{"type":"ScholarlyArticle","title":"Adaptive Manifold Regularized Matrix Factorization for Data Clustering","authors":[{"name":"Lefei Zhang","slug":"lefei-zhang","given":"Lefei","family":"Zhang","affiliation":"School of Computer , Wuhan University ,"},{"name":"Qian Zhang","slug":"qian-zhang","given":"Qian","family":"Zhang","affiliation":"Alibaba Group ,"},{"name":"Bo Du","slug":"bo-du","given":"Bo","family":"Du","affiliation":"School of Computer , Wuhan University ,"},{"name":"Jane You","slug":"jane-you","given":"Jane","family":"You","affiliation":"Department of Computing , The Hong Kong Polytechnic University ,"},{"name":"Dacheng Tao","slug":"dacheng-tao","given":"Dacheng","family":"Tao","affiliation":"UBTech Sydney AI Institute , The School of Information Technologies , The University of Sydney ,"}],"abstract":"Data clustering is the task to group the data samples into certain clusters based on the relationships of samples and structures hidden in data, and it is a fundamental and important topic in data mining and machine learning areas. In the literature, the spectral clustering is one of the most popular approaches and has many variants in recent years. However, the performance of spectral clustering is determined by the affinity matrix, which is always computed by a predefined model (e.g., Gaussian kernel function) with carefully tuned parameters combination, and may far from optimal in practice. In this paper, we propose to consider the observed data clustering as a robust matrix factorization point of view, and learn an affinity matrix simultaneously to regularize the proposed matrix factorization. The solution of the proposed adaptive manifold regularized matrix factorization (AMRMF) is reached by a novel Augmented Lagrangian Multiplier (ALM) based algorithm. The experimental results on standard clustering datasets demonstrate the superior performance over the exist alternatives.","doi":"10.24963/ijcai.2017/475","url":"https://ijcai.org/proceedings/2017/475","pdf":"https://ijcai.org/proceedings/2017/0475.pdf","markdown":"https://ijcai.org/proceedings/2017/475.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/475","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 S-Z","track":"Main track","number":475,"pages":{"first":3399,"last":3405},"keywords":["Machine Learning: Unsupervised Learning","Machine Learning: Classification","Machine Learning: Data Mining"],"videos":[],"references":[{"position":1,"raw":"[Boyd and Vandenberghe, 2004] Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge Univ. Press, U.K., 2004.","title":"Convex Optimization","authors":"Vandenberghe Boyd","year":"2004","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Cai and Chen, 2015] Deng Cai and Xinlei Chen. Large s- cale spectral clustering via landmark-based sparse repre- sentation. IEEE Trans. Cybern., 45(8):1669-1680, 2015.","title":"Large scale spectral clustering via landmark-based sparse representation","authors":"Chen ; ] Deng Cai, Xinlei Cai, Chen","year":"2015","venue":"IEEE Trans. Cybern","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Cai et al., 2011] Deng Cai, Xiaofei He, Jiawei Han, and Thomas S. Huang. Graph regularized nonnegative matrix factorization for data representation. IEEE Trans. Pattern Anal. Mach. Intell., 33(8):1548-1560, 2011.","title":"Graph regularized nonnegative matrix factorization for data representation","authors":"Deng Cai, Xiaofei He, Jiawei Han, Thomas S Huang","year":"2011","venue":"IEEE Trans. Pattern Anal. Mach. Intell","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Chung, 1997] Fan R. K. Chung. Spectral Graph Theory. American Mathematical Society, USA, 1997.","title":"Spectral Graph Theory","authors":"R K Fan, Chung","year":"1997","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Ding et al., 2010] Chris Ding, Tao Li, and Michael I. Jor- dan. Convex and semi-nonnegative matrix factorization- s. IEEE Trans. Pattern Anal. Mach. Intell., 32(1):45-55, 2010.","title":"Convex and semi-nonnegative matrix factorizations","authors":"Chris Ding, Tao Li, Michael I","year":"2010","venue":"IEEE Trans. Pattern Anal. Mach. Intell","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Elhamifar and Vidal, 2013] Ehsan Elhamifar and Rene Vi- dal. Sparse subspace clustering: Algorithm, theory, and applications. IEEE Trans. Pattern Anal. Mach. Intell., 35(11):2765-2781, 2013.","title":"Sparse subspace clustering: Algorithm, theory, and applications","authors":"Ehsan Elhamifar, Rene Vidal","year":"2013","venue":"IEEE Trans. Pattern Anal. Mach. Intell","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Gong et al., 2015] Chen Gong, Tongliang Liu, Dacheng Tao, Keren Fu, Enmei Tu, and Jie Yang. Deformed graph laplacian for semisupervised learning. IEEE Trans. Neural Netw. Learn. Syst., 26(10):2261-2274, 2015.","title":"Deformed graph laplacian for