{"type":"ScholarlyArticle","title":"Online Robust Low-Rank Tensor Learning","authors":[{"name":"Ping Li","slug":"ping-li","given":"Ping","family":"Li","affiliation":"School of Computer Science and Technology , Hangzhou Dianzi University; Department of Electrical and Computer Engineering , National University of Singapore"},{"name":"Jiashi Feng","slug":"jiashi-feng","given":"Jiashi","family":"Feng","affiliation":"Department of Electrical and Computer Engineering , National University of Singapore"},{"name":"Xiaojie Jin","slug":"xiaojie-jin","given":"Xiaojie","family":"Jin","affiliation":"Department of Electrical and Computer Engineering , National University of Singapore"},{"name":"Luming Zhang","slug":"luming-zhang","given":"Luming","family":"Zhang","affiliation":"Department of Computer and Information , Hefei University of Technology; Artificial Intelligence Institute"},{"name":"Xianghua Xu","slug":"xianghua-xu","given":"Xianghua","family":"Xu","affiliation":"School of Computer Science and Technology , Hangzhou Dianzi University"},{"name":"Shuicheng Yan","slug":"shuicheng-yan","given":"Shuicheng","family":"Yan","affiliation":"Qihoo 360; Department of Electrical and Computer Engineering , National University of Singapore"}],"abstract":"The rapid increase of multidimensional data (a.k.a. tensor) like videos brings new challenges for low-rank data modeling approaches such as dynamic data size, complex high-order relations, and multiplicity of low-rank structures. Resolving these challenges require a new tensor analysis method that can perform tensor data analysis online, which however is still absent. In this paper, we propose an Online Robust Low-rank Tensor Modeling (ORLTM) approach to address these challenges. ORLTM dynamically explores the high-order correlations across all tensor modes for low-rank structure modeling. To analyze mixture data from multiple subspaces, ORLTM introduces a new dictionary learning component. ORLTM processes data streamingly and thus requires quite low memory cost that is independent of data size. This makes ORLTM quite suitable for processing large-scale tensor data. Empirical studies have validated the effectiveness of the proposed method on both synthetic data and one practical task, i.e., video background subtraction. In addition, we provide theoretical analysis regarding computational complexity and memory cost, demonstrating the efficiency of ORLTM rigorously.","doi":"10.24963/ijcai.2017/303","url":"https://ijcai.org/proceedings/2017/303","pdf":"https://ijcai.org/proceedings/2017/0303.pdf","markdown":"https://ijcai.org/proceedings/2017/303.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/303","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning A-R","track":"Main track","number":303,"pages":{"first":2180,"last":2186},"keywords":["Machine Learning: Unsupervised Learning","Machine Learning: Online Learning","Machine Learning: Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Brutzer et al., 2011] Sebastian Brutzer, Benjamin Höferlin, and Gunther Heidemann. Evaluation of background subtraction techniques for video surveillance. In CVPR, pages 1937-1944, 2011.","title":"Evaluation of background subtraction techniques for video surveillance","authors":"Sebastian Brutzer, Benjamin Höferlin, Gunther Heidemann","year":"2011","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Candès et al., 2011] Emmanuel J. Candès, Xiaodong Li, Yi Ma, and John Wright. Robust principal component analysis? Journal of the ACM, 58(3):No.11, 2011.","title":"Robust principal component analysis","authors":"Emmanuel J Candès, Xiaodong Li, Yi Ma, John Wright","year":"2011","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Fazel et al., 2001] Maryam Fazel, Haitham Hindi, and Stephen P. Boyd. A rank minimization heuristic with application to minimum order system approximation. In Proceedings of the American Control Conference, volume 6, pages 4734-4739, 2001.","title":"A rank minimization heuristic with application to minimum order system approximation","authors":"Maryam Fazel, Haitham Hindi, Stephen P Boyd","year":"2001","venue":"Proceedings of the American Control Conference","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Feng et al., 2013] Jiashi Feng, Huan Xu, and Shuicheng Yan. Online robust pca via stochastic optimization. In NIPS, pages 404-412, 2013.","title":"Online robust pca via stochastic optimization","authors":"Feng","year":"2013","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Goldfarb and Qin, 2014] Donald Goldfarb and Zhiwei Qin. Robust low-rank tensor recovery: models and algorithms. SIAM Journal on Matrix Analysis and Applications, 35(1):225-253, 2014.","title":"Robust low-rank tensor recovery: models