{"type":"ScholarlyArticle","title":"Robust Multi-view Learning via Half-quadratic Minimization","authors":[{"name":"Yonghua Zhu","slug":"yonghua-zhu","given":"Yonghua","family":"Zhu","affiliation":"Guangxi Key Lab of Multi-source Information Mining & Security , Guangxi Normal University , Guilin , 541004 , China; Guangxi University , Nanning , 530004 , China"},{"name":"Xiaofeng Zhu","slug":"xiaofeng-zhu","given":"Xiaofeng","family":"Zhu","affiliation":"Guangxi Key Lab of Multi-source Information Mining & Security , Guangxi Normal University , Guilin , 541004 , China"},{"name":"Wei Zheng","slug":"wei-zheng","given":"Wei","family":"Zheng","affiliation":"Guangxi Key Lab of Multi-source Information Mining & Security , Guangxi Normal University , Guilin , 541004 , China"}],"abstract":"Although multi-view clustering is capable to usemore information than single view clustering, existing multi-view clustering methods still have issues to be addressed, such as initialization sensitivity, the specification of the number of clusters,and the influence of outliers. In this paper, we propose a robust multi-view clustering method to address these issues. Specifically, we first propose amulti-view based sum-of-square error estimation tomake the initialization easy and simple as well asuse a sum-of-norm regularization to automaticallylearn the number of clusters according to data distribution. We further employ robust estimators constructed by the half-quadratic theory to avoid theinfluence of outliers for conducting robust estimations of both sum-of-square error and the numberof clusters. Experimental results on both syntheticand real datasets demonstrate that our method outperforms the state-of-the-art methods.","doi":"10.24963/ijcai.2018/455","url":"https://ijcai.org/proceedings/2018/455","pdf":"https://ijcai.org/proceedings/2018/0455.pdf","markdown":"https://ijcai.org/proceedings/2018/455.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/455","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Machine Learning","track":"Main track","number":455,"pages":{"first":3278,"last":3284},"keywords":["Machine Learning: Clustering","Machine Learning: Multi-instance;Multi-label;Multi-view learning","Machine Learning: Unsupervised Learning"],"videos":[],"references":[{"position":1,"raw":"[Black and Rangarajan, 1996] Michael J. Black and Anand Rangarajan. On the unification of line processes, outlier rejection, and robust statistics with applications in early vi- sion. International Journal of Computer Vision, 19(1):57- 91, 1996.","title":"On the unification of line processes, outlier rejection, and robust statistics with applications in early vision","authors":"J Michael, Anand Black, Rangarajan","year":"1996","venue":"International Journal of Computer Vision","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Brito et al., 1997] MR Brito, EL Chavez, AJ Quiroz, and JE Yukich. Connectivity of the mutual k-nearest-neighbor graph in clustering and outlier detection. Statistics & Prob- ability Letters, 35(1):33-42, 1997.","title":"Connectivity of the mutual k-nearest-neighbor graph in clustering and outlier detection","authors":"Brito","year":"1997","venue":"Statistics & Probability Letters","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Cao et al., 2015] Xiaochun Cao, Changqing Zhang, Huazhu Fu, Si Liu, and Hua Zhang. Diversity-induced multi-view subspace clustering. In CVPR, pages 586-594, 2015.","title":"Diversity-induced multi-view subspace clustering","authors":"Xiaochun Cao, Changqing Zhang, Huazhu Fu, Si Liu, Hua Zhang","year":"2015","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Charbonnier et al., 1997] Pierre Charbonnier, Laure Blanc- Féraud, Gilles Aubert, and Michel Barlaud. Determinis- tic edge-preserving regularization in computed imaging. IEEE Trans. Image Processing, 6(2):298-311, 1997.","title":"Deterministic edge-preserving regularization in computed imaging","authors":"Pierre Charbonnier, Laure Blanc-Féraud, Gilles