Skip to search formSkip to main content
You are currently offline. Some features of the site may not work correctly.

Persistent homology

Persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected… Expand
Wikipedia

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2017
Highly Cited
2017
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize… Expand
  • figure 1
  • table 1
  • figure 2
  • figure 3
  • figure 4
Is this relevant?
Highly Cited
2015
Highly Cited
2015
We address the fundamental problem of goal-directed path planning in an uncertain environment represented as a probability (of… Expand
  • figure 1
  • figure 2
  • figure 3
  • figure 4
  • figure 5
Is this relevant?
Highly Cited
2014
Highly Cited
2014
We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are… Expand
Is this relevant?
Highly Cited
2014
Highly Cited
2014
The computation of persistent homology has proven a fundamental component of the nascent field of topological data analysis and… Expand
Is this relevant?
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… Expand
  • table 1
Is this relevant?
Highly Cited
2011
Highly Cited
2011
It is known that the brain network has small-world and scale-free topology, but the network structures drastically change… Expand
  • figure 1
  • figure 2
  • figure 3
Is this relevant?
Highly Cited
2011
Highly Cited
2011
The persistence diagram of a filtered simplicial complex is usually computed by reducing the boundary matrix of the complex. We… Expand
  • table 1
  • table 2
Is this relevant?
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… Expand
  • figure 2
  • figure 3
  • figure 4
  • table 1
  • figure 5
Is this relevant?
Highly Cited
2005
Highly Cited
2005
Abstract We show that the persistent homology of a filtered d-dimensional simplicial complex is simply the standard homology of a… Expand
Is this relevant?
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… Expand
  • figure 1
  • figure 3
  • figure 2
  • figure 4
  • figure 5
Is this relevant?