Skip to main content

Constrained Clustering: Current and New Trends

  • Chapter
  • First Online:
A Guided Tour of Artificial Intelligence Research

Abstract

Clustering is an unsupervised process which aims to discover regularities and underlying structures in data. Constrained clustering extends clustering in such a way that expert knowledge can be integrated through the use of user constraints. These guide the clustering process towards a more relevant result. Different means of integrating constraints into the clustering process exist. They consist of extending classical clustering algorithms, such as the well-known k-means algorithm; modelling the constrained clustering problem using a declarative framework; and finally, by directly integrating constraints into a collaborative process that involves several clustering algorithms. A common point of these approaches is that they require the user constraints to be given before the process begins. New trends in constrained clustering highlight the need for better interaction between the automatic process and expert supervision. This chapter is dedicated to constrained clustering. In particular, after a brief overview of constrained clustering and associated issues, it presents the three main approaches in the domain. It also discusses exploratory data mining by presenting models that develop interaction with the user in an incremental and collaborative way. Finally, moving beyond constraints, some aspects of user implicit preferences and their capture are introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Al-Razgan M, Domeniconi C (2009) Clustering ensembles with active constraints. In: Okun O, Valentini G (eds) Applications of supervised and unsupervised ensemble methods. Springer, Berlin, pp 175–189

    Chapter  Google Scholar 

  • Aloise D, Deshpande A, Hansen P, Popat P (2009) NP-hardness of Euclidean sum-of-squares clustering. Mach Learn 75(2):245–248

    Article  MATH  Google Scholar 

  • Aloise D, Hansen P, Liberti L (2012) An improved column generation algorithm for minimum sum-of-squares clustering. Math Program 131(1–2):195–220

    Article  MathSciNet  MATH  Google Scholar 

  • Alzate C, Suykens J (2009) A regularized formulation for spectral clustering with pairwise constraints. In: Proceedings of the international joint conference on neural networks, pp 141–148

    Google Scholar 

  • Anand R, Reddy C (2011) Graph-based clustering with constraints. In: Proceedings of the Pacific-Asia conference on knowledge discovery and data mining, pp 51–62

    Google Scholar 

  • Anand S, Bell D, Hughes J (1995) The role of domain knowledge in data mining. In: Proceedings of the international conference on information and knowledge management, pp 37–43

    Google Scholar 

  • Awasthi P, Zadeh RB (2010) Supervised clustering. In: Proceedings of the international conference on neural information processing systems, pp 91–99

    Google Scholar 

  • Awasthi P, Balcan MF, Voevodski K (2017) Local algorithms for interactive clustering. J Mach Learn Res 18:1–35

    MathSciNet  MATH  Google Scholar 

  • Babaki B, Guns T, Nijssen S (2014) Constrained clustering using column generation. In: Proceedings of the international conference on AI and OR techniques in constriant programming for combinatorial optimization problems, pp 438–454

    Google Scholar 

  • Balcan MF, Blum A (2008) Clustering with interactive feedback. In: Proceedings of the international conference on algorithmic learning theory, pp 316–328

    Google Scholar 

  • Banerjee A, Ghosh J (2006) Scalable clustering algorithms with balancing constraints. Data Min Knowl Discov 13(3):365–395

    Article  MathSciNet  Google Scholar 

  • Bar-Hillel A, Hertz T, Shental N, Weinshall D (2003) Learning distance functions using equivalence relations. In: Proceedings of the international conference on machine learning, pp 11–18

    Google Scholar 

  • Bar-Hillel A, Hertz T, Shental M, Weinshall D (2005) Learning a mahalanobis metric from equivalence constraints. J Mach Learn Res 6:937–965

    MathSciNet  MATH  Google Scholar 

  • Basu S, Banerjee A, Mooney R (2002) Semi-supervised clustering by seeding. In: Proceedings of the international conference on machine learning, pp 19–26

    Google Scholar 

  • Basu S, Banerjee A, Mooney R (2004a) Active semi-supervision for pairwise constrained clustering. In: Proceedings of the SIAM international conference on data mining, pp 333–344

