{"type":"ScholarlyArticle","title":"Balanced Clustering: A Uniform Model and Fast Algorithm","authors":[{"name":"Weibo Lin","slug":"weibo-lin","given":"Weibo","family":"Lin","affiliation":"School of Computer Science , University of Electronic Science and Technology of China"},{"name":"Zhu He","slug":"zhu-he","given":"Zhu","family":"He","affiliation":"School of Computer Science , University of Electronic Science and Technology of China; Zhejiang Cainiao Supply Chain Management Co. Ltd."},{"name":"Mingyu Xiao","slug":"mingyu-xiao","given":"Mingyu","family":"Xiao","affiliation":"School of Computer Science , University of Electronic Science and Technology of China"}],"abstract":"Clustering is a fundamental research topic in data mining and machine learning. In addition, many specific applications demand that the clusters obtained be balanced. In this paper, we present a balanced clustering model that is to minimize the sum of squared distances to cluster centers, with uniform regularization functions to control the balance degree of the clustering results. To solve the model, we adopt the idea of the k-means method. We show that the k-means assignment step has an equivalent minimum cost flow formulation when the regularization functions are all convex. By using a novel and simple acceleration technique for the k-means and network simplex methods our model can be solved quite efficiently. Experimental results over benchmarks validate the advantage of our algorithm compared to the state-of-the-art balanced clustering algorithms. On most datasets, our algorithm runs more than 100 times faster than previous algorithms with a better solution.","doi":"10.24963/ijcai.2019/414","url":"https://ijcai.org/proceedings/2019/414","pdf":"https://ijcai.org/proceedings/2019/0414.pdf","markdown":"https://ijcai.org/proceedings/2019/414.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/414","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Machine Learning A-L","track":"Main track","number":414,"pages":{"first":2987,"last":2993},"keywords":["Constraints and SAT: Constraints and Data Mining ; Machine Learning","Heuristic Search and Game Playing: Combinatorial Search and Optimisation","Machine Learning: Clustering","Constraints and SAT: Modeling;Formulation"],"videos":[],"references":[{"position":1,"raw":"[Aloise et al., 2009] Daniel Aloise, Amit Deshpande, Pierre Hansen, and Preyas Popat. NP-hardness of Euclidean sum- of-squares clustering. Machine learning, 75(2):245-248, 2009.","title":"NP-hardness of Euclidean sumof-squares clustering","authors":"Amit Daniel Aloise, Pierre Deshpande, Preyas Hansen, Popat","year":"2009","venue":"Machine learning","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Althoff et al., 2011] Tim Althoff, Adrian Ulges, and An- dreas Dengel. Balanced clustering for content-based im- age browsing. Series of the Gesellschaft fur Informatik, 1:27-30, 2011.","title":"Balanced clustering for content-based image browsing","authors":"Tim Althoff, Adrian Ulges, Andreas Dengel","year":"2011","venue":"Series of the Gesellschaft fur Informatik","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Anderberg, 1973] Michael R Anderberg. Cluster analysis for applications. Probability and Mathematical Statistics, New York: Academic Press, 1973.","title":"Cluster analysis for applications","authors":"Michael R Anderberg","year":"1973","venue":"Probability and Mathematical Statistics","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Banerjee and Ghosh, 2002] Arindam Banerjee and Joydeep Ghosh. On scaling up balanced clustering algorithms. In Proceedings of the 2002 SIAM International Conference on Data Mining, pages 333-349. SIAM, 2002.","title":"On scaling up balanced clustering algorithms","authors":"Ghosh Banerjee, Arindam Banerjee, Joydeep Ghosh","year":"2002","venue":"Proceedings of the 2002 SIAM International Conference on Data Mining","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bertsekas, 1991] Dimitri P Bertsekas. Linear network opti- mization: algorithms and codes. Mit Press, 1991.","title":"Linear network optimization: algorithms and codes","authors":"Dimitri P Bertsekas","year":"1991","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bradley and Mangasarian, 2000] Paul S Bradley and Olvi L Mangasarian. k-Plane clustering.