L.-H. Lim and K. Ye, "Minimal equivariant embeddings of the Grassmannian and flag manifold," preprint, (2024).
L.-H. Lim and K. Ye, "Simple matrix models for the flag, Grassmann, and Stiefel manifolds," preprint, (2024).
Z. Lai, L.-H. Lim, and Y. Liu, "Attention is a smoothed cubic spline," preprint, (2024).
Z. Lai, L.-H. Lim, and K. Ye, "Grassmannian optimization is NP-hard," preprint, (2024).
Z. Lai, L.-H. Lim, and K. Ye, "Simple matrix expressions for the curvatures of Grassmannian," preprint, (2024).
L.-H. Lim and K. Ye, "Degree of the Grassmannian as an affine variety," preprint, (2024).
L.-H. Lim and B. Nelson, "What is … an equivariant neural network?," Notices of the American Mathematical Society, 70 (2023), no. 4, pp. 619–625.
Y. Liu, S. Jiao, and L.-H. Lim, "LU decomposition and Toeplitz decomposition of a neural network," Applied and Computational Harmonic Analysis, 68 (2024), Art. 101601.
R. Wang, J. Lee, and L.-H. Lim, "Summing divergent matrix series," preprint, (2024).
Z. Dai and L.-H. Lim, "Numerical stability and tensor nuclear norm," Numerische Mathematik, 155 (2023), no. 3–4, pp. 345–376.
Z. Dai, L.-H. Lim, and K. Ye, "Complex matrix inversion via real matrix inversions," Numerische Mathematik, (2024), to appear.
Z. Li and L.-H. Lim, "Generalized matrix nearness problems," SIAM Journal on Matrix Analysis and Applications, 44 (2023), no. 4, pp. 1709–1730.
Y. Cai and L.-H. Lim, "Distances between probability distributions of different dimensions," IEEE Transactions on Information Theory, 68 (2022), no. 6, pp. 4020–4031.
Z. Lai, L.-H. Lim, and K. Ye, "Simpler Grassmannian optimization," preprint, (2020).
Z. Lai and L.-H. Lim, "Recht–Ré noncommutative arithmetic-geometric mean conjecture is false," Proceedings of the 37th International Conference on Machine Learning (ICML), PMLR 119, (2020), pp. 5608–5617.
M. Zhao, Z. Lai, and L.-H. Lim, "Stochastic Steffensen method," Computational Optimization and Applications, 89 (2024), pp. 1–32.
S. Friedland and L.-H. Lim, "Symmetric Grothendieck inequality," preprint, (2020).
L.-H. Lim, "Tensors in computations," Acta Numerica, 30 (2021), pp. 555–764.
L.-H. Lim, M. Michałek, and Y. Qi, "Best k-layer neural network approximations," Constructive Approximation, 55 (2022), no. 1, pp. 583–604.
G. Naitzat, A. Zhitnikov, and L.-H. Lim, "Topology of deep neural networks," Journal of Machine Learning Research, 21 (2020), no. 184, pp. 1–40.
K. Ye, K. Wong, and L.-H. Lim, "Optimization on flag manifolds," Mathematical Programming, 194 (2022), no. 1–2, pp. 621–660.
T. Gao, L.-H. Lim, and K. Ye, "Semi-Riemannian manifold optimization," preprint, (2018).
L. Ding and L.-H. Lim, "Higher-order cone programming," preprint, (2018).
L.-H. Lim, R. Sepulchre, and K. Ye, "Geometric distance between positive definite matrices of different dimensions," IEEE Transactions on Information Theory, 65 (2019), no. 9, pp. 5401–5405.
J. Rodriguez, J.-H. Du, Y. You, and L.-H. Lim, "Fiber product homotopy method for multiparameter eigenvalue problems," Numerische Mathematik, 148 (2021), no. 4, pp. 853–888.
L. Zhang, G. Naitzat, and L.-H. Lim, "Tropical geometry of deep neural networks," Proceedings of the 35th International Conference on Machine Learning (ICML), PMLR 80 (2018), pp. 5824–5832.
P. Comon, L.-H. Lim, Y. Qi, and K. Ye, "Topology of tensor ranks," Advances in Mathematics, 367 (2020), no. 107128, 46 pp.
H. Derksen, S. Friedland, L.-H. Lim, and L. Wang, "Theoretical and computational aspects of entanglement," preprint, (2017).
S. Friedland, L.-H. Lim, and J. Zhang, "An elementary and unified proof of Grothendieck's inequality," L’Enseignement Mathématique, 64 (2018), no. 3/4, pp. 327–351.
L.-H. Lim, K. S.-W. Wong, and K. Ye, "The Grassmannian of affine subspaces," Foundations of Computational Mathematics, 21 (2021), pp. 537–574.
Y. Qi, M. Michałek, and L.-H. Lim, "Complex best r-term approximations almost always exist in finite dimensions," Applied and Computational Harmonic Analysis, 49 (2020), no. 1, pp. 180–207.