    Google Scholar 

  • Basu S, Bilenko M, Mooney R (2004b) A probabilistic framework for semi-supervised clustering. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 59–68

    Google Scholar 

  • Basu S, Davidson I, Wagstaff K (2008) Constrained clustering: advances in algorithms, theory, and applications, 1st edn. Chapman & Hall/CRC, Boca Raton

    Book  MATH  Google Scholar 

  • Beldiceanu N, Carlsson M, Rampon JX (2005) Global constraint catalog. Technical Report T2005-08, SICS and EMN Technical Report

    Google Scholar 

  • Bellet A, Habrard A, Sebban M (2015) Metric learning. Morgan & Claypool Publishers, San Rafael

    Book  MATH  Google Scholar 

  • Berg J, Järvisalo M (2017) Cost-optimal constrained correlation clustering via weighted partial maximum satisfiability. Artif Intell 244:110–142

    Article  MathSciNet  MATH  Google Scholar 

  • Bie TD (2011) Maximum entropy models and subjective interestingness: an application to tiles in binary databases. Data Min Knowl Discov 23(3):407–446

    Article  MathSciNet  MATH  Google Scholar 

  • Bilenko M, Mooney R (2003) Adaptive duplicate detection using learnable string similarity measures. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 39–48

    Google Scholar 

  • Bilenko M, Basu S, Mooney R (2004) Integrating constraints and metric learning in semi-supervised clustering. In: Proceedings of the international conference on machine learning, pp 11–18

    Google Scholar 

  • Boley M, Lucchese C, Paurat D, Gärtner T (2011) Direct local pattern sampling by efficient two-step random procedures. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 582–590

    Google Scholar 

  • Boley M, Mampaey M, Kang B, Tokmakov P, Wrobel S (2013) One click mining: interactive local pattern discovery through implicit preference and performance learning. In: Proceedings of the ACM SIGKDD workshop on interactive data exploration and analytics, pp 27–35

    Google Scholar 

  • Börzsönyi S, Kossmann D, Stocker K (2001) The skyline operator. In: Proceedings of the international conference on data engineering, pp 421–430

    Google Scholar 

  • Boulicaut JF, De Raedt L, Mannila H (eds) (2006) Constraint-based mining and inductive databases. Lecture notes in artificial intelligence, vol 3848. Springer, Berlin

    Google Scholar 

  • Bradley P, Bennett K, Demiriz A (2000) Constrained k-means clustering. Technical Report MSR-TR-2000-65, Microsoft Research

    Google Scholar 

  • Chabert M, Solnon C (2017) Constraint programming for multi-criteria conceptual clustering. In: Proceedings of the international conference on principles and practice of constraint programming, pp 460–476

    Google Scholar 

  • Chang S, Dai P, Hong L, Sheng C, Zhang T, Chi E (2016) AppGrouper: knowledge-based interactive clustering tool for app search results. In: Proceedings of the international conference on intelligent user interfaces, pp 348–358

    Google Scholar 

  • Chen W, Feng G (2012) Spectral clustering: a semi-supervised approach. Neurocomputing 77(1):229–242

    Article  Google Scholar 

  • Cheng H, Hua K, Vu K (2008) Constrained locally weighted clustering. Proc VLDB Endow 1(1):90–101

    Article  Google Scholar 

  • Cho M, Pei J, Wang H, Wang W (2005) Preference-based frequent pattern mining. Int J Data Warehous Min 1(4):56–77

    Article  Google Scholar 

  • Coden A, Danilevsky M, Gruhl D, Kato L, Nagarajan M (2017) A method to accelerate human in the loop clustering. In: Proceedings of the SIAM international conference on data mining, pp 237–245

    Google Scholar 

  • Cohn D, Caruana R, Mccallum A (2003) Semi-supervised clustering with user feedback. Technical Report TR2003-1892. Department of Computer Science, Cornell University

    Google Scholar 

  • Cucuringu M, Koutis I, Chawla S, Miller G, Peng R (2016) Simple and scalable constrained clustering: a generalized spectral method. In: Proceedings of the international conference on artificial intelligence and statistics, pp 445–454