Aubert, Michel Barlaud","year":"1997","venue":"IEEE Trans. Image Processing","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Chi and Lange, 2015] Eric C Chi and Kenneth Lange. Split- ting methods for convex clustering. Journal of Computa- tional and Graphical Statistics, 24(4):994-1013, 2015.","title":"Splitting methods for convex clustering","authors":"C Eric, Kenneth Chi, Lange","year":"2015","venue":"Journal of Computational and Graphical Statistics","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Ding et al., 2005] Chris Ding, Xiaofeng He, and Horst D Simon. On the equivalence of nonnegative matrix factor- ization and spectral clustering. In SDMs, pages 606-610, 2005.","title":"On the equivalence of nonnegative matrix factorization and spectral clustering","authors":"Chris Ding, Xiaofeng He, Horst D Simon","year":"2005","venue":"SDMs","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Elhamifar and Vidal, 2013] Ehsan Elhamifar and Rene Vi- dal. Sparse subspace clustering: Algorithm, theory, and applications. IEEE transactions on pattern analysis and machine intelligence, 35(11):2765-2781, 2013.","title":"Sparse subspace clustering: Algorithm, theory, and applications","authors":"Ehsan Elhamifar, Rene Vidal","year":"2013","venue":"IEEE transactions on pattern analysis and machine intelligence","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Fang and Wang, 2012] Yixin Fang and Junhui Wang. Se- lection of the number of clusters via the bootstrap method. Computational Statistics & Data Analysis, 56(3):468-477, 2012.","title":"Selection of the number of clusters via the bootstrap method","authors":"Wang ; Fang, Yixin Fang, Junhui Wang","year":"2012","venue":"Computational Statistics & Data Analysis","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Frey and Dueck, 2007] Brendan J Frey and Delbert Dueck. Clustering by passing messages between data points. sci- ence, 315(5814):972-976, 2007.","title":"Clustering by passing messages between data points","authors":"J Brendan, Delbert Frey, Dueck","year":"2007","venue":"science","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[He et al., 2014] Ran He, Wei-Shi Zheng, Tieniu Tan, and Zhenan Sun. Half-quadratic-based iterative minimization for robust sparse representation. IEEE transactions on pattern analysis and machine intelligence, 36(2):261-275, 2014.","title":"Half-quadratic-based iterative minimization for robust sparse representation","authors":"Ran He, Wei-Shi Zheng, Tieniu Tan, Zhenan Sun","year":"2014","venue":"IEEE transactions on pattern analysis and machine intelligence","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Hocking et al., 2011] Toby Dylan Hocking, Armand Joulin, Francis Bach, and Jean-Philippe Vert. Clusterpath an al- gorithm for clustering using convex fusion penalties. In ICML, page 1, 2011.","title":"Clusterpath an algorithm for clustering using convex fusion penalties","authors":"Hocking","year":"2011","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Hu et al., 2017] Rongyao Hu, Xiaofeng Zhu, Debo Cheng, Wei He, Yan Yan, Jingkuan Song, and Shichao Zhang. Graph self-representation method for unsupervised feature selection. Neurocomputing, 220:130-137, 2017.","title":"Graph self-representation method for unsupervised feature selection","authors":"Rongyao Hu, Xiaofeng Zhu, Debo Cheng, Wei He, Yan Yan, Jingkuan Song, Shichao Zhang","year":"2017","venue":"Neurocomputing","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Jiang et al., 2015] Yizhang Jiang, Fu-Lai Chung, Shitong Wang, Zhaohong Deng, Jun Wang, and Pengjiang Qian. Collaborative fuzzy clustering from multiple weighted views. IEEE Trans. Cybernetics, 45(4):688-701, 2015.","title":"Collaborative fuzzy clustering from multiple weighted views","authors":"Jiang","year":"2015","venue":"IEEE Trans. Cybernetics","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Kriegel et al., 2009] Hans-Peter Kriegel, Peer Kröger, and Arthur Zimek. Clustering high-dimensional data: A sur- vey