From Graph Centrality to Data Depth
Aamari, Eddie; Arias-Castro, Ery; Berenfeld, Clément (2021), From Graph Centrality to Data Depth. https://basepub.dauphine.psl.eu/handle/123456789/22369
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-03220416
Series titleCahier de recherche du CEREMADE
MetadataShow full item record
Laboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
Department of Mathematics [Univ California San Diego] [MATH - UC San Diego]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)Given a sample of points in a Euclidean space, we can define a notion of depth by forming a neighborhood graph and applying a notion of centrality. In the present paper, we focus on the degree, iterates of the H-index, and the coreness, which are all well-known measures of centrality. We study their behaviors when applied to a sample of points drawn i.i.d. from an underlying density and with a connectivity radius properly chosen. Equivalently, we study these notions of centrality in the context of random neighborhood graphs. We show that, in the large-sample limit and under some standard condition on the connectivity radius, the degree converges to the likelihood depth (unsurprisingly), while iterates of the H-index and the coreness converge to new notions of depth.
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Prifti, Edi; Chevaleyre, Yann; Hanczar, Blaise; Belda, Eugeni; Danchin, Antoine; Clément, Karine (2020) Article accepté pour publication ou publié