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Geometrical homotopy for data visualization

Abstract:

This work presents an approach allowing for an interactive visualization of dimensionality reduction outcomes, which is based on an extended view of conventional homotopy. The pairwise functional followed from a simple homotopic function can be incorporated within a geometrical framework in order to yield a biparametric approach able to combine several kernel matrices. Therefore, the users can establish the mixture of kernels in an intuitive fashion by only varying two parameters. Our approach is tested by using kernel alternatives for conventional methods of spectral dimensionality reduction such as multidimensional scalling, locally linear embedding and laplacian eigenmaps. The proposed mixture represents every single dimensionality reduction approach as well as helps users to find a suitable representation of embedded data.