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On Simultaneous Data-Based Dimension Reduction and Hidden Phase Identification
- Article from:
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Journal of the Atmospheric Sciences
- Article date:
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June 1, 2008
- Author:
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Copyright informationCopyright American Meteorological Society Jun 2008. Provided by ProQuest LLC. (Hide copyright information)
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ABSTRACT
A problem of simultaneous dimension reduction and identification of hidden attractive manifolds in multidimensional data with noise is considered. The problem is approached in two consecutive steps: (i) embedding the original data in a sufficiently high-dimensional extended space in a way proposed by Takens in his embedding theorem, followed by (ii) a minimization of the residual functional. The residual functional is constructed to measure the distance between the original data in extended space and their reconstruction based on a low-dimensional description. The reduced representation of the analyzed data results from projection onto a fixed number of unknown low-dimensional ...
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