Sciweavers

PKDD
2010
Springer

Learning an Affine Transformation for Non-linear Dimensionality Reduction

13 years 9 months ago
Learning an Affine Transformation for Non-linear Dimensionality Reduction
The foremost nonlinear dimensionality reduction algorithms provide an embedding only for the given training data, with no straightforward extension for test points. This shortcoming makes them unsuitable for problems such as classification and regression. We propose a novel dimensionality reduction algorithm which learns a parametric mapping between the high-dimensional space and the embedded space. The key observation is that when the dimensionality of the data exceeds its quantity, it is always possible to find a linear transformation that preserves a given subset of distances, while changing the distances of another subset. Our method first maps the points into a high-dimensional feature space, and then explicitly searches for an affine transformation that preserves local distances while pulling non-neighbor points as far apart as possible. This search is formulated as an instance of semi-definite programming, and the resulting transformation can be used to map outof-sample points i...
Pooyan Khajehpour Tadavani, Ali Ghodsi
Added 14 Feb 2011
Updated 14 Feb 2011
Type Journal
Year 2010
Where PKDD
Authors Pooyan Khajehpour Tadavani, Ali Ghodsi
Comments (0)