Persistent homology

Persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected… (More)
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Papers overview

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Review
2017
Review
2017
Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist… (More)
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2016
2016
Persistent homology provides a new approach for the topological simplification of big data via measuring the life time of… (More)
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2014
2014
We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are (R… (More)
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Highly Cited
2013
Highly Cited
2013
We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its… (More)
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Highly Cited
2012
Highly Cited
2012
The brain network is usually constructed by estimating the connectivity matrix and thresholding it at an arbitrary level. The… (More)
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Highly Cited
2012
Highly Cited
2012
An animal's ability to navigate through space rests on its ability to create a mental map of its environment. The hippocampus is… (More)
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2011
2011
It is known that the brain network has small-world and scale-free topology, but the network structures drastically change… (More)
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Highly Cited
2009
Highly Cited
2009
We study the problem of computing zigzag persistence of a sequence of homology groups and study a particular sequence derived… (More)
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Highly Cited
2005
Highly Cited
2005
We introduce a topological approach to a problem of covering a region in Euclidean space by balls of fixed radius at unknown… (More)
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Highly Cited
2004
Highly Cited
2004
We study the homology of a filtered d-dimensional simplicial complex K as a single algebraic entity and establish a… (More)
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