A block matrix embedding sends whole GMMs into the SPD manifold, and the induced affine-invariant distance is proposed as a lower-bound GMM similarity measure.
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Distance Measure Based on an Embedding of the Manifold of K-Component Gaussian Mixture Models into the Manifold of Symmetric Positive Definite Matrices
A block matrix embedding sends whole GMMs into the SPD manifold, and the induced affine-invariant distance is proposed as a lower-bound GMM similarity measure.