Conformal Mapping by Computationally Efficient Methods

9 years 5 months ago
Conformal Mapping by Computationally Efficient Methods
Dimensionality reduction is the process by which a set of data points in a higher dimensional space are mapped to a lower dimension while maintaining certain properties of these points relative to each other. One important property is the preservation of the three angles formed by a triangle consisting of three neighboring points in the high dimensional space. If this property is maintained for those same points in the lower dimensional embedding then the result is a conformal map. However, many of the commonly used nonlinear dimensionality reduction techniques, such as Locally Linear Embedding (LLE) or Laplacian Eigenmaps (LEM), do not produce conformal maps. Post-processing techniques formulated as instances of semi-definite programming (SDP) problems can be applied to the output of either LLE or LEM to produce a conformal map. However, the effectiveness of this approach is limited by the computational complexity of SDP solvers. This paper will propose an alternative postprocessing ...
Stefan Pintilie, Ali Ghodsi
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2010
Where AAAI
Authors Stefan Pintilie, Ali Ghodsi
Comments (0)