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.
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Skillicorn, D.B. (2012). Spaces with Multiple Centers. In: Understanding High-Dimensional Spaces. SpringerBriefs in Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33398-9_5
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DOI: https://doi.org/10.1007/978-3-642-33398-9_5
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-642-33398-9
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