    Google Scholar 

  • Cutting D, Pedersen J, Karger D, Tukey J (1992) Scatter/gather: a cluster-based approach to browsing large document collections. In: Proceedings of the international ACM SIGIR conference on research and development in information retrieval, pp 318–329

    Google Scholar 

  • Dao TBH, Duong KC, Vrain C (2013) A declarative framework for constrained clustering. In: Proceedings of the joint European conference on machine learning and knowledge discovery in databases, pp 419–434

    Google Scholar 

  • Dao TBH, Vrain C, Duong KC, Davidson I (2016) A framework for actionable clustering using constraint programming. In: Proceedings of the European conference on artificial intelligence, pp 453–461

    Google Scholar 

  • Dao TBH, Duong KC, Vrain C (2017) Constrained clustering by constraint programming. Artif Intell 244:70–94

    Article  MathSciNet  MATH  Google Scholar 

  • Davidson I, Basu S (2007) A survey of clustering with instance level constraints. ACM Trans Knowl Discov Data 77(1):1–41

    Google Scholar 

  • Davidson I, Ravi S (2005) Clustering with constraints: feasibility issues and the k-means algorithm. In: Proceedings of the SIAM international conference on data mining, pp 138–149

    Google Scholar 

  • Davidson I, Ravi S (2006) Identifying and generating easy sets of constraints for clustering. In: Proceedings of the AAAI conference on artificial intelligence, pp 336–341

    Google Scholar 

  • Davidson I, Ravi S (2007) The complexity of non-hierarchical clustering with instance and cluster level constraints. Data Min Knowl Discov 14(1):25–61

    Article  MathSciNet  Google Scholar 

  • Davidson I, Wagstaff K, Basu S (2006) Measuring constraint-set utility for partitional clustering algorithms. In: European conference on principles of data mining and knowledge discovery, pp 115–126

    Google Scholar 

  • Davidson I, Ester M, Ravi S (2007) Efficient incremental constrained clustering. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 240–249

    Google Scholar 

  • Davidson I, Ravi S, Shamis L (2010) A SAT-based framework for efficient constrained clustering. In: Proceedings of the SIAM international conference on data mining, pp 94–105

    Google Scholar 

  • De Bie T (2011) An information theoretic framework for data mining. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 564–572

    Google Scholar 

  • De Bie T (2013) Subjective interestingness in exploratory data mining. In: Proceedings of the international symposium on intelligent data analysis, pp 19–31

    Google Scholar 

  • Delattre M, Hansen P (1980) Bicriterion cluster analysis. IEEE Trans Pattern Anal Mach Intell 2(4):277–291

    Google Scholar 

  • Demiriz A, Bennett K, Embrechts M (1999) Semi-supervised clustering using genetic algorithms. In: Proceedings of the conference on artificial neural networks in engineering, pp 809–814

    Google Scholar 

  • Demiriz A, Bennett K, Bradley P (2008) Using assignment constraints to avoid empty clusters in k-means clustering. In: Basu S, Davidson I, Wagstaff K (eds) Constrained clustering: advances in algorithms, theory, and applications, 1st edn. Chapman & Hall/CRC, pp 201–220

    Google Scholar 

  • Dimitriadou E, Weingessel A, Hornik K (2002) A mixed ensemble approach for the semi-supervised problem. In: Proceedings of the international conference on artificial neural networks, pp 571–576

    Google Scholar 

  • Ding S, Qi B, Jia H, Zhu H, Zhang L (2013) Research of semi-supervised spectral clustering based on constraints expansion. Neural Comput Appl 22:405–410

    Article  Google Scholar 

  • Dinler D, Tural M (2016) A survey of constrained clustering. In: Celebi M, Aydin K (eds) Unsupervised learning algorithms. Springer, Berlin, pp 207–235

    Google Scholar 

  • du Merle O, Hansen P, Jaumard B, Mladenović N (1999) An interior point algorithm for minimum sum-of-squares clustering. SIAM J Sci Comput 21(4):1485–1505

