Intrinsic dimension estimation: relevant techniques and a benchmark framework
type: Item
instance of: scholarly article
title: Intrinsic dimension estimation: relevant techniques and a benchmark framework
zbMATH Open document ID: 1395.68244
DOI: 10.1155/2015/759567
author: C. Ceruti
author: Paola Campadelli
author: Elena Casiraghi
author: Alessandro Rozza
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: When dealing with datasets comprising high-dimensional points, it is usually advantageous to discover some data structure. A fundamental information needed to this aim is the minimum number of parameters required to describe the data while minimizing the information loss. This number, usually called intrinsic dimension, can be interpreted as the dimension of the manifold from which the input data are supposed to be drawn. Due to its usefulness in many theoretical and practical problems, in the last decades the concept of intrinsic dimension has gained considerable attention in the scientific community, motivating the large number of intrinsic dimensionality estimators proposed in the literature. However, the problem is still open since most techniques cannot efficiently deal with datasets drawn from manifolds of high intrinsic dimension and nonlinearly embedded in higher dimensional spaces. This paper surveys some of the most interesting, widespread used, and advanced state-of-the-art methodologies. Unfortunately, since no benchmark database exists in this research field, an objective comparison among different techniques is not possible. Consequently, we suggest a benchmark framework and apply it to comparatively evaluate relevant state-of-the-art estimators.
Mathematics Subject Classification ID: 68T10
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 6927172
Wikidata QID: Q59119825
describes a project that uses: IntDim
describes a project that uses: PRMLT
describes a project that uses: UCI-ml
describes a project that uses: ElemStatLearn
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/759567
OpenAlex ID: W2170567676
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description: scientific article; zbMATH DE number 6927172