• Publications
  • Influence
Singular values and eigenvalues of tensors: a variational approach
  • Lek-Heng Lim
  • Mathematics, Computer Science
  • 1st IEEE International Workshop on Computational…
  • 13 December 2005
TLDR
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
  • 697
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Most Tensor Problems Are NP-Hard
TLDR
We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Expand
  • 723
  • 72
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Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
TLDR
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
  • 759
  • 69
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Symmetric Tensors and Symmetric Tensor Rank
TLDR
A symmetric tensor is a higher order generalization of a symmetric matrix. Expand
  • 443
  • 38
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Statistical ranking and combinatorial Hodge theory
TLDR
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
  • 243
  • 38
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Multilinear PageRank
TLDR
In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Expand
  • 77
  • 17
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Schubert Varieties and Distances between Subspaces of Different Dimensions
  • Ke Ye, Lek-Heng Lim
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 3 July 2014
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 differentExpand
  • 68
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Nuclear norm of higher-order tensors
TLDR
We establish several mathematical and computational properties of the nuclear norm for higher-order tensors. Expand
  • 102
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Rank aggregation via nuclear norm minimization
TLDR
We extend an algorithm for matrix completion to handle skew-symmetric data and use that to extract ranks for each item. Expand
  • 154
  • 11
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Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
TLDR
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
  • 97
  • 9
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