{"type":"ScholarlyArticle","title":"Localized Incomplete Multiple Kernel k-means","authors":[{"name":"Xinzhong Zhu","slug":"xinzhong-zhu","given":"Xinzhong","family":"Zhu","affiliation":"College of Mathematics, Physics and Information Engineering , Zhejiang Normal University , China; School of Electronic Engineering , XIDIAN University , Xi'an , Shanxi , China"},{"name":"Xinwang Liu","slug":"xinwang-liu","given":"Xinwang","family":"Liu","affiliation":"School of Computer , National University of Defense Technology , Changsha , China"},{"name":"Miaomiao Li","slug":"miaomiao-li","given":"Miaomiao","family":"Li","affiliation":"School of Computer , National University of Defense Technology , Changsha , China"},{"name":"En Zhu","slug":"en-zhu","given":"En","family":"Zhu","affiliation":"School of Computer , National University of Defense Technology , Changsha , China"},{"name":"Li Liu","slug":"li-liu","given":"Li","family":"Liu","affiliation":"College of System Engineering , National University of Defense Technology , Changsha , China; University of Oulu , Finland"},{"name":"Zhiping Cai","slug":"zhiping-cai","given":"Zhiping","family":"Cai","affiliation":"School of Computer , National University of Defense Technology , Changsha , China"},{"name":"Jianping Yin","slug":"jianping-yin","given":"Jianping","family":"Yin","affiliation":"Dongguan University of Technology , Guangdong , China"},{"name":"Wen Gao","slug":"wen-gao","given":"Wen","family":"Gao","affiliation":"School of Electronics Engineering and Computer Science , Peking University , Beijing , China"}],"abstract":"The recently proposed multiple kernel k-means with incomplete kernels (MKKM-IK) optimally integrates a group of pre-specified incomplete kernel matrices to improve clustering performance. Though it demonstrates promising performance in various applications, we observe that it does not \\emph{sufficiently  consider the local structure among data and indiscriminately forces all pairwise sample similarity to equally align with their ideal similarity values}. This could make the incomplete kernels less effectively imputed, and in turn adversely affect the clustering performance. In this paper, we propose a novel localized incomplete multiple kernel k-means (LI-MKKM) algorithm to address this issue. Different from existing MKKM-IK, LI-MKKM only requires the similarity of a sample to its k-nearest neighbors to align with their ideal similarity values. This helps the clustering algorithm to focus on closer sample pairs that shall stay together and avoids involving unreliable similarity evaluation for farther sample pairs. We carefully design a three-step iterative algorithm to solve the resultant optimization problem and theoretically prove its convergence. Comprehensive experiments on eight benchmark datasets demonstrate that our algorithm significantly outperforms the state-of-the-art comparable algorithms proposed in the recent literature, verifying the advantage of considering local structure.","doi":"10.24963/ijcai.2018/454","url":"https://ijcai.org/proceedings/2018/454","pdf":"https://ijcai.org/proceedings/2018/0454.pdf","markdown":"https://ijcai.org/proceedings/2018/454.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/454","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":454,"pages":{"first":3271,"last":3277},"keywords":["Machine Learning: Clustering","Machine Learning: Multi-instance;Multi-label;Multi-view learning","Machine Learning: Unsupervised Learning"],"videos":[],"references":[{"position":1,"raw":"[Bhadra et al., 2016] Sahely Bhadra, Samuel Kaski, and Juho Rousu. Multi-view kernel completion. In arX- iv:1602.02518, 2016.","title":"Multi-view kernel completion","authors":"Bhadra","year":"2016","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Cai et al., 2013] Xiao Cai, Feiping Nie, Weidong Cai, and Heng Huang. Heterogeneous image features integration via multi-modal semi-supervised learning model. In IC- CV, pages 1737-1744, 2013.","title":"Heterogeneous