The estimation of the intrinsic dimension is an essential step in many data analyses involving, for example, dimensionality reduction. Likelihood-based estimators, which rely on the distributions of the ratios of distances between nearest neighbors, have been recently proposed. However, these distributional results de- pend on several assumptions. One of the most important is the local homogeneity of the point process characterizing the data-generating mechanism. By exploiting a recent theoretical result, we develop the Consecutive Ratio Paths, a graphical tool to assess the validity of the local-homogeneity assumption in a dataset. This tool is also helpful to uncover the presence of multiple latent manifolds, a potential indicator of the existence of heterogeneous intrinsic dimensions.

Denti, F., Mira, A., A tool to validate the assumptions on ratios of nearest neighbors’ distances: the Consecutive Ratio Paths, in Book of Short Paper SIS 2022, (Caserta, 22-24 June 2022), Pearson, Caserta 2022: 1233-1238 [https://hdl.handle.net/10807/221884]

A tool to validate the assumptions on ratios of nearest neighbors’ distances: the Consecutive Ratio Paths

Denti, Francesco
Primo
;
2022

Abstract

The estimation of the intrinsic dimension is an essential step in many data analyses involving, for example, dimensionality reduction. Likelihood-based estimators, which rely on the distributions of the ratios of distances between nearest neighbors, have been recently proposed. However, these distributional results de- pend on several assumptions. One of the most important is the local homogeneity of the point process characterizing the data-generating mechanism. By exploiting a recent theoretical result, we develop the Consecutive Ratio Paths, a graphical tool to assess the validity of the local-homogeneity assumption in a dataset. This tool is also helpful to uncover the presence of multiple latent manifolds, a potential indicator of the existence of heterogeneous intrinsic dimensions.
Inglese
Book of Short Paper SIS 2022
SIS 2022
Caserta
22-giu-2022
24-giu-2022
9788891932310
Pearson
Denti, F., Mira, A., A tool to validate the assumptions on ratios of nearest neighbors’ distances: the Consecutive Ratio Paths, in Book of Short Paper SIS 2022, (Caserta, 22-24 June 2022), Pearson, Caserta 2022: 1233-1238 [https://hdl.handle.net/10807/221884]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/221884
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