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Riemannian Lp center of mass: existence, uniqueness, and convexity
Let be a complete Riemannian manifold and a probability measure on . Assume . We derive a new bound (in terms of , the injectivity radius of and an upper bound on the sectional curvatures of ) on theExpand
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Sensitivity Analysis for the Problem of Matrix Joint Diagonalization
  • B. Afsari
  • Computer Science, Mathematics
  • SIAM J. Matrix Anal. Appl.
  • 1 September 2008
TLDR
We investigate the sensitivity of the problem of nonorthogonal (matrix) joint diagonalization (NOJD), which is closely related to the issue of uniqueness in tensor decompositions. Expand
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Simple LU and QR Based Non-orthogonal Matrix Joint Diagonalization
  • B. Afsari
  • Mathematics, Computer Science
  • ICA
  • 5 March 2006
TLDR
A class of simple Jacobi-type algorithms for non-orthogonal matrix joint diagonalization based on the LU or QR factorization is introduced. Expand
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Intrinsic consensus on SO(3) with almost-global convergence
TLDR
In this paper we propose a discrete time protocol to align the states of a network of agents evolving in the space of rotations SO(3). Expand
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Riemannian Consensus for Manifolds With Bounded Curvature
TLDR
We propose Riemannian consensus, a natural extension of existing averaging consensus algorithms to the case of Riemmannian manifolds. Expand
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Group action induced distances for averaging and clustering Linear Dynamical Systems with applications to the analysis of dynamic scenes
TLDR
We introduce a framework for defining a distance on the (non-Euclidean) space of Linear Dynamical Systems (LDSs). Expand
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On the Convergence of Gradient Descent for Finding the Riemannian Center of Mass
TLDR
We study the convergence of constant step-size gradient descent algorithms for solving the problem of finding the global Riemannian center of mass of a set of data points on a Riemanian manifold. Expand
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Some Gradient Based Joint Diagonalization Methods for ICA
TLDR
We present a set of gradient based orthogonal and non-orthogonal matrix joint diagonalization algorithms. Expand
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Average consensus on Riemannian manifolds with bounded curvature
TLDR
In this paper, we propose distributed algorithms for averaging measurements lying in a Riemannian manifold. Expand
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MEANS AND AVERAGING ON RIEMANNIAN MANIFOLDS
Processing of manifold-valued data has received considerable attention in recent years. Standard data processing methods are not adequate for such data. Among many related data processing tasksExpand
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