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» Topological Persistence and Simplification
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COMPGEOM
2009
ACM
14 years 2 months ago
Persistent cohomology and circular coordinates
Nonlinear dimensionality reduction (NLDR) algorithms such as Isomap, LLE and Laplacian Eigenmaps address the problem of representing high-dimensional nonlinear data in terms of lo...
Vin de Silva, Mikael Vejdemo-Johansson
COMPGEOM
2011
ACM
12 years 11 months ago
Reeb graphs: approximation and persistence
Given a continuous function f : X → IR on a topological space X, its level set f−1 (a) changes continuously as the real value a changes. Consequently, the connected components...
Tamal K. Dey, Yusu Wang
SIGCOMM
2006
ACM
14 years 1 months ago
Growth codes: maximizing sensor network data persistence
Sensor networks are especially useful in catastrophic or emergency scenarios such as floods, fires, terrorist attacks or earthquakes where human participation may be too dangero...
Abhinav Kamra, Vishal Misra, Jon Feldman, Dan Rube...
COMPGEOM
2004
ACM
14 years 1 months ago
Time-varying reeb graphs for continuous space-time data
The Reeb graph is a useful tool in visualizing real-valued data obtained from computational simulations of physical processes. We characterize the evolution of the Reeb graph of a...
Herbert Edelsbrunner, John Harer, Ajith Mascarenha...
IJCV
2008
88views more  IJCV 2008»
13 years 7 months ago
On the Local Behavior of Spaces of Natural Images
In this study we concentrate on qualitative topological analysis of the local behavior of the space of natural images. To this end, we use a space of 3 by 3 high-contrast patches ...
Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, A...