a fixed scale of localization. The proposed classifier can be conveniently used even when the dimension of the data is larger than the sample size, and it has good discriminatory power for such data has. We shall
demonstrate it using theoretical as well as numerical results.
This is joint work with Subhajit Dutta and Soham Sarkar |