Low-rank tensor completion: a Riemannian manifold preconditioning approach Supplementary material
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چکیده
A Proof and derivation of manifold-related ingredients The concrete computations of the optimization-related ingredients presented in the paper are discussed below. The total space is M := St(r1, n1) × St(r2, n2) × St(r3, n3) × Rr1×r2×r3 . Each element x ∈ M has the matrix representation (U1,U2,U3,G). Invariance of Tucker decomposition under the transformation (U1,U2,U3,G) 7→ (U1O1,U2O2,U3O3,G×1O1×2O T 2×3O T 3 ) for all Od ∈ O(rd), the set of orthogonal matrices of size of rd×rd results in equivalence classes of the form [x] = [(U1,U2,U3,G)] := {(U1O1,U2O2,U3O3,G×1O1×2O T 2×3O T 3 ) : Od ∈ O(rd)}.
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تاریخ انتشار 2016