K. Ye and L.-H. Lim, "Tensor network ranks," preprint, (2018).
M. Ankele, L.-H. Lim, S. Groeschel, and T. Schultz, "Versatile, robust, and efficient tractography with constrained higher-order tensor fODFs," International Journal of Computer Assisted Radiology and Surgery, 12 (2017), no. 8, pp. 1257–1270.
M. Ankele, L.-H. Lim, S. Groeschel, and T. Schultz, "Fast and accurate multi-tissue deconvolution using SHORE and H-PSD tensors," pp. 502–510, S. Ourselin et al. (Eds), Medical Image Computing and Computer Assisted Intervention (MICCAI), III, Springer International, Cham, 2016.
K. Ye and L.-H. Lim, "Cohomology of cyro-electron microscopy," SIAM Journal on Applied Algebra and Geometry, 1 (2017), no. 1, pp. 507–535.
Y. You, J. Rodriguez, and L.-H. Lim, "Accurate solutions of polynomial eigenvalue problems," preprint, (2017).
S. Friedland, L.-H. Lim, and J. Zhang, "Grothendieck constant is norm of Strassen matrix multiplication tensor," Numerische Mathematik, 143 (2019), no. 4, pp. 905–922.
A. Benson, D. Gleich, and L.-H. Lim, "The spacey random walk: a stochastic process for higher-order data," SIAM Review, 59 (2017), no. 2, pp. 321–345.
L.-H. Lim and J. Weare, "Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra," SIAM Review, 59 (2017), no. 3, pp. 547–587. [Supplementary Materials]
Y. Qi, P. Comon, and L.-H. Lim, "Semialgebraic geometry of nonnegative tensor rank," SIAM Journal on Matrix Analysis and Applications, 37 (2016), no. 4, pp. 1556–1580.
K. Ye and L.-H. Lim, "Algorithms for structured matrix-vector product of optimal bilinear complexity," Proceedings of the IEEE Information Theory Workshop (ITW), 16 (2016), pp. 310–314.
K. Ye and L.-H. Lim, "Fast structured matrix computations: tensor rank and Cohn–Umans method," Foundations of Computational Mathematics, 18 (2018), no. 1, pp. 45–95.
S. Friedland and L.-H. Lim, "The computational complexity of duality," SIAM Journal on Optimization, 26 (2016), no. 4, pp. 2378–2393.
D. Gleich, L.-H. Lim, and Y. Yu, "Multilinear PageRank," SIAM Journal on Matrix Analysis and Applications, 36 (2015), no. 4, pp. 1507–1541.
L.-H. Lim, "Hodge Laplacians on graphs," SIAM Review, 62 (2020), no. 3, pp. 685–715.
L.-H. Lim, K. S.-W. Wong, and K. Ye, "Numerical algorithms on the affine Grassmannian," SIAM Journal on Matrix Analysis and Applications, 40 (2019), no. 2, pp. 371–393.
Y. Qi, P. Comon, and L.-H. Lim, "Uniqueness of nonnegative tensor approximations," IEEE Transactions on Information Theory, 62 (2016), no. 4, pp. 2170–2183.
S. Friedland and L.-H. Lim, "Nuclear norm of higher-order tensors," Mathematics of Computation, 87 (2018), no. 311, pp. 1255–1281.
L.-H. Lim, "Self-concordance is NP-hard," Journal of Global Optimization, 68 (2017), no. 2, pp. 357–366.
A. Rajkumar, S. Ghoshal, L.-H. Lim, and S. Agarwal, "Ranking from stochastic pairwise preferences: recovering Condorcet winners and tournament solution sets at the top," Proceedings of the 32nd International Conference on Machine Learning (ICML), JMLR: W&CP 37 (2015), pp. 665–673.
B. St. Thomas, K. You, L. Lin, L.-H. Lim, and S. Mukherjee, "Learning subspaces of different dimensions," Journal of Computational and Graphical Statistics, 31 (2022), no. 2, pp. 337–350.
K. Ye and L.-H. Lim, "Schubert varieties and distances between subspaces of different dimensions," SIAM Journal on Matrix Analysis and Applications, 37 (2016), no. 3, pp. 1176–1197.
C.J. Hillar and L.-H. Lim, "Most tensor problems are NP-hard," Journal of the ACM, 60 (2013), no. 6, Art. 45, 39 pp.
L.-H. Lim, "Tensors and hypermatrices," Chapter 15, 30 pp., in L. Hogben (Ed.), Handbook of Linear Algebra, 2nd Ed., CRC Press, Boca Raton, FL, 2013.
L.-H. Lim and P. Comon, "Blind multilinear identification," IEEE Transactions on Information Theory, 60 (2014), no. 2, pp. 1260–1280.
K. Ye and L.-H. Lim, "Every matrix is a product of Toeplitz matrices," Foundations of Computational Mathematics, 16 (2016), no. 3, pp. 577–598.
D. Gleich and L.-H. Lim, "Rank aggregation via nuclear norm minimization," Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '11), 17 (2011), pp. 60–68.
