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Activity Number:
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187
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Type:
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Contributed
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Date/Time:
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Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #301433 |
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Title:
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Estimating Intrinsic Dimensionality from the Nearest-neighbor Distances
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Author(s):
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Elizaveta Levina*+
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Companies:
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University of Michigan
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Address:
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Dept. of Statistics, 439 West Hall, Ann Arbor, MI, 48109-1092,
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Keywords:
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dimensionality reduction ; intrinsic dimension ; manifold projections ; nearest-neighbor distances
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Abstract:
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Recently developed nonlinear manifold projection methods such as Locally Linear Embedding and Isomap have become popular dimensionality reduction tools. Using these methods successfully for applications such as classification requires estimating intrinsic data dimension. The existing methods for intrinsic dimension estimation are mostly heuristic and very little is known about how they scale with the number of observations and the true dimension. We propose a new method for estimating intrinsic dimensionality, derived through a rigorous analysis of distributions of the nearest-neighbor distances. A simple closed-form maximum likelihood estimator of dimension is obtained by treating observations in a small sphere as a homogeneous Poisson process. We apply the method to some of the popular manifold datasets and study its behavior as the dimension and the sample size grow, analytically and through simulations. This is joint work with Peter Bickel.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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