on subspace clustering, pattern-based clustering, and correlation clustering. TKDD, 3(1):1:1-1:58, 2009.","title":"Clustering high-dimensional data: A survey on subspace clustering, pattern-based clustering, and correlation clustering","authors":"Kriegel","year":"2009","venue":"TKDD","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Li et al., 2017] Jundong Li, Kewei Cheng, Suhang Wang, Fred Morstatter, Robert P. Trevino, Jiliang Tang, and Huan Liu. Feature selection: A data perspective. ACM Comput. Surv., 50(6):94:1-94:45, 2017.","title":"Feature selection: A data perspective","authors":"Jundong Li, Kewei Cheng, Suhang Wang, Fred Morstatter, Robert P Trevino, Jiliang Tang, Huan Liu","year":"2017","venue":"ACM Comput. Surv","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Nie et al., 2017] Feiping Nie, Guohao Cai, and Xuelong Li. Multi-view clustering and semi-supervised classification with adaptive neighbours. In AAAI, pages 2408-2414, 2017.","title":"Multi-view clustering and semi-supervised classification with adaptive neighbours","authors":"Nie","year":"2017","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Nikolova and Chan, 2007] Mila Nikolova and Raymond H. Chan. The equivalence of half-quadratic minimization and the gradient linearization iteration. IEEE Trans. Image Processing, 16(6):1623-1627, 2007.","title":"The equivalence of half-quadratic minimization and the gradient linearization iteration","authors":"Chan ; Nikolova, Mila Nikolova, Raymond H Chan","year":"2007","venue":"IEEE Trans. Image Processing","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Nikolova and Ng, 2005] Mila Nikolova and Michael K. Ng. Analysis of half-quadratic minimization methods for sig- nal and image recovery. SIAM J. Scientific Computing, 27(3):937-966, 2005.","title":"Analysis of half-quadratic minimization methods for signal and image recovery","authors":"Nikolova, ; Ng, Mila Nikolova, Michael K Ng","year":"2005","venue":"SIAM J. Scientific Computing","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Rodriguez and Laio, 2014] Alex Rodriguez and Alessandro Laio. Clustering by fast search and find of density peaks. Science, 344(6191):1492-1496, 2014.","title":"Clustering by fast search and find of density peaks","authors":"Alex Rodriguez, Alessandro Laio","year":"2014","venue":"Science","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Shah and Koltun, 2017] Sohil Atul Shah and Vladlen Koltun. Robust continuous clustering. Proceedings of the National Academy of Sciences of the United States of America, 114(37):9814, 2017.","title":"Robust continuous clustering","authors":"Koltun ; Shah, Vladlen Shah, Koltun","year":"2017","venue":"Proceedings of the National Academy of Sciences of the United States of America","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Sun, 2013] Shiliang Sun. A survey of multi-view ma- chine learning. Neural Computing and Applications, 23(7- 8):2031-2038, 2013.","title":"A survey of multi-view machine learning","authors":"Shiliang Sun","year":"2013","venue":"Neural Computing and Applications","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Xu et al., 2015] Chang Xu, Dacheng Tao, and Chao Xu. Multi-view self-paced learning for clustering. In IJCAI, pages 3974-3980, 2015.","title":"Multi-view self-paced learning for clustering","authors":"Chang Xu, Dacheng Tao, Chao Xu","year":"2015","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/558"},{"position":23,"raw":"[Xu et al., 2016] Jinglin Xu, Junwei Han, Kai Xiong, and Feiping Nie. Robust and sparse fuzzy k-means clustering. In IJCAI, pages 2224-2230, 2016.","title":"Robust and sparse fuzzy k-means clustering","authors":"Jinglin Xu, Junwei Han, Kai Xiong, Feiping Nie","year":"2016","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/317"},{"position":24,"raw":"[Yin et al., 2015] Qiyue Yin, Shu Wu, Ran He, and Liang Wang. Multi-view clustering via pairwise sparse subspace representation. Neurocomputing, 156:12-21, 2015.","title":"Multi-view