Computing Persistent Homology

@article{Zomorodian2004ComputingPH,
  title={Computing Persistent Homology},
  author={Afra Zomorodian and Gunnar E. Carlsson},
  journal={Discrete \& Computational Geometry},
  year={2004},
  volume={33},
  pages={249-274}
}
Abstract We show that the persistent homology of a filtered d-dimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analysis establishes the existence of a simple description of persistent homology groups over arbitrary fields. It also enables us to derive a natural algorithm for computing persistent homology of spaces in arbitrary dimension over any field. This result generalizes and extends the previously known algorithm… 
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