Grassmannian Atlas: A General Framework for Exploring Linear Projections of High-Dimensional Data Shusen Liu 1 , Peer-Timo Bremer 2 , Jayaraman J. Thiagarajan 2 , Bei Wang 1 , Brian Summa 3 , and Valerio Pascucci 1 . Scientific Computing & Imaging Institute, University of Utah 1 , Lawrence Livermore National Laboratory 2 , Tulane University 3 A C B Ranking based on quality measure value A B’ C’ Topological data analysis [1] S. Liu, P‐T. Bremer, J. J. Thiagarajan, B. Wang, B. Summa, and V. Pascucci. “Grassmannian Atlas: A General Framework for Exploring Linear Projections of High‐Dimensional Data.” Computer Graphics Forum, 2016 [2] C. Carlos, P. Lindstrom, and P‐T. Bremer. "Topological spines: A structure‐preserving visual representation of scalar fields." IEEE transactions on visualization and computer graphics (TVCG), 2011 Summarize the function of quality measure in the space of all 2D linear subspaces (Grassmannian) [1] Sample the Grassmannian Build neighborhood graph Construct topological spines Calculate quality measures on all the sampled locations Calculate quality measures on all the sampled locations .... Input data Projection directions Quality measure defined in the space of linear projections Computation Pipeline User Interface and Result Clumpy Measure Countries and Cites Countries and Cites Adjectives and Adverbs Family nouns Fruit nouns No clear separation Local Maxima Global Maxima One of the local maxima produces a more interesting projection than the global maxima Topological Spines Panel Dynamic Projection Panel Maximum Saddle Topological Spine: a terrain metaphor Compute Topological Spines[2] Acknowledgements: This work was performed in part under the auspices of the US DOE by LLNL under Contract DE‐AC52‐07NA27344., LLNL‐ CONF‐658933. This work is also supported in part by NSF IIS‐ 1513616, NSF 0904631, DE‐EE0004449, DE‐ NA0002375, DE‐ SC0007446, DE‐SC0010498, NSG IIS‐1045032, NSF EFT ACI‐ 0906379, DOE/NEUP 120341, DOE/Codesign P01180734. Bei Wang is partially supported by NSF IIS‐1513616.
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Grassmannian Atlas: A General Framework for Exploring Linear Projections of High-Dimensional Data
Shusen Liu1, Peer-Timo Bremer2, Jayaraman J. Thiagarajan2, Bei Wang1, Brian Summa3, and Valerio Pascucci1.Scientific Computing & Imaging Institute, University of Utah1, Lawrence Livermore National Laboratory2, Tulane University3
A
C B
Ranking based on quality measure value
A
B’
C’
Topological data analysis
[1] S. Liu, P‐T. Bremer, J. J. Thiagarajan, B. Wang, B. Summa, and V. Pascucci. “Grassmannian Atlas: A General Framework for Exploring Linear Projections of High‐Dimensional Data.” Computer Graphics Forum, 2016[2] C. Carlos, P. Lindstrom, and P‐T. Bremer. "Topological spines: A structure‐preserving visual representation of scalar fields." IEEE transactions on visualization and computer graphics (TVCG), 2011
Summarize the function of quality measure in the space of all 2D linear subspaces (Grassmannian) [1]
Sample the Grassmannian
Build neighborhood
graph
Construct topological spines
Calculate quality measures on all the sampled locations
Calculate quality measures on all the sampled locations
. . . .
Input dataProjection directions
Quality measure defined in the space of linear projections
Computation Pipeline
User Interface and Result
Clumpy Measure
Countries and Cites Countries and Cites
Adjectives and Adverbs
Family nouns
Fruit nouns
No clear separation
Local Maxima
Global Maxima
One of the local maxima produces a more interesting projection than the global maxima
Topological Spines Panel
Dynamic Projection Panel
Maximum
Saddle
Topological Spine:a terrain metaphor
Compute Topological Spines[2]
Acknowledgements: This work was performed in part under the auspices of the US DOE by LLNL under Contract DE‐AC52‐07NA27344., LLNL‐ CONF‐658933. This work is also supported in part by NSF IIS‐ 1513616, NSF 0904631, DE‐EE0004449, DE‐NA0002375, DE‐ SC0007446, DE‐SC0010498, NSG IIS‐1045032, NSF EFT ACI‐ 0906379, DOE/NEUP 120341, DOE/Codesign P01180734. Bei Wang is partially supported by NSF IIS‐1513616.
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