    Article  MathSciNet  MATH  Google Scholar 

  • Dzyuba V, van Leeuwen M (2013) Interactive discovery of interesting subgroup sets. In: Proceedings of the international symposium on intelligent data analysis, pp 150–161

    Google Scholar 

  • Dzyuba V, van Leeuwen M, Nijssen S, De Raedt L (2014) Interactive learning of pattern rankings. Int J Artif Intell Tools 23(6):1460,026

    Google Scholar 

  • Ester M, Kriegel H, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of the international conference on knowledge discovery and data mining, pp 226–231

    Google Scholar 

  • Fayyad U, Piatetsky-Shapiro G, Smyth P (1996) From data mining to knowledge discovery: an overview. In: Fayyad U, Piatetsky-Shapiro G, Smyth P, Uthurusamy R (eds) Advances in knowledge discovery and data mining. AAAI/MIT Press, pp 1–36

    Google Scholar 

  • Fisher D (1987) Knowledge acquisition via incremental conceptual clustering. Mach Learn 2(2):139–172

    Google Scholar 

  • Forestier G, Gançarski P, Wemmert C (2010a) Collaborative clustering with background knowledge. Data Knowl Eng 69(2):211–228

    Google Scholar 

  • Forestier G, Wemmert C, Gançarski P (2010b) Towards conflict resolution in collaborative clustering. In: IEEE international conference on intelligent systems, pp 361–366

    Google Scholar 

  • Fred ALN, Jain AK (2002) Data clustering using evidence accumulation. In: Proceedings of the IEEE international conference on pattern recognition, pp 276–280

    Google Scholar 

  • Fürnkranz J, Gamberger D, Lavrač N (2012) Foundations of rule learning. Cognitive technologies, Springer, Berlin

    Book  MATH  Google Scholar 

  • Gallo A, De Bie T, Cristianini N (2007) MINI: mining informative non-redundant itemsets. In: Proceedings of the European conference on principles of data mining and knowledge discovery, pp 438–445

    Google Scholar 

  • Gançarski P, Wemmert C (2007) Collaborative multi-step mono-level multi-strategy classification. J Multimed Tools Appl 35(1):1–27

    Article  Google Scholar 

  • Ganji M, Bailey J, Stuckey P (2016) Lagrangian constrained clustering. In: Proceedings of the SIAM international conference on data mining, pp 288–296

    Google Scholar 

  • Ge R, Ester M, Jin W, Davidson I (2007) Constraint-driven clustering. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 320–329

    Google Scholar 

  • Geng L, Hamilton H (2006) Interestingness measures for data mining: a survey. ACM Comput Surv (CSUR) 38(3):9

    Article  Google Scholar 

  • Giacometti A, Soulet A (2016) Frequent pattern outlier detection without exhaustive mining. In: Proceedings of the Pacific-Asia conference on knowledge discovery and data mining, pp 196–207

    Google Scholar 

  • Gilpin S, Davidson I (2011) Incorporating SAT solvers into hierarchical clustering algorithms: an efficient and flexible approach. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 1136–1144

    Google Scholar 

  • Gilpin S, Davidson I (2017) A flexible ILP formulation for hierarchical clustering. Artif Intell 244:95–109

    Article  MathSciNet  MATH  Google Scholar 

  • Gonzalez T (1985) Clustering to minimize the maximum intercluster distance. Theor Comput Sci 38(2):293–306

    Article  MathSciNet  MATH  Google Scholar 

  • Grira N, Crucianu M, Boujemaa N (2006) Fuzzy clustering with pairwise constraints for knowledge-driven image categorization. IEE Proc Vis Image Signal Process (CORE B) 153(3):299–304

    Article  Google Scholar 

  • Guns T, Nijssen S, De Raedt L (2013) \(k\)-pattern set mining under constraints. IEEE Trans Knowl Data Eng 25(2):402–418

    Article  Google Scholar 

  • Guns T, Dao TBH, Vrain C, Duong KC (2016) Repetitive branch-and-bound using constraint programming for constrained minimum sum-of-squares clustering. In: Proceedings of the European conference on artificial intelligence, pp 462–470

