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.

Part I. Large-Scale Data Analysis: In-Situ and Distributed Analysis: 1 A Distributed-Memory Algorithm for Connected Components Labeling of Simulation Data: Cyrus Harrison, Jordan Weiler, Ryan Bleile, Kelly Gaither and Hank Childs.- 2 In-Situ Visualization in Fluid Mechanics Using Open-Source Tools: Integration of Catalyst into Code Saturne: Alejandro Ribes, Benjamin Lorendeau, Julien Jomier and Yvan Fournier.- 3 Sublinear Algorithms for Extreme-Scale Data Analysis: C. Seshadhri, Ali Pinar, David Thompson and Janine Bennett.- Part II. Large-Scale Data Analysis: Efficient Representation of Large-Functions: 4 Optimal General Simplification of Scalar Fields on Surfaces: Julien Tierny, David Guenther and Valerio Pascucci.- 5 Piecewise Polynomial Monotonic Interpolation of 2D Gridded Data: Leo Allemand-Giorgis, Georges-Pierre Bonneau, Stefanie Hahmann and Fabien Vivodtzev.- 6 Shape Analysis and Description Using Real Functions: Silvia Biasotti, Andrea Cerri, Michela Spagnuolo and Bianca Falcidieno.- Part III. Multi-Variate Data Analysis: Structural Techniques: 7 3D Symmetric Tensor Fields: What We Know and Where To Go Next: Eugene Zhang and Yue Zhang.- 8 A Comparison of Pareto Sets and Jacobi Sets: Lars Huettenberger and Christoph Garth.- 9 Deformations Preserving Gauss Curvature: Anne Berres, Hans Hagen and Stefanie Hahmann.- Part IV. Multi-Variate Data Analysis: Classification and Visualization of Vector Fields: 10 Lyapunov Time for 2D Lagrangian Visualization: Filip Sadlo.- 11 Geometric Algebra for Vector Fields Analysis and Visualization: Mathematical Settings, Overview and Applications: Chantal Oberson Ausoni and Pascal Frey.- 12 Computing Accurate Morse-Smale Complexes from Gradient Vector Fields: Attila Gyulassy, Harsh Bhatia, Peer-Timo Bremer and Valerio Pascucci.- Part V. High-Dimensional Data Analysis: Exploration of High-Dimensional Models: 13 Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k-d Darts: Mohamed S. Ebeida, Scott A. Mitchell, Anjul Patney, Andrew A. Davidson, Stanley Tzeng, Muhammad A. Awad, Ahmed H. Mahmoud, and John D. Owens.- 14 Realization of Regular Maps of Large Genus: Faniry Razafindrazaka and Konrad Polthier.- Part VI. High-Dimensional Data Analysis: Analysis of Large Systems: 15 Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving: Eleanor Anthony, Sheridan Grant, Peter Gritzmann, and J. Maurice Rojas.- 16 Slycat Ensemble Analysis of Electrical Circuit Simulations: Patricia J. Crossno, Timothy M. Shead, Milosz A. Sielicki, Warren L. Hunt, Shawn Martin, and Ming-Yu Hsieh.