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For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem.
Journal of Mathematics and Physics 6
Hitchcock, F. L.: The expression of a tensor or a polyadic as a sum of products · 1927
Earlier work this paper cites.
J. Res. Nat. Bur. Standards Sect. B 71B
Edmonds, J.: Systems of distinct representatives and linear algebra · 1967
Earlier work this paper cites.
Psychometrika 35
Carroll, J. D., Chang, J.-J.: Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition · 1970
Earlier work this paper cites.
UCLA Working Papers in Phonetics 16
Harshman, R. A.: Foundations of the PARAFAC procedure: Models and conditions for an “explanatory” multi-modal factor analysis · 1970
Earlier work this paper cites.
Nordisk Tidskr. Informationsbehandling (BIT) 12
Wedin, P.-Å.: Perturbation bounds in connection with singular value decomposition · 1972
Earlier work this paper cites.
SIAM J. Algebraic Discrete Methods 7
Coleman, T. F., Pothen, A.: The null space problem. I. Complexity · 1986
Earlier work this paper cites.
Bol. Soc. Brasil. Mat. (N.S.) 20
Lovász, L.: Singular spaces of matrices and their application in combinatorics · 1989
Earlier work this paper cites.
J. Algorithms 11
Håstad, J.: Tensor rank is NP-complete · 1990
Earlier work this paper cites.
Computer Science and Scientific Computing. Academic Press, Inc., Boston, MA (1990)
Stewart, G. W., Sun, J. G.: Matrix perturbation theory · 1990
Earlier work this paper cites.
In: N. White (ed.) Matroid Applications, vol. 40, pp. 73–90. Cambridge University Press (1992)
Oxley, J.: Infinite matroids · 1992
Earlier work this paper cites.
SIAM J. Matrix Anal. Appl. 14
Leurgans, S. E., Ross, R. T., Abel, R. B.: A decomposition for three-way arrays · 1993
Earlier work this paper cites.
Neural Comput. 7
Bell, A. J., Sejnowski, T. J.: An information-maximization approach to blind separation and blind deconvolution · 1995
Earlier work this paper cites.
Linear Algebra Appl. 215
Helmke, U., Shayman, M. A.: Critical points of matrix least squares distance functions · 1995
Earlier work this paper cites.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1997)
Demmel, J. W.: Applied numerical linear algebra · 1997
Earlier work this paper cites.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2000)
Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., van der Vorst, H. (eds.): Templates for the solution of algebraic eigenvalue problems. A practical guide · 2000
Earlier work this paper cites.
SIAM J. Matrix Anal. Appl. 21
De Lathauwer, L., De Moor, B., Vandewalle, J.: A multilinear singular value decomposition · 2000
Earlier work this paper cites.
In: In Proceedings of the 2001 American Control Conference, pp. 4734–4739 (2001)
Fazel, M., Hindi, H., Boyd, S. P.: A rank minimization heuristic with application to minimum order system approximation · 2001
Earlier work this paper cites.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2001)
Stewart, G. W.: Matrix algorithms. Vol. II · 2001
Earlier work this paper cites.
Ph.D. thesis, Electrical Engineering Deptartment Stanford University (2002)
Fazel, M.: Matrix rank minimization with applications · 2002
Earlier work this paper cites.
SIAM J. Matrix Anal. Appl. 26
De Lathauwer, L., De Moor, B., Vandewalle, J.: Computation of the canonical decomposition by means of a simultaneous generalized Schur decomposition · 2004
Earlier work this paper cites.
J. Comput. System Sci. 69
Gurvits, L.: Classical complexity and quantum entanglement · 2004
Earlier work this paper cites.
In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 489–498 (2005)
Harvey, N. J. A., Karger, D. R., Murota, K.: Deterministic network coding by matrix completion · 2005
Earlier work this paper cites.
IEEE Trans. Inform. Theory 52
Candes, E. J., Tao, T.: Near-optimal signal recovery from random projections: universal encoding strategies? · 2006
Earlier work this paper cites.
SIAM J. Matrix Anal. Appl. 28
De Lathauwer, L.: A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization · 2006
Cited alongside, same era.
In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 1103–1111 (2006)
Harvey, N. J. A., Karger, D. R., Yekhanin, S.: The complexity of matrix completion · 2006
Cited alongside, same era.
Tech. Rep. 07-49, University of Massachusetts, Amherst (2007)
Huang, G. B., Ramesh, M., Berg, T., Learned-Miller, E.: Labeled faces in the wild: A database for studying face recognition in unconstrained environments · 2007
Cited alongside, same era.
C. R. Math. Acad. Sci. Paris 346
Candès, E. J.: The restricted isometry property and its implications for compressed sensing · 2008
Cited alongside, same era.
SIAM J. Matrix Anal. Appl. 30
De Lathauwer, L.: Decompositions of a higher-order tensor in block terms. II. Definitions and uniqueness · 2008
Cited alongside, same era.
Math. Oper. Res. 33
Lewis, A. S., Malick, J.: Alternating projections on manifolds · 2008
J. ACM 60
Hillar, C. J., Lim, L.-H.: Most tensor problems are NP-hard · 2013
Later among the works it cites.