    Google Scholar 

  • Hadjitodorov ST, Kuncheva LI (2007) Selecting diversifying heuristics for cluster ensembles. In: Proceedings of the international workshop on multiple classifier systems, pp 200–209

    Google Scholar 

  • Hansen P, Delattre M (1978) Complete-link cluster analysis by graph coloring. J Am Stat Assoc 73(362):397–403

    Article  MATH  Google Scholar 

  • Hansen P, Jaumard B (1997) Cluster analysis and mathematical programming. Math Program 79(1–3):191–215

    MathSciNet  MATH  Google Scholar 

  • Hiep T, Duc N, Trung B (2016) Local search approach for the pairwise constrained clustering problem. In: Proceedings of the symposium on information and communication technology, pp 115–122

    Google Scholar 

  • Hoi S, Jin R, Lyu M (2007) Learning nonparametric kernel matrices from pairwise constraints. In: International conference on machine learning, pp 361–368

    Google Scholar 

  • Hoi S, Liu W, Chang SF (2008) Semi-supervised distance metric learning for collaborative image retrieval. In: Proceedings of the IEEE international conference on computer vision and pattern recognition

    Google Scholar 

  • Hoi S, Liu W, Chang SF (2010) Semi-supervised distance metric learning for collaborative image retrieval and clustering. ACM Trans Multimed Comput Commun Appl 6(3):18

    Article  Google Scholar 

  • Huang H, Cheng Y, Zhao R (2008) A semi-supervised clustering algorithm based on must-link set. In: Proceedings of the international conference on advanced data mining and applications, pp 492–499

    Google Scholar 

  • Iqbal A, Moh’d A, Zhan Z (2012) Semi-supervised clustering ensemble by voting. In: Proceedings of the international conference on information and communication systems, pp 1–5

    Google Scholar 

  • Jain A, Murty M, Flynn P (1999) Data clustering: a review. ACM Comput Surv 31(3):264–323

    Article  Google Scholar 

  • Kamvar S, Klein D, Manning C (2003) Spectral learning. In: Proceedings of the international joint conference on artificial intelligence, pp 561–566

    Google Scholar 

  • Ke Y, Cheng J, Yu JX (2009) Top-k correlative graph mining. In: Proceedings of the SIAM international conference on data mining, pp 1038–1049

    Google Scholar 

  • Khiari M, Boizumault P, Crémilleux B (2010) Constraint programming for mining n-ary patterns. In: Proceedings of the international conference on principles and practice of constraint programming, pp 552–567

    Google Scholar 

  • Kittler J (1998) On combining classifiers. IEEE Trans Pattern Anal Mach Intell 20(3):226–239

    Article  Google Scholar 

  • Klein D, Kamvar S, Manning C (2002) From instance-level constraints to space-level constraints: making the most of prior knowledge in data clustering. In: Proceedings of the international conference on machine learning, pp 307–314

    Google Scholar 

  • Kopanas I, Avouris N, Daskalaki S (2002) The role of domain knowledge in a large scale data mining project. In: Proceedings of the Hellenic conference on artificial intelligence, pp 288–299

    Google Scholar 

  • Kuhn H, Tucker A (1951) Nonlinear programming. In: Proceedings of the Berkeley symposium, pp 481–492

    Google Scholar 

  • Kulis B, Basu S, Dhillon I, Mooney R (2005) Semi-supervised graph clustering: a kernel approach. In: Proceedings of the international conference on machine learning, pp 457–464

    Google Scholar 

  • Kulis B, Basu S, Dhillon I, Mooney R (2009) Semi-supervised graph clustering: a kernel approach. Mach Learn 74(1):1–22

    Article  Google Scholar 

  • Kuo CT, Ravi S, Dao TBH, Vrain C, Davidson I (2017) A framework for minimal clustering modification via constraint programming. In: Proceedings of the AAAI conference on artificial intelligence, pp 1389–1395

    Google Scholar 

  • LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521:436–444

    Article  Google Scholar 

  • Li T, Ding C (2008) Weighted consensus clustering. In: Proceedings of the SIAM international conference on data mining, pp 798–809

