Geometric distance and mean for positive semi-definite matrices of fixed rank

摘要: This paper introduces a new metric and mean on the set of positive semidefinite matrices fixed-rank. The proposed is derived from well-chosen Riemannian quotient geometry that generalizes reductive cone associated natural metric. resulting space has strong geometrical properties: it geodesically complete, invariant with respect to all transformations preserve angles (orthogonal transformations, scalings, pseudoinversion). A meaningful approximation distance proposed, can be efficiently numerically computed via simple algorithm based SVD. induced preserves rank, possesses most desirable characteristics geometric mean, easy compute.