Integration of Stochastic Models by Minimizing α-Divergence
Neural Computation
Parameter estimation for α-gmm based on maximum likelihood criterion
Neural Computation
Sided and symmetrized Bregman centroids
IEEE Transactions on Information Theory
Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank
SIAM Journal on Matrix Analysis and Applications
Anisotropy Preserving DTI Processing
International Journal of Computer Vision
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It is shown that any two-variable-mean of positive matrices (studied by Kubo and Ando) can be extended to more variables. The $n$-variable-mean $M_n(A_1,A_2,\ldots,A_n)$ is defined by a symmetrization procedure when the $n$-tuple $(A_1, A_2, \ldots, A_n)$ is ordered, is monotone in each variable, and satisfies the transformer inequality. This approach is motivated by the paper of Ando, Li, and Mathias on geometric means [Linear Algebra Appl., 385 (2004), pp. 305-334]. Special attention is paid to the logarithmic mean. It is conjectured that for matrix means the symmetrization procedure converges for all triplets.