The Grassmannian Atlas: A General Framework for Exploring Linear Projections of High-Dimensional Data
Linear projections are one of the most common approaches to visualize high‐dimensional data. Since the space of possible projections is large, existing systems usually select a small set of interesting projections by ranking a large set of candidate projections based on a chosen quality measure. How...
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| Vydáno v: | Computer graphics forum Ročník 35; číslo 3; s. 1 - 10 |
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| Hlavní autoři: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford
Blackwell Publishing Ltd
01.06.2016
Wiley |
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | Linear projections are one of the most common approaches to visualize high‐dimensional data. Since the space of possible projections is large, existing systems usually select a small set of interesting projections by ranking a large set of candidate projections based on a chosen quality measure. However, while highly ranked projections can be informative, some lower ranked ones could offer important complementary information. Therefore, selection based on ranking may miss projections that are important to provide a global picture of the data. The proposed work fills this gap by presenting the Grassmannian Atlas, a framework that captures the global structures of quality measures in the space of all projections, which enables a systematic exploration of many complementary projections and provides new insights into the properties of existing quality measures. |
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| AbstractList | Linear projections are one of the most common approaches to visualize high-dimensional data. Since the space of possible projections is large, existing systems usually select a small set of interesting projections by ranking a large set of candidate projections based on a chosen quality measure. However, while highly ranked projections can be informative, some lower ranked ones could offer important complementary information. Therefore, selection based on ranking may miss projections that are important to provide a global picture of the data. The proposed work fills this gap by presenting the Grassmannian Atlas, a framework that captures the global structures of quality measures in the space of all projections, which enables a systematic exploration of many complementary projections and provides new insights into the properties of existing quality measures. Linear projections are one of the most common approaches to visualize high-dimensional data. Since the space of possible projections is large, existing systems usually select a small set of interesting projections by ranking a large set of candidate projections based on a chosen quality measure. However, while highly ranked projections can be informative, some lower ranked ones could offer important complementary information. Therefore, selection based on ranking may miss projections that are important to provide a global picture of the data. Here, the proposed work fills this gap by presenting the Grassmannian Atlas, a framework that captures the global structures of quality measures in the space of all projections, which enables a systematic exploration of many complementary projections and provides new insights into the properties of existing quality measures. |
| Author | Summa, B. Jayaraman, J. J. Wang, B. Liu, S. Bremer, P.-T Pascucci, V. |
| Author_xml | – sequence: 1 givenname: S. surname: Liu fullname: Liu, S. organization: Scientific Computing and Imaging Institute, University of Utah – sequence: 2 givenname: P.-T surname: Bremer fullname: Bremer, P.-T organization: Lawrence Livermore National Laboratory – sequence: 3 givenname: J. J. surname: Jayaraman fullname: Jayaraman, J. J. organization: Lawrence Livermore National Laboratory – sequence: 4 givenname: B. surname: Wang fullname: Wang, B. organization: Scientific Computing and Imaging Institute, University of Utah – sequence: 5 givenname: B. surname: Summa fullname: Summa, B. organization: Department of Computer Science, Tulane University – sequence: 6 givenname: V. surname: Pascucci fullname: Pascucci, V. organization: Scientific Computing and Imaging Institute, University of Utah |
| BackLink | https://www.osti.gov/servlets/purl/1417962$$D View this record in Osti.gov |
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| CitedBy_id | crossref_primary_10_1109_TVCG_2020_3011155 crossref_primary_10_1111_cgf_13416 crossref_primary_10_1007_s12650_017_0431_9 crossref_primary_10_1109_TVCG_2020_3030432 crossref_primary_10_1007_s12650_018_0531_1 crossref_primary_10_1109_TVCG_2017_2705189 crossref_primary_10_1109_TVCG_2019_2934812 crossref_primary_10_1016_j_jvlc_2018_08_003 |
| Cites_doi | 10.1109/VAST.2012.6400488 10.1057/palgrave.ivs.9500091 10.1111/cgf.12366 10.1198/106186005X77702 10.1137/0906011 10.1109/TVCG.2006.94 10.1057/palgrave.ivs.9500053 10.1145/312129.312199 10.1016/j.neucom.2012.11.046 10.1002/0470013192.bsa501 10.1109/MSP.2010.939739 10.1007/978-1-4757-2189-8 10.1109/TVCG.2011.229 10.1109/TVCG.2010.213 10.1109/TVCG.2011.244 10.2307/1390644 10.1109/LDAV.2014.7013202 10.1109/TVCG.2015.2467132 10.1016/S0167-9473(02)00286-4 10.1109/T-C.1974.224051 10.1198/106186008X318440 |
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| Copyright | 2016 The Author(s) Computer Graphics Forum © 2016 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2016 The Eurographics Association and John Wiley & Sons Ltd. |
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| References_xml | – reference: Horton P., Nakai K.: A probabilistic classification system for predicting the cellular localization sites of proteins. In Ismb (1996), vol. 4, pp. 109-115. 8 – reference: Gerber S., Bremer P.-T., Pascucci V., Whitaker R.: visual exploration of high dimensional scalar functions. IEEE Transactions on Visualization and Computer Graphics 16, 6 (2010), 1271-1280. 5 – reference: Lehmann D., Theisel H.: Optimal sets of projections of high-dimensional data. Visualization and Computer Graphics, IEEE Transactions on 22, 1 (Jan 2016), 609-618. 2 – reference: Wilkinson L., Anand A., Grossman R.: High-dimensional visual analytics: interactive exploration guided by pairwise views of point distributions. Visualization and Computer Graphics, IEEE Transactions on 12, 6 (2006), 1363-1372. 1, 2, 4 – reference: Cook D., Buja A., Cabrera J.: Projection pursuit indexes based on orthonormal function expansions. Journal of Computational and Graphical Statistics 2, 3 (1993), 225-250. 4 – reference: Mokbel B., Lueks W., Gisbrecht A., Hammer B.: Visualizing the quality of dimensionality reduction. Neurocomputing 112 (2013), 109-123. 2 – reference: Seo J., Shneiderman B.: A rank-by-feature framework for interactive exploration of multidimensional data. Information Visualization 4, 2 (2005), 96-113. 1 – reference: Van der Maaten L., Hinton G.: Visualizing data using t-sne. Journal of Machine Learning Research 9, 2579-2605 (2008), 85. 8 – reference: Guo D.: Coordinating computational and visual approaches for interactive feature selection and multivariate clustering. Information Visualization 2, 4 (2003), 232-246. 2 – reference: Borg I., Groenen P.J.: Modern multidimensional scaling: Theory and applications. Springer Science & Business Media, 2005. 2 – reference: Buja A., Swayne D.F., Littman M.L., Dean N., Hofmann H., Chen L.: Data visualization with multidimensional scaling. Journal of Computational and Graphical Statistics 17, 2 (2008), 444-472. 4, 7 – reference: Asimov D.: The grand tour: a tool for viewing multidimensional data. SIAM SISC 6, 1 (1985), 128-143. 1 – reference: Friedman J., Tukey J.: A projection pursuit algorithm for exploratory data analysis. IEEE TC C-23, 9 (1974), 881-890. 1, 2, 4 – reference: Elmqvist N., Dragicevic P., Fekete J.-D.: Rolling the dice: Multidimensional visual exploration using scatterplot matrix navigation. IEEE TVCG 14, 6 (2008), 1539-1148. 1 – reference: Wilkinson L., Anand A., Grossman R.L.: Graph-theoretic scagnostics. In INFOVIS (2005), vol. 5, p. 21. 1, 2, 4 – reference: Bertini E., Tatu A., Keim D.: Quality metrics in high-dimensional data visualization: An overview and systematization. Visualization and Computer Graphics, IEEE Transactions on 17, 12 (2011), 2203-2212. 2 – reference: Jennings A., McKeown J.J.: Matrix computation. Wiley New York, 1992. 3 – reference: Jolliffe I.: Principal component analysis. Wiley Online Library, 2005. 6 – reference: Correa C., Lindstrom P., Bremer P.-T.: Topological spines: A structure-preserving visual representation of scalar fields. IEEE Transactions on Visualization and Computer Graphics 17, 12 (2011), 1842-1851. 1, 5 – reference: Swayne D.F., Temple Lang D., Buja A., Cook D.: GGobi: evolving from XGobi into an extensible framework for interactive data visualization. Computational Statistics & Data Analysis 43 (2003), 423-444. 1, 5 – reference: Harris J.: Algebraic geometry: a first course, vol. 133. Springer Science & Business Media, 1992. 1, 3 – reference: Seo J., Shneiderman B.: Knowledge discovery in high-dimensional data: Case studies and a user survey for the rank-by-feature framework. IEEE TVCG 12, 3 (2006), 311-322. 2 – reference: Lee E.-K., Cook D., Klinke S., Lumley T.: Projection pursuit for exploratory supervised classification. Journal of Computational and Graphical Statistics 14, 4 (2005). 4 – reference: Liu S., Wang B., Bremer P.-T., Pascucci V.: Distortionguided structure-driven interactive exploration of high-dimensional data. 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| SubjectTerms | Analysis Categories and Subject Descriptors (according to ACM CCS) Computer Graphics Exploration I.3.3 [Computer Graphics]: Picture/Image Generation-Line and curve generation Line and curve generation MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE Picture/Image Generation Pictures Projection Ranking Studies Visualization |
| Title | The Grassmannian Atlas: A General Framework for Exploring Linear Projections of High-Dimensional Data |
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