image features integration via multi-modal semi-supervised learning model","authors":"Xiao Cai, Feiping Nie, Weidong Cai, Heng Huang","year":"2013","venue":"IC-CV","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":"[Gao et al., 2015] Hongchang Gao, Feiping Nie, Xuelong Li, and Heng Huang. Multi-view subspace clustering. In ICCV, pages 4238-4246, 2015.","title":"Multi-view subspace clustering","authors":"Hongchang Gao, Feiping Nie, Xuelong Li, Heng Huang","year":"2015","venue":"ICCV","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Ghahramani and Jordan, 1993] Zoubin Ghahramani and Michael I. Jordan. Supervised learning from incomplete data via an EM approach. In NIPS, pages 120-127, 1993.","title":"Supervised learning from incomplete data via an EM approach","authors":"Zoubin Ghahramani, Michael I Jordan","year":"1993","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Gönen and Margolin, 2014] Mehmet Gönen and Adam A. Margolin. Localized data fusion for kernel k-means clus- tering with application to cancer biology. In NIPS, pages 1305-1313, 2014.","title":"Localized data fusion for kernel k-means clustering with application to cancer biology","authors":"Mehmet Gönen, Adam A Margolin","year":"2014","venue":"NIPS","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Kumar et al., 2013] Ritwik Kumar, Ting Chen, Moritz Hardt, David Beymer, Karen Brannon, and Tanveer Fathi- ma Syeda-Mahmood. Multiple kernel completion and it- s application to cardiac disease discrimination. In ISBI, pages 764-767, 2013.","title":"Multiple kernel completion and its application to cardiac disease discrimination","authors":"Ritwik Kumar, Ting Chen, Moritz Hardt, David Beymer, Karen Brannon, Tanveer Fathima Syeda-Mahmood","year":"2013","venue":"ISBI","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Li et al., 2014] Shao-Yuan Li, Yuan Jiang, and Zhi-Hua Zhou. Partial multi-view clustering. In AAAI, pages 1968- 1974, 2014.","title":"Partial multi-view clustering","authors":"Shao-Yuan, Yuan Li, Zhi-Hua Jiang, Zhou","year":"2014","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Li et al., 2016] Miaomiao Li, Xinwang Liu, Lei Wang, Y- ong Dou, Jianping Yin, and En Zhu. Multiple kernel clus- tering with local kernel alignment maximization. In IJCAI, pages 1704-1710, 2016.","title":"Multiple kernel clustering with local kernel alignment maximization","authors":"Miaomiao Li, Xinwang Liu, Lei Wang, Yong Dou, Jianping Yin, En Zhu","year":"2016","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/244"},{"position":10,"raw":"[Liu et al., 2014] Xinwang Liu, Lei Wang, Jian Zhang, Jian- ping Yin, and Huan Liu. Global and local structure p- reservation for feature selection. IEEE Trans. Neural Netw. Learning Syst., 25(6):1083-1095, 2014.","title":"Global and local structure preservation for feature selection","authors":"Xinwang Liu, Lei Wang, Jian Zhang, Jianping Yin, Huan Liu","year":"2014","venue":"IEEE Trans. Neural Netw. Learning Syst","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Liu et al., 2016] Xinwang Liu, Yong Dou, Jianping Yin, Lei Wang, and En Zhu. Multiple kernel k-means clustering with matrix-induced regularization. In AAAI, pages 1888- 1894, 2016.","title":"Multiple kernel k-means clustering with matrix-induced regularization","authors":"Xinwang Liu, Yong Dou, Jianping Yin, Lei Wang, En Zhu","year":"2016","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Liu et al., 2017a] Xinwang Liu, Miaomiao Li, Lei Wang, Yong Dou, Jianping Yin, and En Zhu. Multiple kernel k-means with incomplete kernels. In AAAI, pages 2259- 2265, 2017.","title":"Multiple kernel k-means with incomplete kernels","authors":"Liu","year":"2017","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Liu et al., 2017b] Xinwang Liu, Sihang Zhou, Yueqing Wang, Miaomiao Li, Yong Dou, En Zhu, and Jianping Yin. Optimal neighborhood kernel clustering with multiple ker- nels. In AAAI, pages 2266-2272, 2017.","title":"Optimal neighborhood kernel clustering with multiple