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Activity Number:
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56
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Type:
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Topic Contributed
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Date/Time:
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Sunday, July 29, 2007 : 4:00 PM to 5:50 PM
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Sponsor:
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IMS
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| Abstract - #309993 |
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Title:
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Local Multidimensional Scaling for Nonlinear Dimension Reduction, Graph Layout, and Approximity Analysis
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Author(s):
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Lisha Chen*+ and Andreas Buja
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Companies:
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Yale University and University of Pennsylvania
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Address:
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24 Hillhouse Ave, New Have, 06511,
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Keywords:
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nonlinear dimension reduction ; MDS ; graph layout ; proximity analysis
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Abstract:
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Dimensional reduction has many applications in science. Classical methods like PCA or MDS fail to recover the intrinsic dimensions of the data if there is nonlinear structure in them. There has been a resurgence of interest in nonlinear dimension reduction (NLDR) methods. We will review some of the recently proposed methods and introduce a family of new nonlinear dimension reduction methods called "Local Multidimensional Scaling" or LMDS. LMDS only uses local information from user-chosen neighborhoods like other NLDR methods, but it differs from them in that it uses the force paradigm from graph layout by proposing a parameterized family of stress or energy functions. This family provides users with considerable flexibility for achieving desirable embeddings. Facing an embarrassment of riches of energy functions, we propose a metacriterion for selecting viable energy functions.
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