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Activity Number:
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411
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 9, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #305381 |
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Title:
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Classical Multidimensional Scaling and Laplacian Eigenmaps
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Author(s):
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Michael W. Trosset*+
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Companies:
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The College of William & Mary
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Address:
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Department of Mathematics, Williamsburg, VA, 23187-8795,
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Keywords:
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classical multidimensional scaling ; Laplacian eigenmaps ; isomap ; embedding ; nonlinear dimension reduction ; manifold learning
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Abstract:
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An eigenmap is a data matrix constructed from the eigenvectors of a centered inner product matrix, as in classical multidimensional scaling (CMDS or principal coordinate analysis). Eigenmaps are popular in manifold learning (e.g., Isomap applies CMDS to the shortest path distances of a certain graph, while Laplacian eigenmaps are constructed from graphs via centered inner product matrices known as graph Laplacians). I will describe several relations between CMDS and Laplacian eigenmaps and explore the implications of these relations for their proper use in embedding and nonlinear dimension reduction.
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