Linear Algebra Appl. 438
Li, N., Kindermann, S., Navasca, C.: Some convergence results on the regularized alternating least-squares method for tensor decomposition · 2013
Later among the works it cites.
Linear Algebra Appl. 438
Mohlenkamp, M. J.: Musings on multilinear fitting · 2013
Later among the works it cites.
In: Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, IJCAI ’13, pp. 3087–3090. AAAI Press (2013)
Spielman, D. A., Wang, H., Wright, J.: Exact recovery of sparsely-used dictionaries · 2013
Later among the works it cites.
SIAM J. Imaging Sci. 6
Xu, Y., Yin, W.: A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion · 2013
Later among the works it cites.
In: 18th International Conference on Digital Signal Processing (DSP), pp. 1–6. IEEE (2013)
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Cited alongside, same era.
Found. Comput. Math. 9
Candès, E. J., Recht, B.: Exact matrix completion via convex optimization · 2009
Cited alongside, same era.
SIAM Rev. 51
Kolda, T. G., Bader, B. W.: Tensor decompositions and applications · 2009
Cited alongside, same era.
Found. Comput. Math. 9
Lewis, A. S., Luke, D. R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections · 2009
Cited alongside, same era.
SIAM J. Matrix Anal. Appl. 31
Liu, Z., Vandenberghe, L.: Interior-point method for nuclear norm approximation with application to system identification · 2009
Cited alongside, same era.
SIAM J. Optim. 20
Cai, J.-F., Candès, E. J., Shen, Z.: A singular value thresholding algorithm for matrix completion · 2010
Cited alongside, same era.
IEEE Trans. Inform. Theory 56
Candès, E. J., Tao, T.: The power of convex relaxation: near-optimal matrix completion · 2010
Cited alongside, same era.
Zhao, X., Zhou, G., Dai, W., Xu, T., Wang, W.: Joint image separation and dictionary learning · 2013
Later among the works it cites.
In: Proceedings of the 46th Annual ACM Symposium on Theory of Computing, pp. 31–40 (2014)
Barak, B., Kelner, J. A., Steurer, D.: Rounding sum-of-squares relaxations · 2014
Later among the works it cites.
Inf. Inference 3
Demanet, L., Hand, P.: Scaling law for recovering the sparsest element in a subspace · 2014
Later among the works it cites.
SIAM J. Matrix Anal. Appl. 35
Domanov, I., De Lathauwer, L.: Canonical polyadic decomposition of third-order tensors: reduction to generalized eigenvalue decomposition · 2014
Later among the works it cites.
URL http://cvxr.com/cvx
Grant, M., Boyd, S.: CVX: Matlab Software for Disciplined Convex Programming, version 2.1, March 2014 · 2014
Later among the works it cites.
In: Proceedings of the 31st International Symposium on Theoretical Aspects of Computer Science, vol. 117543, pp. 397–408 (2014)
Ivanyos, G., Karpinski, M., Qiao, Y., Santha, M.: Generalized Wong sequences and their applications to Edmonds’ problems · 2014
Later among the works it cites.
Numer. Linear Algebra Appl. 21
Kindermann, S., Navasca, C.: News algorithms for tensor decomposition based on a reduced functional · 2014
Later among the works it cites.
In: Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, K. Weinberger (eds.) Advances in Neural Information Processing Systems 27, pp. 3401–3409. Curran Associates, Inc. (2014)
Qu, Q., Sun, J., Wright, J.: Finding a sparse vector in a subspace: Linear sparsity using alternating directions · 2014
Later among the works it cites.
Qu, Q., Sun, J., Wright, J.: Finding a sparse vector in a subspace: Linear sparsity using alternating directions · 2014
Later among the works it cites.
URL http://www.tensorlab.net/
Sorber, L., Van Barel, M., De Lathauwer, L.: Tensorlab v2.0, Available online, January 2014 · 2014
Later among the works it cites.
SIAM J. Matrix Anal. Appl. 35
Wang, L., Chu, M. T.: On the global convergence of the alternating least squares method for rank-one approximation to generic tensors · 2014
Later among the works it cites.
IEEE Signal Proc. Mag. 32
Cichocki, A., Mandic, D., De Lathauwer, L., Zhou, G., Zhao, Q., Caiafa, C., Phan, H. A.: Tensor decompositions for signal processing applications: From two-way to multiway component analysis · 2015
Closest in time.
Found. Comput. Math. 15
Drusvyatskiy, D., Ioffe, A. D., Lewis, A. S.: Transversality and alternating projections for nonconvex sets · 2015
Closest in time.
Sun, J., Qu, Q., Wright, J.: Complete dictionary recovery over the sphere I: Overview and the geometric picture · 2015
Closest in time.
Sun, J., Qu, Q., Wright, J.: Complete dictionary recovery over the sphere II: Recovery by Riemannian trust-region method · 2015
Closest in time.
Pac. J. Optim. 11
Uschmajew, A.: A new convergence proof for the higher-order power method and generalizations · 2015
Closest in time.
Found. Comput. Math. 16
Noll, D., Rondepierre, A.: On local convergence of the method of alternating projections · 2016
Closest in time.