(98-08), August 1998. Journal of Global Optimization, 16(1), 2000.","title":"k-Plane clustering","authors":"S Paul, Bradley, Olvi L Mangasarian","year":"1998","venue":"Journal of Global Optimization","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Bradley et al., 1997] Paul S Bradley, Olvi L Mangasarian, and W Nick Street. Clustering via concave minimization. In Advances in neural information processing systems, pages 368-374, 1997.","title":"Clustering via concave minimization","authors":"Paul S Bradley, W Nick Olvi L Mangasarian, Street","year":"1997","venue":"Advances in neural information processing systems","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Bradley et al., 2000] Paul S Bradley, Kristin P Bennett, and Ayhan Demiriz. Constrained k-means clustering. Mi- crosoft Research, Redmond, pages 1-8, 2000.","title":"Constrained k-means clustering","authors":"Kristin P Paul S Bradley, Ayhan Bennett, Demiriz","year":"2000","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Bühlmann and Van De Geer, 2011] Peter Bühlmann and Sara Van De Geer. Statistics for high-dimensional data: methods, theory and applications. Springer Science & Business Media, 2011.","title":"Statistics for high-dimensional data: methods, theory and applications","authors":"Van Bühlmann, Peter De Geer ;, Sara Bühlmann, Van De, Geer","year":"2011","venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Chen et al., 2006] Yixin Chen, Ya Zhang, and Xiang Ji. Size regularized cut for data clustering. In Advances in Neural Information Processing Systems, pages 211-218, 2006.","title":"Size regularized cut for data clustering","authors":"Yixin Chen, Ya Zhang, Xiang Ji","year":"2006","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Costa et al., 2017] Leandro R Costa, Daniel Aloise, and Nenad Mladenović. Less is more: basic variable neigh- borhood search heuristic for balanced minimum sum-of- squares clustering. Information Sciences, 415:247-253, 2017.","title":"Less is more: basic variable neighborhood search heuristic for balanced minimum sum-ofsquares clustering","authors":"Daniel Leandro R Costa, Nenad Aloise, Mladenović","year":"2017","venue":"Information Sciences","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Desrosiers et al., 2005] Jacques Desrosiers, Nenad Mlade- nović, and Daniel Villeneuve. Design of balanced MBA student teams. Journal of the Operational Research Soci- ety, 56(1):60-66, 2005.","title":"Design of balanced MBA student teams","authors":"Jacques Desrosiers, Nenad Mladenović, Daniel Villeneuve","year":"2005","venue":"Journal of the Operational Research Society","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Duda and Hart, 1973] Richard O Duda and Peter E Hart. Pattern classification and scene analysis. A Wiley- Interscience Publication, New York: Wiley, 1973.","title":"Pattern classification and scene analysis","authors":"O Richard, Peter E Duda, Hart","year":"1973","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Feldman et al., 2019] Dan Feldman, Jeryes Danial Jeryes, and Ariel Hutterer. Position estimation of moving objects: Practical provable approximation. IEEE Robotics and Automation Letters, 2019.","title":"Position estimation of moving objects: Practical provable approximation","authors":"Feldman","year":"2019","venue":"IEEE Robotics and Automation Letters","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Kuhn, 1955] Harold W Kuhn. The Hungarian method for the assignment problem. Naval research logistics quar- terly, 2(1-2):83-97, 1955.","title":"The Hungarian method for the assignment problem","authors":"Harold W Kuhn, Kuhn","year":"1955","venue":"Naval research logistics quarterly","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Li et al., 2018] Zhihui Li, Feiping Nie, Xiaojun Chang, Zhi- gang Ma, and Yi Yang. Balanced clustering via exclusive lasso: A pragmatic approach. