786 citations · 2.4k across the 106 of their papers we have counts for
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Rank-preserving geometric means of positive semi-definite matrices
Silvere Bonnabel, Anne Collard, Rodolphe Sepulchre
The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalize…
Regression on fixed-rank positive semidefinite matrices: a Riemannian approach
Gilles Meyer, Silvere Bonnabel, Rodolphe Sepulchre
The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space…
Consensus in non-commutative spaces
Rodolphe Sepulchre, Alain Sarlette, Pierre Rouchon
Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. Tsitsiklis Lyapunov function is shown to be the Hilbert distance to consensus in log…