On Generalization and Computation of Tukey's Depth: Part II





Riemannian depth, principal component analysis, slacked data depth, reduced rank regression, sparsity-promoting regularizers


This paper studies how to generalize Tukey's depth to problems defined in a restricted space that may be curved or have boundaries, and to problems with a nondifferentiable objective. First, using a manifold approach, we propose a broad class of Riemannian

depth for smooth problems defined on a Riemannian manifold, and showcase its applications in spherical data analysis, principal component analysis, and multivariate orthogonal regression. Moreover, for nonsmooth problems, we introduce additional slack variables and inequality constraints to define a novel slacked data depth, which can perform center-outward rankings of estimators arising from sparse learning and reduced rank regression. Real data examples illustrate the usefulness of some proposed data depths.


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How to Cite

She, Y. ., Tang, S. ., & Liu , J. (2022). On Generalization and Computation of Tukey’s Depth: Part II. Journal of Data Science, Statistics, and Visualisation, 2(2). https://doi.org/10.52933/jdssv.v2i2.61