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018.","title":"Balanced clustering via exclusive lasso: A pragmatic approach","authors":"Zhihui Li, Feiping Nie, Xiaojun Chang, Zhigang Ma, Yi Yang","year":"2018","venue":"Thirty-Second AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Liu et al., 2017] Hanyang Liu, Junwei Han, Feiping Nie, and Xuelong Li. Balanced clustering with least square regression. In Thirty-First AAAI Conference on Artificial Intelligence, 2017.","title":"Balanced clustering with least square regression","authors":"Liu","year":"2017","venue":"Thirty-First AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Malinen and Fränti, 2014] Mikko I Malinen and Pasi Fränti. Balanced k-means for clustering. In Joint IAPR Inter- national Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (SSPR), pages 32-41. Springer, 2014.","title":"Balanced k-means for clustering","authors":"Fränti ; Malinen, I Mikko, Pasi Malinen, Fränti","year":"2014","venue":"Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (SSPR)","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Mangasarian, 1994] Olvi L Mangasarian. Nonlinear pro- gramming, volume 10 of classics in applied mathematics. SIAM, Philadelphia, 1994.","title":"Nonlinear programming","authors":"Olvi L Mangasarian","year":"1994","venue":"classics in applied mathematics","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Murty, 1983] Katta G Murty. Linear programming, vol- ume 60. Wiley New York, 1983.","title":"Linear programming","authors":"G Katta, Murty","year":"1983","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Nallusamy et al., 2010] R Nallusamy, K Duraiswamy, R Dhanalaksmi, and P Parthiban. Optimization of non- linear multiple traveling salesman problem using k-means clustering, shrink wrap algorithm and meta-heuristics. International Journal of Nonlinear Science, 9(2):171-177, 2010.","title":"Optimization of nonlinear multiple traveling salesman problem using k-means clustering, shrink wrap algorithm and meta-heuristics","authors":"Nallusamy, R Duraiswamy, Dhanalaksmi, Parthiban","year":"2010","venue":"International Journal of Nonlinear Science","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Pyatkin et al., 2017] Artem Pyatkin, Daniel Aloise, and Ne- nad Mladenović. NP-Hardness of balanced minimum sum-of-squares clustering. Pattern Recognition Letters, 97:44-45, 2017.","title":"NP-Hardness of balanced minimum sum-of-squares clustering","authors":"Artem Pyatkin, Aloise Daniel, Nenad Mladenović","year":"2017","venue":"Pattern Recognition Letters","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Siavoshi et al., 2016] Saman Siavoshi, Yousef S Kavian, and Hamid Sharif. Load-balanced energy efficient clus- tering protocol for wireless sensor networks. IET Wireless Sensor Systems, 6(3):67-73, 2016.","title":"Load-balanced energy efficient clustering protocol for wireless sensor networks","authors":"Saman Siavoshi, Hamid Yousef S Kavian, Sharif","year":"2016","venue":"IET Wireless Sensor Systems","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Späth, 1980] Helmuth Späth. Cluster analysis algorithms for data reduction and classification of objects. John Wiley & sons, New York, 1980.","title":"Cluster analysis algorithms for data reduction and classification of objects","authors":"Helmuth Späth","year":"1980","venue":null,"doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Steinley, 2006] Douglas Steinley. K-means clustering: a half-century synthesis. British Journal of Mathematical and Statistical Psychology, 59(1):1-34, 2006.","title":"K-means clustering: a half-century synthesis","authors":"Douglas Steinley","year":"2006","venue":"British Journal of Mathematical and Statistical Psychology","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Su et al., 2015] Wenbo Su, Jie Hu, Chuang Lin, and Sher- man Shen. SLA-aware tenant placement and dynamic resource provision in SaaS. In Web Services (ICWS), 2015 IEEE International Conference on, pages 615-622. IEEE, 2015.","title":"SLA-aware tenant placement and dynamic resource provision in SaaS","authors":"Wenbo Su, Jie Hu, Chuang Lin, Sherman Shen","year":"2015","venue":"Web Services (ICWS), 2015 IEEE International Conference on","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Zhong and Ghosh, 2003] Shi Zhong and Joydeep Ghosh. Model-based clustering with soft balancing. In Data Mining, 2003. ICDM 2003. Third IEEE International Con- ference on, pages 459-466. IEEE, 2003.","title":"Model-based clustering with soft balancing","authors":"Shi Zhong, Joydeep Ghosh","year":"2003","venue":"Third IEEE International Conference on","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Zhu et al., 2010] Shunzhi Zhu, Dingding Wang, and Tao Li. Data clustering with size constraints. Knowledge-Based Systems, 23(8):883-889, 2010.","title":"Data clustering with size constraints","authors":"Shunzhi Zhu, Dingding Wang, Tao Li","year":"2010","venue":"Knowledge-Based Systems","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}