TY - JOUR
T1 - Modeling of persistent homology
AU - Agami, Sarit
AU - Adler, Robert J.
N1 - Publisher Copyright:
© 2019 Taylor & Francis Group, LLC.
PY - 2020/10/17
Y1 - 2020/10/17
N2 - Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence diagrams. In an earlier article we proposed a parametric representation for the probability distributions of persistence diagrams, and based on it provided a method for their replication. Since the typical situation for big data is that only one persistence diagram is available, these replications allow for conventional statistical inference, which, by its very nature, requires some form of replication. In the current paper we continue this analysis, and further develop its practical statistical methodology, by investigating a wider class of examples than treated previously.
AB - Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence diagrams. In an earlier article we proposed a parametric representation for the probability distributions of persistence diagrams, and based on it provided a method for their replication. Since the typical situation for big data is that only one persistence diagram is available, these replications allow for conventional statistical inference, which, by its very nature, requires some form of replication. In the current paper we continue this analysis, and further develop its practical statistical methodology, by investigating a wider class of examples than treated previously.
KW - Hamiltonian
KW - MCMC
KW - Persistence diagram
KW - Replicated persistence diagrams
UR - http://www.scopus.com/inward/record.url?scp=85066073258&partnerID=8YFLogxK
U2 - 10.1080/03610926.2019.1615091
DO - 10.1080/03610926.2019.1615091
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AN - SCOPUS:85066073258
SN - 0361-0926
VL - 49
SP - 4871
EP - 4888
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 20
ER -