6 citations · 9 across the 4 of their papers we have counts for
6 papers
Topological Node2vec: Enhanced Graph Embedding via Persistent Homology
Yasuaki Hiraoka, Yusuke Imoto, Killian Meehan +2
Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numeri…
Interleavings and Matchings as Representations
Emerson G. Escolar, Killian Meehan, Michio Yoshiwaki
In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular,…
Persistence and Stability of the Quiver
Killian Meehan, David C. Meyer
We introduce two new distances for zigzag persistence modules. The first uses Auslander-Reiten quiver theory, and the second is an extension of the classical interleaving distance.…
Interleaving Distance as a Limit
Killian Meehan, David Meyer
Persistent homology is a way of determining the topological properties of a data set. It is well known that each persistence module admits the structure of a representation of a fi…
An Isometry Theorem for Generalized Persistence Modules
Killian Meehan, David Meyer
In recent work, generalized persistence modules have proved useful in distinguishing noise from the legitimate topological features of a data set. Algebraically, generalized persis…
On the Structural Theorem of Persistent Homology
Killian Meehan, Andrei Pavlichenko, Jan Segert
We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is c…