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» Principal Graphs and Manifolds
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ICASSP
2011
IEEE
12 years 9 months ago
Sampling on locally defined principal manifolds
We start with a locally defined principal curve definition for a given probability density function (pdf) and define a pairwise manifold score based on local derivatives of the...
Erhan Bas, Deniz Erdogmus
CORR
2008
Springer
77views Education» more  CORR 2008»
13 years 5 months ago
Principal Graphs and Manifolds
In many physical statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpo...
Alexander N. Gorban, Andrei Yu. Zinovyev
IJCNN
2007
IEEE
13 years 12 months ago
Branching Principal Components: Elastic Graphs, Topological Grammars and Metro Maps
— To approximate complex data, we propose new type of low-dimensional “principal object”: principal cubic complex. This complex is a generalization of linear and nonlinear pr...
Alexander N. Gorban, Neil R. Sumner, Andrei Yu. Zi...
ECCV
2010
Springer
13 years 10 months ago
Manifold Valued Statistics, Exact Principal Geodesic Analysis and the Effect of Linear Approximations
Manifolds are widely used to model non-linearity arising in a range of computer vision applications. This paper treats statistics on manifolds and the loss of accuracy occurring wh...