 Procrustes distance between covariance operators

ID: procrustes-distance-between-covariance-operators

C_{i} = L_{i} L_{i}^{*}

, the Procrustes distance is

d_{P} (C_{1}, C_{2}) = in f_{R} ∥ L_{1} - L_{2} R ∥_{HS}

, where

R

ranges over unitary operators on the factor space. Equivalently,

d_{P} (C_{1}, C_{2})^{2} = tr C_{1} + tr C_{2} - 2 tr ((C_{1}^{1/2} C_{2} C_{1}^{1/2})^{1/2}) .

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