M. Gu, L.-H. Lim, and C.J. Wu, "PARNES: A rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals," Numerical Algorithms, 64 (2013), no. 2, pp. 321–347.
X. Jiang, L.-H. Lim, Y. Yao, and Y. Ye, "Statistical ranking and combinatorial Hodge theory," Mathematical Programming, Series B: Special Issue on Optimization and Machine Learning, 127 (2011), no. 1, pp. 203–244. [AMS Feature Column: "Who's number 1? Hodge theory will tell us"]
T. Schultz, A. Fuster, A. Ghosh, L. Florack, R. Deriche, and L.-H. Lim, "Higher-order tensors in diffusion imaging," pp. 129–161, C.-F. Westin et al. (Eds.), Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data, Springer-Verlag, Berlin Heidelberg, 2014.
L.-H. Lim and P. Comon, "Multiarray signal processing: tensor decomposition meets compressed sensing," Comptes Rendus de l'Académie des sciences, Series IIB – Mechanics, 338 (2010), no. 6, pp. 311–320.
B. Savas and L.-H. Lim, "Quasi-Newton methods on Grassmannians and multilinear approximations of tensors," SIAM Journal on Scientific Computing, 32 (2010), no. 6, pp. 3352–3393.
L.-H. Lim and P. Comon, "Nonnegative approximations of nonnegative tensors," Journal of Chemometrics, 23 (2009), no. 7–8, pp. 432–441.
M. Mørup, L. Hansen, S. Arnfred, L.-H. Lim, and K. Madsen, "Shift invariant multilinear decomposition of neuroimaging data," NeuroImage, 42 (2008), no. 4, pp. 1439–1450.
J. Morton and L.-H. Lim, "Principal cumulant component analysis," (extended abstract), preprint, (2009).
P. Comon, G. Golub, L.-H. Lim, and B. Mourrain, "Symmetric tensors and symmetric tensor rank," SIAM Journal on Matrix Analysis and Applications, 30 (2008), no. 3, pp. 1254–1279.
V. De Silva and L.-H. Lim, "Tensor rank and the ill-posedness of the best low-rank approximation problem," SIAM Journal on Matrix Analysis and Applications, 30 (2008), no. 3, pp. 1084–1127.
P. Comon, G. Golub, L.-H. Lim, and B. Mourrain, "Genericity and rank deficiency of high order symmetric tensors," Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '06), 31 (2006), no. 3, pp. 125–128.
L.-H. Lim, "Singular values and eigenvalues of tensors: a variational approach," Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP '05), 1 (2005), pp. 129–132.
L.-H. Lim, J. Packer, and K. Taylor, "Direct integral decomposition of the wavelet representation," Proceedings of the American Mathematical Society, 129 (2001), no. 10, pp. 3057–3067.
L.-H. Lim, "Security of the Cao–Li public key cryptosystem," Electronics Letters, 34 (1998), no. 2, pp. 170–172.
J. Foo, L.-H. Lim, and K. S.-W. Wong, "Discovering latent macroeconomic effects on peer-to-peer lending," Journal of FinTech, (2023), to appear.
L.-H. Lim, "Feature interviews: "The field is as exciting as ever" — interview of Shmuel Friedland," IMAGE: Bulletin of the International Linear Algebra Society, 59 (2017), Fall, pp. 3–8.
M. Mahoney, L.-H. Lim, and G. Carlsson, "MMDS 2008: Algorithmic and statistical challenges in modern large-scale data analysis are the focus," Statistical Computing and Graphics, 20 (2009), no. 1, pp. 12–18.
M. Mahoney, L.-H. Lim, and G. Carlsson, "Algorithmic, statistical challenges in data analysis focus of MMDS 2008," AMSTAT News, 384 (2009), pp. 16–19.
M. Mahoney, L.-H. Lim, and G. Carlsson, "MMDS 2008: Algorithmic and statistical challenges in modern large-scale data analysis, Parts I & II," SIAM News, 42 (2009), no. 1, pp. 8, & no. 2, pp. 8–9. [Chinese translation: "MMDS 2008: 现代大规模数据集分析中的算法和统计方面的挑战," 数学译林, 31 (2012), no. 1, pp. 83–88.]
M. Mahoney, L.-H. Lim, and G. Carlsson, "Algorithmic and statistical challenges in modern large-scale data analysis are the focus of MMDS 2008," KDD Explorations, 10 (2008), no. 2, pp. 57–60.
M. Mahoney, L.-H. Lim, and G. Carlsson, "Algorithms for modern massive data sets," IMS Bulletin, 37 (2008), no. 10, pp. 10–11.
G. Golub, M. Mahoney, P. Drineas, and L.-H. Lim, "Bridging the gap between numerical linear algebra, theoretical computer science, and data applications," SIAM News, 39 (2006), no. 8, pp. 1 & 16.
God grant that no one else has done
The work I want to do,
Then give me the wit to write it up
In decent English too.
Applied Optics, 8 (1969), no. 2, p. 273.
Contact: Comments on these pages are welcome. Please write to lekheng@uchicago.edu.