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Title: Discovering the Whole by the Coarse: A topological paradigm for data analysis

Journal Article · · IEEE Signal Processing Magazine
 [1];  [2];  [3]
  1. North Carolina State Univ., Raleigh, NC (United States). Dept. of Electrical and Computer Engineering
  2. National and Kapodistrian Univ. of Athens (Greece)
  3. Pomona College, Claremont, CA (United States). Mathematics Dept.

The increasing interest in big data applications is ushering in a large effort in seeking new, efficient, and adapted data models to reduce complexity, while preserving maximal intrinsic information. Graph-based models have recently been getting a lot of attention on account of their intuitive and direct connection to the data. The cost of these models, however, is to some extent giving up geometric insight as well as algebraic flexibility. Topology, as an intermediate analysis medium, focuses on coarse structures of an object/signal in general. It affords a formalism of transitioning from a local to a global description of an object, while providing significant information, which respects the local structure of measurements. It may also support a global visualization (e.g., data variation trends) and enhances the understanding of the underlying phenomenon. Throughout this article, measurements may be considered proximal in various ways, depending on the specific application, and the selected proximity metrics are subsequently used in the construction of a graph structure, thus highlighting various groups of neighboring data. As described later, these groups, often based on proximity criteria, are represented by n-simplices, where n + 1 corresponds to the number of points in an associated group. Collectively, they form what is (and will be throughout) referred to as a simplicial complex, a special representation of a topological space. We find the key advantage of computational topology is its inherently algebraic structure on the basic elements of the resulting graph-like structure.

Research Organization:
North Carolina State University, Raleigh, NC (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22); Defense Threat Reduction Agency (DTRA)
Grant/Contract Number:
Journal Information:
IEEE Signal Processing Magazine, Vol. 33, Issue 2; ISSN 1053-5888
IEEECopyright Statement
Country of Publication:
United States

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