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Extreme-value-theoretic estimation of local intrinsic dimensionality

Laurent Amsaleg 1 Oussama Chelly 2 Teddy Furon 1 Stephane Girard 3 Michael Houle 2, * Ken-Ichi Kawarabayashi 2 Michael Nett 4
* Corresponding author
1 LinkMedia - Creating and exploiting explicit links between multimedia fragments
IRISA-D6 - MEDIA ET INTERACTIONS, Inria Rennes – Bretagne Atlantique
3 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : This paper is concerned with the estimation of a local measure of intrinsic dimensionality (ID) recently proposed by Houle. The local model can be regarded as an extension of Karger and Ruhl’s expansion dimension to a statistical setting in which the distribution of distances to a query point is modeled in terms of a continuous random variable. This form of intrinsic dimensionality can be particularly useful in search, classification, outlier detection, and other contexts in machine learning, databases, and data mining, as it has been shown to be equivalent to a measure of the discriminative power of similarity functions. Several estimators of local ID are proposed and analyzed based on extreme value theory, using maximum likelihood estimation, the method of moments, probability weighted moments, and regularly varying functions. An experimental evaluation is also provided, using both real and artificial data.
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Submitted on : Thursday, August 30, 2018 - 11:00:49 AM
Last modification on : Monday, February 22, 2021 - 3:41:59 PM



Laurent Amsaleg, Oussama Chelly, Teddy Furon, Stephane Girard, Michael Houle, et al.. Extreme-value-theoretic estimation of local intrinsic dimensionality. Data Mining and Knowledge Discovery, Springer, 2018, 32 (6), pp.1768-1805. ⟨10.1007/s10618-018-0578-6⟩. ⟨hal-01864580⟩



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