Matrix Completion with Graph Information: A Provable Nonconvex Optimization Approach

References

• Banerjee S, Sanghavi S, Shakkottai S (2016) Online collaborative filtering on graphs. Oper. Res. 64(3):756–769.Link, Google Scholar
• Bertsimas D, Li ML (2023) Interpretable matrix completion: A discrete optimization approach. INFORMS J. Comput. 35(5):952–965.Link, Google Scholar
• Candes E, Recht B (2012) Exact matrix completion via convex optimization. Comm. ACM 55(6):111–119.Crossref, Google Scholar
• Chen Y (2015) Incoherence-optimal matrix completion. IEEE Trans. Inform. Theory 61(5):2909–2923.Crossref, Google Scholar
• Chen Y, Wainwright MJ (2015) Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guarantees. Preprint, submitted September 10, https://arxiv.org/abs/1509.03025.Google Scholar
• Chen X, Wang L, Qu J, Guan NN, Li JQ (2018) Predicting miRNA–Disease association based on inductive matrix completion. Bioinformatics 34(24):4256–4265.Crossref, Google Scholar
• Chi Y, Lu YM, Chen Y (2019) Nonconvex optimization meets low-rank matrix factorization: An overview. IEEE Trans. Signal Processing 67(20):5239–5269.Crossref, Google Scholar
• Dong S, Absil PA, Gallivan K (2021) Riemannian gradient descent methods for graph-regularized matrix completion. Linear Algebra Appl. 623:193–235.Crossref, Google Scholar
• Escobedo AR (2024) Exact matrix factorization updates for nonlinear programming. INFORMS J. Comput. 36(1):245–265.Link, Google Scholar
• Farias VF, Li AA (2019) Learning preferences with side information. Management Sci. 65(7):3131–3149.Link, Google Scholar
• Hamedani RM, Ali I, Hong J, Kim SW (2021) TrustRec: An effective approach to exploit implicit trust and distrust relationships along with explicitones for accurate recommendations. Comput. Sci. Inform. Systems 18(1):93–114.Crossref, Google Scholar
• Hardt M, Wootters M (2014) Fast matrix completion without the condition number. Proc. 27th Conf. Learn. Theory (PMLR, New York), 638–678.Google Scholar
• Harper FM, Konstan JA (2015) The MovieLens datasets: History and context. ACM Trans. Interactive Intelligent Systems 5(4):1–19.Crossref, Google Scholar
• Jain P, Netrapalli P, Sanghavi S (2013) Low-rank matrix completion using alternating minimization. STOC: Proc. 45th Annual ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 665–674.Google Scholar
• Jia X, Wang H, Peng J, Feng X, Meng D (2024) Preconditioning matters: Fast global convergence of non-convex matrix factorization via scaled gradient descent. Oh A, Naumann T, Globerson A, Saenko K, Hardt M, Levine S, eds. NIPS’23: Proc. 37th Internat. Conf. Neural Inform. Processing Systems (Curran Associates Inc., Red Hook, NY), 76202–76213.Google Scholar
• Kalofolias V, Bresson X, Bronstein M (2014) Matrix completion on graphs. Preprint, submitted August 7, https://arxiv.org/abs/1408.1717.Google Scholar
• Lei M, Labbe A, Wu Y, Sun L (2022) Bayesian kernelized matrix factorization for spatiotemporal traffic data imputation and kriging. IEEE Trans. Intelligent Transportation Systems 23(10):18962–18974.Crossref, Google Scholar
• Muter I, Aytekin T (2017) Incorporating aggregate diversity in recommender systems using scalable optimization approaches. INFORMS J. Comput. 29(3):405–421.Link, Google Scholar
• Perraudin N, Paratte J, Shuman D, Martin L, Kalofolias V, Vandergheynst P, Hammond DK (2014) GSPBOX: A toolbox for signal processing on graphs. Preprint, submitted August 24, https://arxiv.org/abs/1408.5781.Google Scholar
• Rao N, Yu HF, Ravikumar PK, Dhillon IS (2015) Collaborative filtering with graph information: Consistency and scalable methods. Cortes C, Lee DD, Sugiyama M, Garnett R, eds. NIPS’15: Proc. 29th Internat. Conf. Neural Inform. Processing Systems, vol. 2 (MIT Press, Cambridge, MA), 2107–2115.Google Scholar
• Sun R, Luo ZQ (2016) Guaranteed matrix completion via non-convex factorization. IEEE Trans. Inform. Theory 62(11):6535–6579.Crossref, Google Scholar
• Tong T, Ma C, Chi Y (2021) Accelerating ill-conditioned low-rank matrix estimation via scaled gradient descent. J. Machine Learn. Res. 22(150):1–63.Google Scholar
• Tong T, Ma C, Prater-Bennette A, Tripp E, Chi Y (2022) Scaling and scalability: Provable nonconvex low-rank tensor estimation from incomplete measurements. J. Machine Learn. Res. 23(163):1–77.Google Scholar
• Yao Q, Kwok JT (2018) Accelerated and inexact soft-impute for large-scale matrix and tensor completion. IEEE Trans. Knowledge Data Engrg. 31(9):1665–1679.Crossref, Google Scholar
• Zhao T, Wang Z, Liu H (2015) A nonconvex optimization framework for low rank matrix estimation. Cortes C, Lee DD, Sugiyama M, Garnett R, eds. NIPS’15: Proc. 29th Internat. Conf. Neural Inform. Processing Systems, vol. 2 (MIT Press, Cambridge, MA), 559–567.Google Scholar
• Zhao Z, Zhang L, He X, Ng W (2014) Expert finding for question answering via graph regularized matrix completion. IEEE Trans. Knowledge Data Engrg. 27(4):993–1004.Crossref, Google Scholar
• Zheng Q, Lafferty J (2016) Convergence analysis for rectangular matrix completion using Burer-Monteiro factorization and gradient descent. Preprint, submitted May 23, https://arxiv.org/abs/1605.07051.Google Scholar
• Zhou T, Shan H, Banerjee A, Sapiro G (2012) Kernelized probabilistic matrix factorization: Exploiting graphs and side information. Proc. 2012 SIAM Internat. Conf. Data Mining (SIAM, Philadelphia), 403–414.Google Scholar
• Zilber P, Nadler B (2022) Inductive matrix completion: No bad local minima and a fast algorithm. Proc. Internat. Conf. Machine Learn. (ICML), vol. 162 (PMLR, New York), 27671–27692.Google Scholar