Relationships between tail entropies and local intrinsic dimensionality and their use for estimation and feature representation
Document Type
Article
Publication Date
9-1-2023
Abstract
The local intrinsic dimensionality (LID) model assesses the complexity of data within the vicinity of a query point, through the growth rate of the probability measure within an expanding neighborhood. In this paper, we show how LID is asymptotically related to the entropy of the lower tail of the distribution of distances from the query. We establish relationships for cumulative Shannon entropy, entropy power, Bregman formulation of cumulative Kullback–Leibler divergence, and generalized Tsallis entropy variants. Leveraging these relationships, we propose four new estimators of LID, one of them expressible in an intuitive analytic form. We investigate the effectiveness of these new estimators, as well as the effectiveness of entropy power as the basis for feature representations in classification.
Identifier
85163806100 (Scopus)
Publication Title
Information Systems
External Full Text Location
https://doi.org/10.1016/j.is.2023.102245
ISSN
03064379
Volume
118
Grant
18H03296
Fund Ref
Japan Society for the Promotion of Science
Recommended Citation
Bailey, James; Houle, Michael E.; and Ma, Xingjun, "Relationships between tail entropies and local intrinsic dimensionality and their use for estimation and feature representation" (2023). Faculty Publications. 1472.
https://digitalcommons.njit.edu/fac_pubs/1472