Approximate computation of projection depths

Rainer Dyckerhoff, Pavlo Mozharovskyi and Stanislav Nagy

Computational Statistics & Data Analysis, 2021, vol. 157, issue C

Abstract: Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in Rd. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional projections of the data, then the depth satisfies the so-called projection property. Such depths form an important class that includes many of the depths that have been proposed in literature. For depths that satisfy the projection property an approximate algorithm can easily be constructed since taking the minimum of the depths with respect to only a finite number of one-dimensional projections yields an upper bound for the depth with respect to the multivariate data. Such an algorithm is particularly useful if no exact algorithm exists or if the exact algorithm has a high computational complexity, as is the case with the halfspace depth or the projection depth. To compute these depths in high dimensions, the use of an approximate algorithm with better complexity is surely preferable. Instead of focusing on a single method we provide a comprehensive and fair comparison of several methods, both already described in the literature and original.

Keywords: Data depth; Projection property; Approximate computation; Non-convex optimization; Unit sphere; Random search; Grid search; Simulated annealing; Great circles; Coordinate descent; Nelder–Mead (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:157:y:2021:i:c:s0167947320302577

DOI: 10.1016/j.csda.2020.107166

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