The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
Geodesic Entropic Graphs for Dimension and Entropy Estimation in Manifold Learning
Abstract
In the manifold learning problem, one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper, we consider the closely related problem of estimating the manifold's intrinsic dimension and the intrinsic entropy of the sample points. Specifically, we view the sample points as realizations of an unknown multivariate density supported on an unknown smooth manifold. We introduce a novel geometric approach based on entropic graph methods. Although the theory presented applies to this general class of graphs, we focus on the geodesic-minimal-spanning-tree (GMST) to obtaining asymptotically consistent estimates of the manifold dimension and the Re/spl acute/nyi /spl alpha/-entropy of the sample density on the manifold. The GMST approach is striking in its simplicity and does not require reconstruction of the manifold or estimation of the multivariate density of the samples. The GMST method simply constructs a minimal spanning tree (MST) sequence using a geodesic edge matrix and uses the overall lengths of the MSTs to simultaneously estimate manifold dimension and entropy. We illustrate the GMST approach on standard synthetic manifolds as well as on real data sets consisting of images of faces.
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On the Intrinsic Dimensionality of Image Representations
Gong, S., Boddeti, V. N., & Jain, A. K. (2019) · 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2019.00411 · Cited by 59
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Metadata
- Authors
- Costa, J. A., & Hero, A. O.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 2004-08
- Volume
- 52
- Issue
- 8
- Pages
- 2210-2221
- ISSN
- 1053-587X (ISSN-L)
- OpenAlex
- W2116402476
- Cited by
- 288
- References
- 22
- FWCI
- 18.03
- Type
- journal article
- Language
- en
- Open access
- closed
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