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A survey and comparison of contemporary algorithms for computing the matrix geometric mean
In this paper we present a survey of various algorithms for computing matrix geometric means and derive new second-order optimization algorithms to compute the Karcher mean. These new algorithms areExpand
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  • Open Access
The Kähler Mean of Block-Toeplitz Matrices with Toeplitz Structured Blocks
tl;dr
We derive the generalized barycenter, or generalized Kahler mean, and a greedy approximation. Expand
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  • Open Access
Riemannian Optimization for Averaging Positive Definite Matrices
Large data collections often need to be represented by an average value which upholds certain properties, such as reducing the noise level of repeated measurements or representing the centralExpand
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The Derivative of the Matrix Geometric Mean with an Application to the Nonnegative Decomposition of Tensor Grids
We provide an expression for the derivative of the weighted matrix geometric mean, with respect to both the matrix arguments and the weights, that can be easily translated to an algorithm for itsExpand
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Protein fold recognition using geometric kernel data fusion
tl;dr
We design several techniques to combine kernel matrices by taking more involved, geometry inspired means of these matrices instead of convex linear combinations. Expand
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  • Open Access
Geometric means of structured matrices
The geometric mean of positive definite matrices is usually identified with the Karcher mean, which possesses all properties—generalized from the scalar case—a geometric mean is expected to satisfy.Expand
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  • Open Access
Geometric Mean Algorithms Based on Harmonic and Arithmetic Iterations
tl;dr
The geometric mean of a series of positive numbers a 1,…,a n is defined as the nth root of its product: \(\sqrt[n]{a_1\cdots a_n}\). Expand
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Nonnegative Tensor Grid Decomposition
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