Eric M. Hanson

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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)
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)
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)
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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