    Google Scholar 

  • Li T, Ding C, Jordan M (2007) Solving consensus and semi-supervised clustering problems using nonnegative matrix factorization. In: Proceedings of the IEEE international conference on data mining, pp 577–582

    Google Scholar 

  • Li Z, Liu J, Tang X (2008) Pairwise constraint propagation by semidefinite programming for semi-supervised classification. In: Proceedings of the international conference on machine learning, pp 576–583

    Google Scholar 

  • Li Z, Liu J, Tang X (2009) Constrained clustering via spectral regularization. In: Proceedings of the international conference on computer vision and pattern recognition, pp 421–428

    Google Scholar 

  • Lu Z, Carreira-Perpinán M (2008) Constrained spectral clustering through affinity propagation. In: IEEE conference on computer vision and pattern recognition, pp 1–8

    Google Scholar 

  • Lu Z, Ip H (2010) Constrained spectral clustering via exhaustive and efficient constraint propagation. In: Proceedings of the European conference on computer vision, pp 1–14

    Google Scholar 

  • Métivier KP, Boizumault P, Crémilleux B, Khiari M, Loudni S (2012) Constrained clustering using SAT. In: Proceedings of the international symposium on advances in intelligent data analysis, pp 207–218

    Google Scholar 

  • Monti S, Tamayo P, Mesirov J, Golub T (2003) Consensus clustering: a resampling-based method for class discovery and visualization of gene expression microarray data. Mach Learn 52(1):91–118

    Article  MATH  Google Scholar 

  • Mueller M, Kramer S (2010) Integer linear programming models for constrained clustering. In: Proceedings of the international conference on discovery science, pp 159–173

    Google Scholar 

  • Ng M (2000) A note on constrained k-means algorithms. Pattern Recognit 33(3):515–519

    Article  Google Scholar 

  • Ouali A, Loudni S, Lebbah Y, Boizumault P, Zimmermann A, Loukil L (2016) Efficiently finding conceptual clustering models with integer linear programming. In: Proceedings of the international joint conference on artificial intelligence, pp 647–654

    Google Scholar 

  • Pedrycz W (2002) Collaborative fuzzy clustering. Pattern Recognit Lett 23(14):1675–1686

    Article  MATH  Google Scholar 

  • Pelleg D, Baras D (2007) K-means with large and noisy constraint sets. In: Proceedings of the European conference on machine learning, pp 674–682

    Google Scholar 

  • Raj S, Raj P, Ravindran B (2013) Incremental constrained clustering: a decision theoretic approach. In: Proceedings of the Pacific-Asia conference on knowledge discovery and data mining, pp 475–486

    Google Scholar 

  • Rand W (1971) Objective criteria for the evaluation of clustering methods. J Am Stat Assoc 66(366):846–850

    Article  Google Scholar 

  • Rangapuram S, Hein M (2012) Constrained 1-spectral clustering. In: Proceedings of the International Conference on Artificial Intelligence and Statistics, pp 1143–1151

    Google Scholar 

  • Rauber A, Pampalk E, Paralič J (2000) Empirical evaluation of clustering algorithms. J Inf Organ Sci 24(2):195–209

    MATH  Google Scholar 

  • Rossi F, van Beek P, Walsh T (eds) (2006) Handbook of constraint programming. Foundations of artificial intelligence. Elsevier B.V, New York

    MATH  Google Scholar 

  • Rutayisire T, Yang Y, Lin C, Zhang J (2011) A modified cop-kmeans algorithm based on sequenced cannot-link set. In: Proceedings of the international conference on rough sets and knowledge technology, pp 217–225

    Google Scholar 

  • Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905

    Article  Google Scholar 

  • Soulet A, Raïssi C, Plantevit M, Cremilleux B (2011) Mining dominant patterns in the sky. In: Proceedings of the IEEE international conference on data mining, pp 655–664

    Google Scholar 

  • Srivastava A, Zou J, Adams R, Sutton C (2016) Clustering with a reject option: interactive clustering as bayesian prior elicitation. In: Proceedings of the ICML workshop on human interpretability in machine learning, pp 16–20

