Title
A framework for exploring high-dimensional geometry
Abstract
To extract useful information from high-dimensional geometric or structural data, we must find low-dimensional projections that are informative and interesting to look at. The conventional, manual-interaction methods used for this purpose are ineffective when the dimensionality of the data is high, or when the geometric models are complex. Standard methods for determining useful low-dimensional views are either limited to discrete data, or to geometric information embedded in at most three dimensions. Since geometric data embedded in dimensions above three have distinct characteristics and visualization requirements, finding directly applicable techniques is a challenge. We present a comprehensive framework for exploring high-dimensional geometric data motivated by projection pursuit techniques. Our approach augments manual exploration by generating sets of salient views that optimize a customizable family of geometry-sensitive measures. These views serve to reveal novel facets of complex manifolds and equations.
Year
DOI
Venue
2007
10.1007/978-3-540-76858-6_77
ISVC (1)
Keywords
Field
DocType
low-dimensional projection,geometric model,discrete data,complex manifold,geometric data,high-dimensional geometry,geometric information,high-dimensional geometric data,useful information,structural data,useful low-dimensional view,three dimensions,projection pursuit,structured data
Random projection,Computer vision,Geometric data analysis,Projection pursuit,Computer science,Visualization,Curse of dimensionality,Artificial intelligence,Manifold,Machine learning,Salient
Conference
Volume
ISSN
ISBN
4841
0302-9743
3-540-76857-2
Citations 
PageRank 
References 
0
0.34
22
Authors
2
Name
Order
Citations
PageRank
Sidharth Thakur1424.28
A. J. Hanson2928.43