and algorithms","authors":"Donald Goldfarb, Zhiwei Qin","year":"2014","venue":"SIAM Journal on Matrix Analysis and Applications","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Hale et al., 2008] Elaine T Hale, Wotao Yin, and Yin Zhang. Fixed-point continuation for ℓ1-minimization: Methodology and convergence. SIAM Journal on Optimization, 19(3):1107-1130, 2008.","title":"Fixed-point continuation for ℓ1-minimization: Methodology and convergence","authors":"Elaine T Hale, Wotao Yin, Yin Zhang","year":"2008","venue":"SIAM Journal on Optimization","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Hillar and Lim, 2013] Christopher J. Hillar and Lek-Heng Lim. Most tensor problems are np-hard. Journal of the ACM, 60(6):No.45, 2013.","title":"Most tensor problems are np-hard","authors":"Christopher J Hillar, Lek-Heng Lim","year":"2013","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Kilmer and Martin, 2011] Misha E Kilmer and Carla D Martin. Factorization strategies for third-order tensors. Linear Algebra and its Applications, 435(3):641-658, 2011.","title":"Factorization strategies for third-order tensors","authors":"Misha E Kilmer, Carla D Martin","year":"2011","venue":"Linear Algebra and its Applications","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Kolda and Bader, 2009] Tamara G. Kolda and Brett W. Bader. Tensor decompositions and applications. SIAM Review, 51(3):455-500, 2009.","title":"Tensor decompositions and applications","authors":"Tamara G Kolda, Brett W Bader","year":"2009","venue":"SIAM Review","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Li et al., 2004] Liyuan Li, Weimin Huang, Irene Yu-Hua Gu, and Qi Tian. Statistical modeling of complex backgrounds for foreground object detection. IEEE Transactions on Image Processing, 13(11):1459-1472, 2004.","title":"Statistical modeling of complex backgrounds for foreground object detection","authors":"Liyuan Li, Weimin Huang, Irene Yu-Hua, Qi Gu, Tian","year":"2004","venue":"IEEE Transactions on Image Processing","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Liu and Yan, 2011] Guangcan Liu and Shuicheng Yan. Latent low-rank representation for subspace segmentation and feature extraction. In ICCV, pages 1615-1622, 2011.","title":"Latent low-rank representation for subspace segmentation and feature extraction","authors":"Yan ; Liu, Guangcan Liu, Shuicheng Yan","year":"2011","venue":"ICCV","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Liu et al., 2013] Guangcan Liu, Zhouchen Lin, Shuicheng Yan, Ju Sun, Yong Yu, and Yi Ma. Robust recovery of subspace structures by low-rank representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(1):171-184, 2013.","title":"Robust recovery of subspace structures by low-rank representation","authors":"Guangcan Liu, Zhouchen Lin, Shuicheng Yan, Ju Sun, Yong Yu, Yi Ma","year":"2013","venue":"IEEE Transactions on Pattern Analysis and Machine Intelligence","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Liu et al., 2017] Guangcan Liu, Qingshan Liu, and Ping Li. Blessing of dimensionality: recovering mixture data via dictionary pursuit. IEEE Transactions on Pattern Analysis and Machine Intelligence, 39(1):47-60, 2017.","title":"Blessing of dimensionality: recovering mixture data via dictionary pursuit","authors":"Liu","year":"2017","venue":"IEEE Transactions on Pattern Analysis and Machine Intelligence","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Lu et al., 2016] Canyi Lu, Jiashi Feng, Yudong Chen, Wei Liu, Zhouchen Lin, and Shuicheng Yan. Tensor robust principal component analysis: Exact recovery of corrupted low-rank tensors via convex optimization. In CVPR, pages 5249-5257, 2016.","title":"Tensor robust principal component analysis: Exact recovery of corrupted low-rank tensors via convex optimization","authors":"Lu","year":"2016","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Mensch et al., 2016] Arthur Mensch, Julien Mairal, Bertrand Thirion, and Gaël Varoquaux. Dictionary learning for massive matrix factorization. In ICML, volume 48, pages 1737-1746, 2016.","title":"Dictionary learning for massive matrix factorization","authors":"Arthur Mensch, Julien Mairal, Bertrand Thirion, Gaël Varoquaux","year":"2016","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Recht et al., 2010] Benjamin Recht, Maryam Fazel, and Pablo A. Parrilo. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM review, 52:471- 501, 2010.","title":"Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization","authors":"Benjamin Recht, Maryam Fazel, Pablo A Parrilo","year":"2010","venue":"SIAM review","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Richtárik and Takáč, 2014] Peter Richtárik and Martin Takáč. Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function. Mathematical Programming, 144(1-2):1-38, 2014.","title":"Peter Richtárik and Martin Takáč. Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function","authors":"Takáč Richtárik","year":"2014","venue":"Mathematical Programming","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Shen et al., 2016] Jie Shen, Ping Li, and Huan Xu. Online low- rank subspace clustering by basis dictionary pursuit. In ICML, volume 48, pages 622-631, 2016.","title":"Online lowrank subspace clustering by basis dictionary pursuit","authors":"Jie Shen, Ping Li, Huan Xu","year":"2016","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Sobral et al., 2015] Andrews Sobral, Sajid Javed, Soon Ki Jung, Thierry Bouwmans, and El-hadi Zahzah. Online stochastic tensor decomposition for background subtraction in multispectral video sequences. In ICCV Workshop, pages 106-113, 2015.","title":"Online stochastic tensor decomposition for background subtraction in multispectral video sequences","authors":"Andrews Sobral, Sajid Javed, Soon Ki Jung, Thierry Bouwmans, El-Hadi Zahzah","year":"2015","venue":"ICCV Workshop","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Srebro et al., 2004] Nathan Srebro, Jason D. M. Rennie, and Tommi S. Jaakkola. Maximum-margin matrix factorization. In NIPS, pages 1329-1336, 2004.","title":"Maximum-margin matrix factorization","authors":"Nathan Srebro, Jason D M Rennie, Tommi S Jaakkola","year":"2004","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Sun et al., 2008] Jimeng Sun, Dacheng Tao, Spiros Papadimitriou, Philip S Yu, and Christos Faloutsos. Incremental tensor analysis: Theory and applications. ACM Transactions on Knowledge Discovery from Data (TKDD), 2(3):11, 2008.","title":"Incremental tensor analysis: Theory and applications","authors":"Sun","year":"2008","venue":"ACM Transactions on Knowledge Discovery from Data (TKDD)","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Wright, 2015] Stephen J Wright. Coordinate descent algorithms. Mathematical Programming, 151(1):3-34, 2015.","title":"Coordinate descent algorithms","authors":"Wright Stephen","year":"2015","venue":"Mathematical Programming","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Yin et al., 2015] Ming Yin, Junbin Gao, Zhouchen Lin, Qinfeng Shi, and Yi Guo. Dual graph regularized latent low-rank representation for subspace clustering. IEEE Transactions on Image Processing, 24(12):4918-4933, 2015.","title":"Dual graph regularized latent low-rank representation for subspace clustering","authors":"Ming Yin, Junbin Gao, Zhouchen Lin, Qinfeng Shi, Yi Guo","year":"2015","venue":"IEEE Transactions on Image Processing","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Yu et al., 2015] Rose Yu, Dehua Cheng, and Yan Liu. Accelerated online low-rank tensor learning for multivariate spatio-temporal streams. In ICML, pages 238-247, 2015.","title":"Accelerated online low-rank tensor learning for multivariate spatio-temporal streams","authors":"Rose Yu, Dehua Cheng, Yan Liu","year":"2015","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Zhan et al., 2016] Jinchun Zhan, Brian Lois, Han Guo, and Namrata Vaswani. Online (and offline) robust pca: novel algorithms and performance guarantees. In AISTATS, pages 1488-1496, 2016.","title":"Online (and offline) robust pca: novel algorithms and performance guarantees","authors":"Zhan","year":"2016","venue":"AISTATS","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Zhang et al., 2013] Xiaoqin Zhang, Di Wang, Zhengyuan Zhou, and Yi Ma. Simultaneous rectification and alignment via robust recovery of low-rank tensors. In NIPS, pages 1637-1645, 2013.","title":"Simultaneous rectification and alignment via robust recovery of low-rank tensors","authors":"Xiaoqin Zhang, Di Wang, Zhengyuan Zhou, Yi Ma","year":"2013","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Zhou and Tao, 2012] Tianyi Zhou and Dacheng Tao. Bilateral random projections. In Proceedings of the IEEE International Symposium on Information Theory, pages 1286-1290, 2012.","title":"Bilateral random projections","authors":"Tao ; ] Tianyi Zhou, Dacheng Zhou, Tao","year":"2012","venue":"Proceedings of the IEEE International Symposium on Information Theory","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Zhou et al., 2016] Shuo Zhou, Nguyen Xuan Vinh, James Bailey, Yunzhe Jia, and Ian Davidson. Accelerating online cp decompositions for higher order tensors. In SIGKDD, pages 1375-1384, 2016.","title":"Accelerating online cp decompositions for higher order tensors","authors":"Shuo Zhou, Xuan Nguyen, James Vinh, Yunzhe Bailey, Ian Jia, Davidson","year":"2016","venue":"SIGKDD","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}