Extracting Persistent Clusters in Dynamic Data via Möbius Inversion
Identifying and representing clusters in time-varying network data is of particular importance
when studying collective behaviors emerging in nature, in mobile device networks or in …
when studying collective behaviors emerging in nature, in mobile device networks or in …
Sketches of a platypus: persistent homology and its algebraic foundations
M Vejdemo-Johansson - arXiv preprint arXiv:1212.5398, 2012 - arxiv.org
The subject of persistent homology has vitalized applications of algebraic topology to point
cloud data and to application fields far outside the realm of pure mathematics. The area has …
cloud data and to application fields far outside the realm of pure mathematics. The area has …
Computing persistent features in big data: A distributed dimension reduction approach
AC Wilkerson, H Chintakunta… - 2014 IEEE international …, 2014 - ieeexplore.ieee.org
Persistent homology has become one of the most popular tools used in topological data
analysis for analyzing big data sets. In an effort to minimize the computational complexity of …
analysis for analyzing big data sets. In an effort to minimize the computational complexity of …
When and why the topological coverage criterion works
NJ Cavanna, KP Gardner, DR Sheehy - … of the Twenty-Eighth Annual ACM …, 2017 - SIAM
In their seminal work on homological sensor networks, de Silva and Ghrist showed the
surprising fact that it's possible to certify the coverage of a coordinate-free sensor network …
surprising fact that it's possible to certify the coverage of a coordinate-free sensor network …
A distributed collapse of a network's dimensionality
AC Wilkerson, H Chintakunta, H Krim… - 2013 IEEE global …, 2013 - ieeexplore.ieee.org
Algebraic topology has been successfully applied to detect and localize sensor network
coverage holes with minimal assumptions on sensor locations. These methods all use a …
coverage holes with minimal assumptions on sensor locations. These methods all use a …
A distributed approach to the evasion problem
The Evasion Problem is the question of whether—given a collection of sensors and a
particular movement pattern over time—it is possible to stay undetected within the domain …
particular movement pattern over time—it is possible to stay undetected within the domain …
Extracting Persistent Clusters in Dynamic Data via M\" obius inversion
Identifying and representing clusters in time-varying network data is of particular importance
when studying collective behaviors emerging in nature, in mobile device networks or in …
when studying collective behaviors emerging in nature, in mobile device networks or in …
Methods in Homology Inference
NJ Cavanna - 2019 - digitalcommons.lib.uconn.edu
Methods in Homology Inference Page 1 Masthead Logo University of Connecticut
OpenCommons@UConn Doctoral Dissertations University of Connecticut Graduate School …
OpenCommons@UConn Doctoral Dissertations University of Connecticut Graduate School …
Geometric metrics for topological representations
In this chapter, we present an overview of recent techniques from the emerging area of
topological data analysis (TDA), with a focus on machine-learning applications. TDA …
topological data analysis (TDA), with a focus on machine-learning applications. TDA …
Visualizing sensor network coverage with location uncertainty
T Sodergren, J Hair, JM Phillips… - 2017 IEEE Visualization …, 2017 - ieeexplore.ieee.org
We present an interactive visualization system for exploring the coverage in sensor networks
with uncertain sensor locations. We consider a simple case of uncertainty where the location …
with uncertain sensor locations. We consider a simple case of uncertainty where the location …