Topological and Statistical Methods for Complex Data: Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces

✍ Scribed by Janine Bennett, Fabien Vivodtzev, Valerio Pascucci (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2015
• Tongue: English
• Leaves: 297
• Series: Mathematics and Visualization
• Edition: 1
• Category: Library

✦ Synopsis

This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data.

The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends.

Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.

✦ Table of Contents

Front Matter....Pages i-xv
Front Matter....Pages 1-1
A Distributed-Memory Algorithm for Connected Components Labeling of Simulation Data....Pages 3-19
In-Situ Visualization in Computational Fluid Dynamics Using Open-Source tools: Integration of Catalyst into Code_Saturne ....Pages 21-37
Sublinear Algorithms for Extreme-Scale Data Analysis....Pages 39-54
Front Matter....Pages 55-55
Optimal General Simplification of Scalar Fields on Surfaces....Pages 57-71
Piecewise Polynomial Monotonic Interpolation of 2D Gridded Data....Pages 73-91
Shape Analysis and Description Using Real Functions....Pages 93-107
Front Matter....Pages 109-109
3D Symmetric Tensor Fields: What We Know and Where To Go Next....Pages 111-124
A Comparison of Pareto Sets and Jacobi Sets....Pages 125-141
Deformations Preserving Gauss Curvature....Pages 143-163
Front Matter....Pages 165-165
Lyapunov Time for 2D Lagrangian Visualization....Pages 167-181
Geometric Algebra for Vector Field Analysis and Visualization: Mathematical Settings, Overview and Applications....Pages 183-203
Computing Accurate Morse-Smale Complexes from Gradient Vector Fields....Pages 205-218
Front Matter....Pages 219-219
Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k -d Darts....Pages 221-238
Realization of Regular Maps of Large Genus....Pages 239-252
Front Matter....Pages 253-253
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving....Pages 255-277
Slycat Ensemble Analysis of Electrical Circuit Simulations....Pages 279-294
Back Matter....Pages 295-297

✦ Subjects

Topology; Statistical Theory and Methods; Applications of Mathematics; Algorithms; Visualization; Manifolds and Cell Complexes (incl. Diff.Topology)