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Understanding High-Dimensional SpacesSpaces with Multiple Centers

Understanding High-Dimensional Spaces: Spaces with Multiple Centers [The assumption that, in a natural geometry, spaces derived from data have a single center with a single cluster is implicitly an assumption that there is one underlying process responsible for generating the data, and that the spatial variation around some notional center is caused by some variation overlaying this process. Often, perhaps most of the time, it is much more plausible that there are multiple, interacting processes generating the data, and so at least multiple clusters. Each of these clusters might have a notional center with some variation around it, but there is typically also some relationship among the clusters themselves. In other words, the skeleton for such data must describe both the clusters and the connections. The analysis is significantly more complex, but more revealing.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Understanding High-Dimensional SpacesSpaces with Multiple Centers

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Publisher
Springer Berlin Heidelberg
Copyright
© The Author 2012
ISBN
978-3-642-33397-2
Pages
47 –65
DOI
10.1007/978-3-642-33398-9_5
Publisher site
See Chapter on Publisher Site

Abstract

[The assumption that, in a natural geometry, spaces derived from data have a single center with a single cluster is implicitly an assumption that there is one underlying process responsible for generating the data, and that the spatial variation around some notional center is caused by some variation overlaying this process. Often, perhaps most of the time, it is much more plausible that there are multiple, interacting processes generating the data, and so at least multiple clusters. Each of these clusters might have a notional center with some variation around it, but there is typically also some relationship among the clusters themselves. In other words, the skeleton for such data must describe both the clusters and the connections. The analysis is significantly more complex, but more revealing.]

Published: Sep 25, 2012

Keywords: Cluster Algorithm; Span Tree; Class Label; Outer Boundary; Complete Graph

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