×

The shape of data. (English) Zbl 1349.55001

Cucker, Felipe (ed.) et al., Foundations of computational mathematics, Budapest 2011. Collected papers based on the plenary talks presented at the conference of the Society for the Foundations of Computational Mathematics, FoCM, July 4–14, 2011. Cambridge: Cambridge University Press (ISBN 978-1-107-60407-0/pbk). London Mathematical Society Lecture Note Series 403, 16-44 (2013).
From the introduction: In each of the examples given in this introduction, an aspect of the shape of the data what is relevant in reflecting the information about the data. Connectedness (the simplest property of shape) reflects the presence of a discrete classification of the data into disperate groups. The presence of loops in the data, another simple aspect of shape, often reflects periodic or recurrent behavior.
Finally, in the third example, the shape containing flares can also suggest a classification of the data, but in such a way that the classification describes ways in which a phenomenon can deviate from the norm, which would be represented by the central core. These examples support the idea that the shape of data (suitably defined) is an important aspect of its structure, and that it is therefore important to develop methods for analyzing and understanding its shape.
The part of mathematics which concerns itself with the study of shape is called topology, and an important theme in recent research is the adaptation of techniques from this discipline to the study of data. We will discuss this direction in this paper, beginning with a summary of topology as practiced within pure mathematics, and then discussing how the methods are adapted to the world of data.
For the entire collection see [Zbl 1255.00017].

MSC:

55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology
62-07 Data analysis (statistics) (MSC2010)
62H11 Directional data; spatial statistics
62H30 Classification and discrimination; cluster analysis (statistical aspects)
PDFBibTeX XMLCite