clustering via pairwise sparse subspace representation","authors":"Qiyue Yin, Shu Wu, Ran He, Liang Wang","year":"2015","venue":"Neurocomputing","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Zhang et al., 2006] Shichao Zhang, Yongsong Qin, Xi- aofeng Zhu, Jilian Zhang, and Chengqi Zhang. Optimized parameters for missing data imputation. In PRICAI, pages 1010-1016, 2006.","title":"Optimized parameters for missing data imputation","authors":"Zhang","year":"2006","venue":"PRICAI","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Zhang et al., 2017] Shichao Zhang, Xuelong Li, Ming Zong, Xiaofeng Zhu, and Ruili Wang. Efficient knn classification with different numbers of nearest neighbors. IEEE transactions on neural networks and learning sys- tems,DOI: 10.1109/TNNLS.2017.2673241, 2017.","title":"Efficient knn classification with different numbers of nearest neighbors","authors":"Zhang","year":"2017","venue":"IEEE transactions on neural networks and learning systems","doi":"10.1109/tnnls.2017.2673241","url":null,"internal_url":null},{"position":27,"raw":"[Zhu and Martinez, 2006] Manli Zhu and Aleix M Martinez. Subclass discriminant analysis. IEEE Transactions on Pat- tern Analysis and Machine Intelligence, 28(8):1274-1286, 2006.","title":"Subclass discriminant analysis","authors":"Manli Zhu, Aleix M Martinez","year":"2006","venue":"IEEE Transactions on Pattern Analysis and Machine Intelligence","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Zhu et al., 2014a] Xiaofeng Zhu, Heung-Il Suk, and Ding- gang Shen. Multi-modality canonical feature selection for alzheimer's disease diagnosis. In MICCAI, pages 162- 169, 2014.","title":"Multi-modality canonical feature selection for alzheimer's disease diagnosis","authors":"Zhu","year":"2014","venue":"MICCAI","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Zhu et al., 2014b] Yingying Zhu, Dong Huang, Fernando De La Torre, and Simon Lucey. Complex non-rigid mo- tion 3d reconstruction by union of subspaces. In CVPR, pages 1542-1549, 2014.","title":"Complex non-rigid motion 3d reconstruction by union of subspaces","authors":"Zhu","year":"2014","venue":"CVPR","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Zhu et al., 2016] Yingying Zhu, Xiaofeng Zhu, Minjeong Kim, Dinggang Shen, and Guorong Wu. Early diagnosis of alzheimer's disease by joint feature selection and classi- fication on temporally structured support vector machine. In MICCAI, pages 264-272, 2016.","title":"Early diagnosis of alzheimer's disease by joint feature selection and classification on temporally structured support vector machine","authors":"Yingying Zhu, Xiaofeng Zhu, Minjeong Kim, Dinggang Shen, Guorong Wu","year":"2016","venue":"MICCAI","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Zhu et al., 2017a] Pengfei Zhu, Wencheng Zhu, Qinghua Hu, Changqing Zhang, and Wangmeng Zuo. Subspace clustering guided unsupervised feature selection. Pattern Recognition, 66:364-374, 2017.","title":"Subspace clustering guided unsupervised feature selection","authors":"Zhu","year":"2017","venue":"Pattern Recognition","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Zhu et al., 2017b] Yingying Zhu, Xiaofeng Zhu, Minjeong Kim, Daniel Kaufer, and Guorong Wu. A novel dynamic hyper-graph inference framework for computer assisted diagnosis of neuro-diseases. In IPMI, pages 158-169. Springer, 2017.","title":"A novel dynamic hyper-graph inference framework for computer assisted diagnosis of neuro-diseases","authors":"Zhu","year":"2017","venue":"IPMI","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Zhu et al., 2018] Pengfei Zhu, Qian Xu, Qinghua Hu, Changqing Zhang, and Hong Zhao. Multi-label feature se- lection with missing labels. Pattern Recognition, 74:488- 502, 2018.","title":"Multi-label feature selection with missing labels","authors":"Pengfei Zhu, Qian Xu, Qinghua Hu, Changqing Zhang, Hong Zhao","year":"2018","venue":"Pattern Recognition","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}