kernels","authors":"Liu","year":"2017","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Nie et al., 2014] Feiping Nie, Xiaoqian Wang, and Heng Huang. Clustering and projected clustering with adaptive neighbors. In KDD, pages 977-986, 2014.","title":"Clustering and projected clustering with adaptive neighbors","authors":"Nie","year":"2014","venue":"KDD","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Shao et al., 2015] Weixiang Shao, Lifang He, and Philip S. Yu. Multiple incomplete views clustering via weighted nonnegative matrix factorization with ℓ 2,1 regularization. In ECML PKDD, pages 318-334, 2015.","title":"Multiple incomplete views clustering via weighted nonnegative matrix factorization with ℓ 2,1 regularization","authors":"Weixiang Shao, Lifang He, Philip S Yu","year":"2015","venue":"ECML PKDD","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Trivedi et al., 2010] Anusua Trivedi, Piyush Rai, Hal Daumé III, and Scott L. DuVall. Multiview clustering with incomplete views. In NIPS 2010: Machine Learning for Social Computing Workshop ,Whistler, Canada, 2010.","title":"Multiview clustering with incomplete views","authors":"Trivedi","year":"2010","venue":"NIPS 2010: Machine Learning for Social Computing Workshop","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Xiang et al., 2013] Shuo Xiang, Lei Yuan, Wei Fan, Yalin Wang, Paul M. Thompson, and Jieping Ye. Multi-source learning with block-wise missing data for alzheimer's dis- ease prediction. In ACM SIGKDD, pages 185-193, 2013.","title":"Multi-source learning with block-wise missing data for alzheimer's disease prediction","authors":"Shuo Xiang, Lei Yuan, Wei Fan, Yalin Wang, Paul M Thompson, Jieping Ye","year":"2013","venue":"ACM SIGKDD","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Xu et al., 2015a] Chang Xu, Dacheng Tao, and Chao Xu. Multi-view intact space learning. IEEE Trans. Pattern Anal. Mach. Intell., 37(12):2531-2544, 2015.","title":"Multi-view intact space learning","authors":"Xu","year":"2015","venue":"IEEE Trans. Pattern Anal. Mach. Intell","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Xu et al., 2015b] Chang Xu, Dacheng Tao, and Chao Xu. Multi-view learning with incomplete views. IEEE Trans. Image Processing, 24(12):5812-5825, 2015.","title":"Multi-view learning with incomplete views","authors":"Xu","year":"2015","venue":"IEEE Trans. Image Processing","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Yin et al., 2015] Qiyue Yin, Shu Wu, and Liang Wang. In- complete multi-view clustering via subspace learning. In CIKM, pages 383-392, 2015.","title":"Incomplete multi-view clustering via subspace learning","authors":"Qiyue Yin, Shu Wu, Liang Wang","year":"2015","venue":"CIKM","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Yu et al., 2012] Shi Yu, Léon-Charles Tranchevent, Xinhai Liu, Wolfgang Glänzel, Johan A. K. Suykens, Bart De Moor, and Yves Moreau. Optimized data fusion for k- ernel k-means clustering. IEEE TPAMI, 34(5):1031-1039, 2012.","title":"Optimized data fusion for kernel k-means clustering","authors":"Shi Yu, Léon-Charles Tranchevent, Xinhai Liu, Wolfgang Glänzel, Johan A K Suykens, Bart De Moor, Yves Moreau","year":"2012","venue":"IEEE TPAMI","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Zhang et al., 2015] Changqing Zhang, Huazhu Fu, Si Liu, Guangcan Liu, and Xiaochun Cao. Low-rank tensor con- strained multiview subspace clustering. In ICCV, pages 1582-1590, 2015.","title":"Low-rank tensor constrained multiview subspace clustering","authors":"Changqing Zhang, Huazhu Fu, Si Liu, Guangcan Liu, Xiaochun Cao","year":"2015","venue":"ICCV","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Zhao et al., 2016] Handong Zhao, Hongfu Liu, and Yun Fu. Incomplete multimodal visual data grouping. In IJCAI, pages 2392-2398, 2016.","title":"Incomplete multimodal visual data grouping","authors":"Handong Zhao, Hongfu Liu, Yun Fu","year":"2016","venue":"IJCAI","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}