Optimized intrinsic dimension estimator using nearest neighbor graphs

Author

Sricharan, Kumar ; Raich, Raviv ; Hero, Alfred O., III

Author_Institution

Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, USA

fYear

2010

fDate

14-19 March 2010

Firstpage

5418

Lastpage

5421

Abstract

We develop an approach to intrinsic dimension estimation based on k-nearest neighbor (kNN) distances. The dimension estimator is derived using a general theory on functionals of kNN density estimates. This enables us to predict the performance of the dimension estimation algorithm. In addition, it allows for optimization of free parameters in the algorithm. We validate our theory through simulations and compare our estimator to previous kNN based dimensionality estimation approaches.

Keywords

estimation theory; graph theory; optimisation; random processes; k-nearest neighbor distance; kNN based dimensionality estimation approach; nearest neighbor graph; optimized intrinsic dimension estimator; Analysis of variance; Eigenvalues and eigenfunctions; Entropy; Fluctuations; Knee; Laplace equations; Nearest neighbor searches; Principal component analysis; Random variables; State estimation; geodesics; intrinsic dimension; k nearest neighbor; kNN density estimation; manifold learning;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on

Conference_Location

Dallas, TX

ISSN

1520-6149

Print_ISBN

978-1-4244-4295-9

Electronic_ISBN

1520-6149

Type

conf

DOI

10.1109/ICASSP.2010.5494931

Filename

5494931