2 citations · 2 across the 3 of their papers we have counts for
5 papers
U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology
Haibin Hang, Chad Giusti, Lori Ziegelmeier +1
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…
Detecting Carbon Nanotube Orientation with Topological Data Analysis of Scanning Electron Micrographs
Liyu Dong, Haibin Hang, Jin Gyu Park +2
As the aerospace industry becomes increasingly demanding for stronger lightweight materials, the ultra-strong carbon nanotube (CNT) composites with highly aligned CNT network struc…
Manifold Matching via Deep Metric Learning for Generative Modeling
Mengyu Dai, Haibin Hang
We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real…
Decorated Merge Trees for Persistent Topology
Justin Curry, Haibin Hang, Washington Mio +2
This paper introduces decorated merge trees (DMTs) as a novel invariant for persistent spaces. DMTs combine both and information into a single data structure that disti…
A Topological Study of Functional Data and Fréchet Functions of Metric Measure Spaces
Haibin Hang, Facundo Mémoli, Washington Mio
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define…