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...
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...
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...
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...
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...