Self-organizing mappings on the flag manifold with applications to hyper-spectral image data analysis

Abstract A flag is a nested sequence of vector spaces. The type the encodes dimensions spaces making up flag. manifold whose points parameterize all flags fixed in space. This paper provides mathematical framework necessary for implementing self-organizing mappings on manifolds. Flags arise implicitly many data analysis contexts including wavelet, Fourier, and singular value decompositions. proposed geometric this enables computation distances between flags, geodesics ability to move one prescribed distance direction another Using these operations as building blocks, we implement SOM algorithm manifold. basic applied problem parameterizing set type.