We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalue.Expand

We show that, unlike matrices, tensors of order 3 or higher can fail to have best rank-$r$ approximations, regardless of the choice of norm (or even Bregman divergence).Expand

We propose a technique that we call HodgeRank for ranking data that may be incomplete and imbalanced, characteristics common in modern datasets coming from e-commerce and internet applications.Expand

We resolve a basic problem on subspace distances that often arises in applications: How can the usual Grassmann distance between equidimensional subspaces be extended to subspaces of different… Expand

We proposed BFGS and limited memory BFGS updates in local and global coordinates for objective functions defined on Grassmannians or a product of these.Expand