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- Sofya Chepushtanova, Tegan Emerson, Eric M. Hanson, Michael Kirby, Francis C. Motta, Rachel Neville +3 others
- ArXiv
- 2015

Many datasets can be viewed as a noisy sampling of an underlying topological space. Topo-logical data analysis aims to understand and exploit this underlying structure for the purpose of knowledge discovery. A fundamental tool of the discipline is persistent homology, which captures underlying data-driven, scale-dependent homological information. A… (More)

- Henry Adams, Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta +4 others
- 2015

Many data sets can be viewed as a noisy sampling of an underlying topological space. A suite of tools in topological data analysis allows one to exploit this structure for the purpose of knowledge discovery. One such tool is persistent homology which provides a multiscale description of the homological features within a data set. A useful representation of… (More)

- Daniel J Bates, Brent Davis, David Eklund, Eric Hanson, Chris Peterson, Sweden Stockholm
- 2013

Given a polynomial system f : C N → C n , the methods of numerical algebraic geometry produce numerical approximations of the isolated solutions of f (z) = 0, as well as points on any positive-dimensional components of the solution set, V(f). One of the most recent advances in this field is regeneration, an equation-by-equation solver that is often more… (More)

1 Abstract Persistent homology is a relatively new tool from topo-logical data analysis that has transformed, for many, the way data sets (and the information contained in those sets) are viewed. It is derived directly from techniques in computational homology but has the added feature that it is able to capture structure at multiple scales. One way that… (More)

- Henry Adams, Sofya Chepushtanova, Tegan Emerson, Eric Hanson, Michael Kirby, Francis Motta +4 others
- 2015

Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a dataset. A useful representation of this homological… (More)

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