DeepAI AI Chat
Log In Sign Up

Updating Zigzag Persistence and Maintaining Representatives over Changing Filtrations

by   Tamal K. Dey, et al.

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 computing these vines over changing filtrations for zigzag persistence. We observe that eight atomic operations are sufficient for changing one zigzag filtration to another and provide an update algorithm for each of them. As with the zigzag persistence algorithms for a static filtration, these updates are implemented with the maintenance of representatives. Since finding consistent representatives for zigzag persistence is more involved, the updates for the zigzag case are more costly than their counterparts in the non-zigzag case. As motivations, we identify some potential use of our update algorithms including the case of dynamic point cloud data, where a vineyard of zigzag persistence diagrams captures changing homological features across distance and time.


page 1

page 2

page 3

page 4


A Stable Cardinality Distance for Topological Classification

This work incorporates topological and geometric features via persistenc...

Computing Zigzag Vineyard Efficiently Including Expansions and Contractions

Vines and vineyard connecting a stack of persistence diagrams have been ...

Move Schedules: Fast persistence computations in sparse dynamic settings

The standard procedure for computing the persistent homology of a filter...

Correct, Fast Remote Persistence

Persistence of updates to remote byte-addressable persistent memory (PM)...

Persistence in Complex Systems

Persistence is an important characteristic of many complex systems in na...

Malicious Cyber Activity Detection Using Zigzag Persistence

In this study we synthesize zigzag persistence from topological data ana...

Simultaneously Updating All Persistence Values in Reinforcement Learning

In reinforcement learning, the performance of learning agents is highly ...