53 citations · 219 across the 20 of their papers we have counts for
10 papers · 1 filter
Linked Barcode for Persistence Induced by Filtrations
Tamal K. Dey, Gilberto Gonzalez-Arroyo, Tao Hou
The well-known persistence algorithm summarizes the evolution of homological cycles into what is called a \emph{barcode} while scanning an input simplicial filtration. We show that…
Computing Zigzag Vineyard Efficiently Including Expansions and Contractions
Tamal K. Dey, Tao Hou
Vines and vineyard connecting a stack of persistence diagrams have been introduced in the non-zigzag setting by Cohen-Steiner et al. We consider computing these vines over changing…
Revisiting Graph Persistence for Updates and Efficiency
Tamal K. Dey, Tao Hou, Salman Parsa
It is well known that ordinary persistence on graphs can be computed more efficiently than the general persistence. Recently, it has been shown that zigzag persistence on graphs al…
Fast Computation of Zigzag Persistence
Tamal K. Dey, Tao Hou
Zigzag persistence is a powerful extension of the standard persistence which allows deletions of simplices besides insertions. However, computing zigzag persistence usually takes c…
Updating Barcodes and Representatives for Zigzag Persistence
Tamal K. Dey, Tao Hou
Computing persistence over changing filtrations give rise to a stack of 2D persistence diagrams where the birth-death points are connected by the so-called `vines'. We consider com…
On Association between Absolute and Relative Zigzag Persistence
Tamal K. Dey, Tao Hou
Duality results connecting persistence modules for absolute and relative homology provides a fundamental understanding into persistence theory. In this paper, we study similar asso…
Computing Optimal Persistent Cycles for Levelset Zigzag on Manifold-like Complexes
Tamal K. Dey, Tao Hou, Anirudh Pulavarthy
In standard persistent homology, a persistent cycle born and dying with a persistence interval (bar) associates the bar with a concrete topological representative, which provides m…
Computing Zigzag Persistence on Graphs in Near-Linear Time
Tamal K. Dey, Tao Hou
Graphs model real-world circumstances in many applications where they may constantly change to capture the dynamic behavior of the phenomena. Topological persistence which provides…
Computing Minimal Persistent Cycles: Polynomial and Hard Cases
Tamal K. Dey, Tao Hou, Sayan Mandal
Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also terme…
Persistent 1-Cycles: Definition, Computation, and Its Application
Tamal K. Dey, Tao Hou, Sayan Mandal
Persistence diagrams, which summarize the birth and death of homological features extracted from data, are employed as stable signatures for applications in image analysis and othe…