1089-49-215
Brent R Davis* (bdavis1@rams.colostate.edu), Brent R. Davis, Department of Mathematics,
1874 Campus Delivery, Fort Collins, CO 80523-187, and Daniel Bates, Chris Peterson,
Michael Kirby and Justin Marks. A nonconvex method to find a subspace mean on a disjoint
union of grassmann manifolds. Preliminary report.
Let {V1 , . . . , Vk } be a set of subspaces of a finite-dimensional vector space V. Consider the problem
min
l∈V
k
X
cos(θ(Vi , l))
i=1
where l is a 1-dimensional subspace of V.
θ(Vi , l) = {vi · w | vi ∈ Vi , w ∈ l, kvi k = kwk= 1} is called the first principal angle between Vi and l. The problem is of
interest in data analysis and inherently non-convex. It is equivilent to finding a computable subspace mean on a disjoin
union of grasmannians each of varying dimensions.
A method has been developed to solve this optimization problem. Utilizing tools from algebraic geometry and linear
algebra, a numerical algorithm will be proposed to find the global solution to this problem. (Received February 15, 2013)
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