On local intrinsic dimension estimation and its applications

Authors:
Kevin M. Carter;Raviv Raich;Alfred O. Hero
Affiliations:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI;School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR;Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

In this paper, we present multiple novel applications for local intrinsic dimension estimation. There has been much work done on estimating the global dimension of a data set, typically for the purposes of dimensionality reduction. We show that by estimating dimension locally, we are able to extend the uses of dimension estimation to many applications, which are not possible with global dimension estimation. Additionally, we show that local dimension estimation can be used to obtain a better global dimension estimate, alleviating the negative bias that is common to all known dimension estimation algorithms. We illustrate local dimension estimation's uses towards additional applications, such as learning on statistical manifolds, network anomaly detection, clustering, and image segmentation.