• Corpus ID: 237213570

U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology

@article{Hang2021UmatchFS,
  title={U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology},
  author={Haibin Hang and Chad Giusti and Lori Ziegelmeier and Gregory Henselman-Petrusek},
  journal={ArXiv},
  year={2021},
  volume={abs/2108.08831}
}
Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological – and indeed, linear – algebra. However, matrices in this domain are typically large, with rows and columns numbered in billions. Low-rank approximation of such arrays typically destroys essential information; thus, new mathematical and computational paradigms are needed for very large, sparse matrices. We present the U-match matrix factorization scheme to address this… 
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