semisupervised learning","authors":"Chen Gong, Tongliang Liu, Dacheng Tao, Keren Fu, Enmei Tu, Jie Yang","year":"2015","venue":"IEEE Trans. Neural Netw. Learn. Syst","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Guo, 2015] Xiaojie Guo. Robust subspace segmentation by simultaneously learning data representations and their affinity matrix. In Proc. IJCAI, pages 3547-3553, 2015.","title":"Robust subspace segmentation by simultaneously learning data representations and their affinity matrix","authors":"Xiaojie Guo","year":"2015","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/499"},{"position":9,"raw":"[Hartigan and Wong, 1979] J. A. Hartigan and M. A. Wong. Algorithm as 136: A k-means clustering algorithm. J. R. Statist. Soc. C, 28(1):100-108, 1979.","title":"Algorithm as 136: A k-means clustering algorithm","authors":"Hartigan, ; ] J A Wong, M A Hartigan, Wong","year":"1979","venue":"J. R. Statist. Soc. C","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[He et al., 2011] Xiaofei He, Deng Cai, Yuanlong Shao, Hu- jun Bao, and Jiawei Han. Laplacian regularized gaussian mixture model for data clustering. IEEE Trans. Knowl. Data Eng., 23(9):1406-1418, 2011.","title":"Laplacian regularized gaussian mixture model for data clustering","authors":"Xiaofei He, Deng Cai, Yuanlong Shao, Hujun Bao, Jiawei Han","year":"2011","venue":"IEEE Trans. Knowl. Data Eng","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Huang et al., 2014] Jin Huang, Feiping Nie, Heng Huang, and Chris Ding. Robust manifold nonnegative matrix fac- torization. ACM TKDD, 8(3):11: 1-21, 2014.","title":"Robust manifold nonnegative matrix factorization","authors":"Jin Huang, Feiping Nie, Heng Huang, Chris Ding","year":"2014","venue":"ACM TKDD","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Huang et al., 2015] Jin Huang, Feiping Nie, and Heng Huang. A new simplex sparse learning model to measure data similarity for clustering. In Proc. IJCAI, pages 3569- 3575, 2015.","title":"A new simplex sparse learning model to measure data similarity for clustering","authors":"Jin Huang, Feiping Nie, Heng Huang","year":"2015","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/502"},{"position":13,"raw":"[Jain et al., 1999] A. K. Jain, M. N. Murty, and P. J. Fly- nn. Data clustering: A review. ACM Comput. Surv., 31(3):264-323, 1999.","title":"Data clustering: A review","authors":"A K Jain, M N Murty, P J Flynn","year":"1999","venue":"ACM Comput. Surv","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Liu and Tao, 2016] Tongliang Liu and Dacheng Tao. On the performance of manhattan nonnegative matrix factoriza- tion. IEEE Trans. Neural Netw. Learn. Syst., 27(9):1851- 1863, 2016.","title":"Tongliang Liu and Dacheng Tao. On the performance of manhattan nonnegative matrix factorization","authors":"Tao Liu","year":"2016","venue":"IEEE Trans. Neural Netw. Learn. Syst","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Liu et al., 2013] Guangcan Liu, Zhouchen Lin, Shuicheng Yan, Ju Sun, Yong Yu, and Yi Ma. Robust recovery of sub- space structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell., 35(1):171-184, 2013.","title":"Robust recovery of subspace structures by low-rank representation","authors":"Liu","year":"2013","venue":"IEEE Trans. Pattern Anal. Mach. Intell","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Liu et al., 2017] Hongfu Liu, Junjie Wu, Tongliang Liu, Dacheng Tao, and Yun Fu. Spectral ensemble clus- tering via weighted k-means: Theoretical and practi- cal evidence. IEEE Trans. Knowl. Data Eng., 29:DOI 10.1109/TKDE.2017.2650229, 2017.","title":"Spectral ensemble clustering via weighted k-means: Theoretical and practical evidence","authors":"Hongfu Liu, Junjie Wu, Tongliang Liu, Dacheng Tao, Yun Fu","year":"2017","venue":"IEEE Trans. Knowl. Data Eng","doi":"10.1109/tkde.2017.2650229","url":null,"internal_url":null},{"position":17,"raw":"[Lu et al., 2012] Can-Yi Lu, Hai Min, Zhong-Qiu Zhao, Lin Zhu, De-Shuang Huang, and Shuicheng Yan. Robust and efficient subspace segmentation via least squares regres- sion. In Proc. ECCV, pages 347-360, 2012.","title":"Robust and efficient subspace segmentation via least squares regression","authors":"Lu","year":"2012","venue":"Proc. ECCV","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Meng and la Torre, 2013] Deyu Meng and Fernando De la Torre. Robust matrix factorization with unknown noise. In Proc. ICCV, pages 1337-1344, 2013.","title":"Robust matrix factorization with unknown noise","authors":"La Torre ; Deyu Meng, Fernando Meng, Torre De La","year":"2013","venue":"Proc. ICCV","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Nie et al., 2014] Feiping Nie, Xiaoqian Wang, and Heng Huang. Clustering and projected clustering with adaptive neighbors. In Proc. KDD, pages 977-986, 2014.","title":"Clustering and projected clustering