Geodesic Interpolation on the Grassmann Manifold: GLERP and Recursive GIDER Interpolants (opens in new tab)

This article develops a geodesic interpolation framework for data on the Grassmann manifold. The motivation is that many matrix-valued data sets represent subspaces rather than fixed bases: if the columns of two matrices differ only by a right orthogonal transformation, then they describe the same point on $Gr(r,m)$. Interpolation should therefore be invariant under this basis ambiguity. We first introduce $GLERP$, a Grassmann analogue of spheri...