Accession Number : AD1000735


Title :   Algorithms on Flag Manifolds for Knowledge Discovery in N-way Arrays


Descriptive Note : Technical Report


Corporate Author : Colorado State University Fort Collins


Personal Author(s) : Kirby,Michael


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/1000735.pdf


Report Date : 20 Nov 2015


Pagination or Media Count : 24


Abstract : We proposed an approach for hyperspectral imagery classification that exploits the geometric framework of the Grassmannmanifold i.e., a parameterization of k dimensional subspaces of n-dimnsional space. The algorithm is particularly well suited to applications where sets of pixels are to be classified. Multiple pixels from a data class characterize the variability of the class information using a subspace representation. We use two metrics defined on the Grassmannian, chordal and geodesic, and one pseudometric, to compute pairwise distances between the points--subspaces. Once a distance matrix is generated, we use the classical multidimensional scaling to find a configuration of points with preserved or approximated original distances, thus realizing an embedding of the Grassmannian into Euclidean space. A sparse support vector machine (SSVM) trained in the embedding space simultaneously classifies embedded subspaces and selects a subset of optimal dimensions of the embedding for subsequentmodel reduction and data visualization.


Descriptors :   hyperspectral imagery , manifolds(mathematics) , algorithms , arrays , geometric forms


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE