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...
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...
— 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...
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...