Computing the Karcher mean of symmetric positive definite matrices

By Dario Bini, Bruno Iannazzo. 2013

160 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/866d05dad2eac08db3f3efd0375fe082f0db5916

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In Applied Mathematics

In Computational Theory and Mathematics

In Statistics and Probability

Citations in the corpus

Weighted deterministic walks for the least squares mean on Hadamard spaces (2014, methodology): “In the case when the NPC space of interest is in fact a non-positively curved Riemannian manifold, then one can use gradient or Newton like optimization methods [6, 14, 16, 17, 19] for approximating the mean.”
Log-Hilbert-Schmidt metric between positive definite operators on Hilbert spaces (2014, background): “This approach has recently been employed by [10] to compute Bregman divergences between RKHS covariance operators.”
Transfer Learning: A Riemannian Geometry Framework With Applications to Brain–Computer Interfaces (2018, background): “Other faster and computational lighter approaches look for some suitable approximation of the center of mass, see for instance [6], [13], [14].”
First-order Methods for Geodesically Convex Optimization (2016, methodology): “The computation and properties of various notions of geometric means have been studied by many (e.g. Moakher (2005); Bini and Iannazzo (2013); Sra and Hosseini (2015)).”
Riemannian Approaches in Brain-Computer Interfaces: A Review (2017, unknown): “Such an averaging method has attracted a lot of attention from the optimization community and for example, for SPD matrices, several algorithms have been proposed [34]–[36].”
Generalized locally Toeplitz sequences : Theory and applications (2017, methodology): “Besides the mathematical interest, the Karcher mean has been used in several applications (see [67, Section 7] and the references in [15]), and suitable algorithms for its computation have been designed [15, 68].”