NDLI: Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization

Content Provider	IEEE Xplore Digital Library
Author	Lafon, S. Lee, A.B.
Copyright Year	1979
Abstract	We provide evidence that nonlinear dimensionality reduction, clustering, and data set parameterization can be solved within one and the same framework. The main idea is to define a system of coordinates with an explicit metric that reflects the connectivity of a given data set and that is robust to noise. Our construction, which is based on a Markov random walk on the data, offers a general scheme of simultaneously reorganizing and subsampling graphs and arbitrarily shaped data sets in high dimensions using intrinsic geometry. We show that clustering in embedding spaces is equivalent to compressing operators. The objective of data partitioning and clustering is to coarse-grain the random walk on the data while at the same time preserving a diffusion operator for the intrinsic geometry or connectivity of the data set up to some accuracy. We show that the quantization distortion in diffusion space bounds the error of compression of the operator, thus giving a rigorous justification for k-means clustering in diffusion space and a precise measure of the performance of general clustering algorithms
Sponsorship	IEEE Computer Society
Page Count	11
File Size	1411319
Starting Page	1393
Ending Page	1403
File Format	PDF
ISSN	01628828
Volume Number	28
Issue Number	9
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Geometry Quantization Distortion measurement Clustering algorithms Eigenvalues and eigenfunctions Noise robustness Noise shaping Nonlinear distortion Extraterrestrial measurements Text analysis graph algorithms. Machine learning text analysis knowledge retrieval quantization graph-theoretic methods compression (coding) clustering clustering similarity measures information visualization Markov processes
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Computational Theory and Mathematics Computer Vision and Pattern Recognition Software

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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