Abstract:This paper concerns the minimax center of a collection of linear subspaces. When the subspaces are k-dimensional subspaces of R n , this can be cast as finding the center of a minimum enclosing ball on a Grassmann manifold, Gr(k, n). For subspaces of different dimension, the setting becomes a disjoint union of Grassmannians rather than a single manifold, and the problem is no longer well-defined. However, natural geometric maps exist between these manifolds with a well-defined notion of distance for the images… Show more
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