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The Grassmannian Atlas: A General Framework for Exploring Linear Projections of High‐Dimensional Data
Author(s) -
Liu S.,
Bremer P.T,
Jayaraman J. J.,
Wang B.,
Summa B.,
Pascucci V.
Publication year - 2016
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12876
Subject(s) - atlas (anatomy) , computer science , ranking (information retrieval) , grassmannian , measure (data warehouse) , data mining , set (abstract data type) , linear space , information retrieval , artificial intelligence , mathematics , paleontology , geometry , combinatorics , biology , programming language
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.