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 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.
Intrinsic dimension estimation : relevant techniques and a Benchmark Framework / P. Campadelli, E. Casiraghi, C. Ceruti, A. Rozza. - In: MATHEMATICAL PROBLEMS IN ENGINEERING. - ISSN 1024-123X. - 2015(2015 May 17), pp. 759567.1-759567.22.
|Titolo:||Intrinsic dimension estimation : relevant techniques and a Benchmark Framework|
|Parole Chiave:||Survey; Intrinsic dimension estimation; Manifold learning; Dimensionality reduction; Benchmark framework|
|Settore Scientifico Disciplinare:||Settore INF/01 - Informatica|
|Data di pubblicazione:||17-mag-2015|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1155/2015/759567|
|Appare nelle tipologie:||01 - Articolo su periodico|