An entropy-based persistence barcode

作者：

Highlights：

• We define the notion of “minimal” barcodes in terms of entropy.

• Given a simplicial complex, an algorithm for computing a proper filter F is detailed.

• F preserves the partial ordering imposed by the filtration.

• F achieves a persistence barcode with small entropy.

• Examples demonstrating the utility of computing such a proper filter are given.

摘要

Highlights•We define the notion of “minimal” barcodes in terms of entropy.•Given a simplicial complex, an algorithm for computing a proper filter F is detailed.•F preserves the partial ordering imposed by the filtration.•F achieves a persistence barcode with small entropy.•Examples demonstrating the utility of computing such a proper filter are given.

论文关键词：Persistent homology,Persistence barcodes,Hasse diagram,Simplicial complexes,Entropy,Filtration,Filter

论文评审过程：Received 1 October 2013, Revised 27 June 2014, Accepted 28 June 2014, Available online 8 July 2014.

论文官网地址：https://doi.org/10.1016/j.patcog.2014.06.023