ABID: Angle Based Intrinsic Dimensionality — Theory and analysis

Thordsen, Erik; Schubert, Erich

doi:10.1016/j.is.2022.101989

Cited by 4 publications

(1 citation statement)

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“…For local intrinsic dimensionality, a popular estimator is the maximum likelihood estimator, studied in the Euclidean setting by Levina and Bickel [ 39 ] and later formulated under the more general assumptions of extreme value theory by Houle [ 2 ] and Amsaleg et al [ 40 ], who showed it to be equivalent to the classic Hill estimator [ 41 ]. Other local estimators include expected simplex skewness [ 42 ], the tight locality estimator [ 43 ], the MiND framework [ 17 ], manifold adaptive dimension [ 44 ], statistical distance [ 45 ] and angle-based approaches [ 46 ]. Smoothing approaches for estimation have also been used with success [ 47 , 48 ].…”

Section: Related Workmentioning

confidence: 99%

Local Intrinsic Dimensionality, Entropy and Statistical Divergences

Bailey

Houle

2022

Entropy

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Properties of data distributions can be assessed at both global and local scales. At a highly localized scale, a fundamental measure is the local intrinsic dimensionality (LID), which assesses growth rates of the cumulative distribution function within a restricted neighborhood and characterizes properties of the geometry of a local neighborhood. In this paper, we explore the connection of LID to other well known measures for complexity assessment and comparison, namely, entropy and statistical distances or divergences. In an asymptotic context, we develop analytical new expressions for these quantities in terms of LID. This reveals the fundamental nature of LID as a building block for characterizing and comparing data distributions, opening the door to new methods for distributional analysis at a local scale.

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