with adaptive neighbors","authors":"Nie","year":"2014","venue":"Proc. KDD","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Nie et al., 2016a] Feiping Nie, Xiaoqian Wang, Michael I. Jordan, and Heng Huang. The constrained laplacian rank algorithm for graph-based clustering. In Proc. AAAI, pages 1969-1976, 2016.","title":"The constrained laplacian rank algorithm for graph-based clustering","authors":"Nie","year":"2016","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Nie et al., 2016b] Feiping Nie, Wei Zhu, and Xuelong Li. Unsupervised feature selection with structured graph opti- mization. In Proc. AAAI, pages 1302-1308, 2016.","title":"Unsupervised feature selection with structured graph optimization","authors":"Nie","year":"2016","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Shi and Malik, 2000] Jianbo Shi and Jitendra Malik. Nor- malized cuts and image segmentation. IEEE Trans. Pat- tern Anal. Mach. Intell., 22(8):888-905, 2000.","title":"Normalized cuts and image segmentation","authors":"Jianbo Shi, Jitendra Malik","year":"2000","venue":"IEEE Trans. Pattern Anal. Mach. Intell","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Trigeorgis et al., 2014] George Trigeorgis, Konstantinos Bousmalis, Stefanos Zafeiriou, and Bjorn W. Schuller. A deep semi-nmf model for learning hidden representations. In Proc. ICML, pages 1692-1700, 2014.","title":"A deep semi-nmf model for learning hidden representations","authors":"George Trigeorgis, Konstantinos Bousmalis, Stefanos Zafeiriou, Bjorn W Schuller","year":"2014","venue":"Proc. ICML","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Vidal, 2011] Rene Vidal. Subspace clustering. IEEE Signal Process. Mag., 28(2):52-68, 2011.","title":"Subspace clustering","authors":"Rene Vidal","year":"2011","venue":"IEEE Signal Process. Mag","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[von Luxburg, 2007] Ulrike von Luxburg. A tutorial on spec- tral clustering. Stat. Comput., 17(4):395-416, 2007.","title":"A tutorial on spectral clustering","authors":"Ulrike Von, Luxburg","year":"2007","venue":"Stat. Comput","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Wang et al., 2013] Can Wang, Zhong She, and Longbing Cao. Coupled clustering ensemble: Incorporating cou- pling relationships both between base clusterings and ob- jects. In Proc. ICDE, pages 374-385, 2013.","title":"Coupled clustering ensemble: Incorporating coupling relationships both between base clusterings and objects","authors":"Wang","year":"2013","venue":"Proc. ICDE","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Wang et al., 2015] Suhang Wang, Jiliang Tang, and Huan Liu. Embedded unsupervised feature selection. In Proc. AAAI, pages 470-476, 2015.","title":"Embedded unsupervised feature selection","authors":"Wang","year":"2015","venue":"Proc. AAAI","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Xu et al., 2016] Jinglin Xu, Junwei Han, Kai Xiong, and Feiping Nie. Robust and sparse fuzzy k-means clustering. In Proc. 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":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/317"},{"position":29,"raw":"[Xu et al., 2017] Jinglin Xu, Junwei Han, Feiping Nie, and Xuelong Li. Re-weighted discriminatively embedded k- means for multi-view clustering. IEEE Trans. Image Pro- cess., 26(6):3016-3027, 2017.","title":"Re-weighted discriminatively embedded kmeans for multi-view clustering","authors":"Jinglin Xu, Junwei Han, Feiping Nie, Xuelong Li","year":"2017","venue":"IEEE Trans. Image Process","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Yang et al., 2016] Yang Yang, Fumin Shen, Zi Huang, and Heng Tao Shen. A unified framework for discrete spectral clustering. In Proc. IJCAI, pages 2273-2279, 2016.","title":"A unified framework for discrete spectral clustering","authors":"Yang Yang, Fumin Shen, Zi Huang, Heng Tao Shen","year":"2016","venue":"Proc. IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/324"},{"position":31,"raw":"[Zhang et al., 2012] Lijun Zhang, Chun Chen, Jiajun Bu, Zhengguang Chen, Deng Cai, and Jiawei Han. Locally discriminative coclustering. IEEE Trans. Knowl. Data En- g., 24(6):1025-1035, 2012.","title":"Locally discriminative coclustering","authors":"Lijun Zhang, Chun Chen, Jiajun Bu, Zhengguang Chen, Deng Cai, Jiawei Han","year":"2012","venue":"IEEE Trans. Knowl. Data Eng","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Zhang et al., 2015] Lefei Zhang, Qian Zhang, Liangpei Zhang, Dacheng Tao, Xin Huang, and Bo Du. En- semble manifold regularized sparse low-rank approxima- tion for multiview feature embedding. Pattern Recognit., 48(10):3102-3112, 2015.","title":"Ensemble manifold regularized sparse low-rank approximation for multiview feature embedding","authors":"Zhang","year":"2015","venue":"Pattern Recognit","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}