    Google Scholar 

  • Strehl A, Ghosh J (2002) Cluster ensembles-a knowledge reuse framework for combining multiple partitions. J Mach Learn Res 3:583–617

    MathSciNet  MATH  Google Scholar 

  • Tan W, Yang Y, Li T (2010) An improved cop-k means algorithm for solving constraint violation. In: Proceedings of the international FLINS conference on foundations and applications of computational intelligence, pp 690–696

    Google Scholar 

  • Tang W, Xiong H, Zhong S, Wu J (2007) Enhancing semi-supervised clustering: a feature projection perspective. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 707–716

    Google Scholar 

  • van Leeuwen M (2014) Interactive data exploration using pattern mining. Interactive knowledge discovery and data mining in biomedical informatics, vol 9. Lecture notes in computer science. Springer, Berlin, pp 169–182

    Google Scholar 

  • van Leeuwen M, Ukkonen A (2013) Discovering skylines of subgroup sets. In: Proceedings of the joint European conference on machine learning and knowledge discovery in databases, pp 272–287

    Google Scholar 

  • van Leeuwen M, De Bie T, Spyropoulou E, Mesnage C (2016) Subjective interestingness of subgraph patterns. Mach Learn 105(1):41–75

    Article  MathSciNet  MATH  Google Scholar 

  • von Luxburg U (2007) A tutorial on spectral clustering. Stat Comput 17(4):395–416

    Article  MathSciNet  Google Scholar 

  • Vu VV, Labroche N (2017) Active seed selection for constrained clustering. Intell Data Anal 21(3):537–552

    Article  Google Scholar 

  • Wagstaff K, Cardie C (2000) Clustering with instance-level constraints. In: Proceedings of the international conference on machine learning, pp 1103–1110

    Google Scholar 

  • Wagstaff K, Cardie C, Rogers S, Schroedl S (2001) Constrained k-means clustering with background knowledge. In: Proceedings of the international conference on machine learning, pp 577–584

    Google Scholar 

  • Wagstaff K, Basu S, Davidson I (2006) When is constrained clustering beneficial, and why? In: Proceedings of the National Conference on Artificial Intelligence and the Eighteenth Innovative Applications of Artificial Intelligence Conference

    Google Scholar 

  • Wang X, Davidson I (2010a) Active spectral clustering. In: Proceedings of the IEEE international conference on data mining, pp 561–568

    Google Scholar 

  • Wang X, Davidson I (2010b) Flexible constrained spectral clustering. In: Proceedings of the ACM SIGKDD international conference on knowledge discovery and data mining, pp 563–572

    Google Scholar 

  • Wang J, Han J, Lu Y, Tzvetkov P (2005) TFP: an efficient algorithm for mining top-k frequent closed itemsets. IEEE Trans Knowl Data Eng 17(5):652–663

    Article  Google Scholar 

  • Wang X, Qian B, Davidson I (2014) On constrained spectral clustering and its applications. Data Min Knowl Discov 28(1):1–30

    Article  MathSciNet  MATH  Google Scholar 

  • Wemmert C, Gançarski P, Korczak J (2000) A collaborative approach to combine multiple learning methods. Int J Artif Intell Tools 9(1):59–78

    Article  Google Scholar 

  • Xiao W, Yang Y, Wang H, Li T, Xing H (2016) Semi-supervised hierarchical clustering ensemble and its application. Neurocomputing 173(3):1362–1376

    Article  Google Scholar 

  • Xing E, Ng A, Jordan M, Russell S (2002) Distance metric learning learning, with application to clustering with side-information. In: Proceedings of the international conference on neural information processing systems, pp 521–528

    Google Scholar 

  • Xu R, Wunsch D (2005) Survey of clustering algorithms. IEEE Trans Neural Netw 16(3):645–678

    Article  Google Scholar 

  • Yang Y, Tan W, Li T, Ruan D (2012) Consensus clustering based on constrained self-organizing map and improved cop-kmeans ensemble in intelligent decision support systems. Knowl-Based Syst 32:101–115

    Article  Google Scholar 

  • Yang F, Li T, Zhou Q, Xiao H (2017) Cluster ensemble selection with constraints. Neurocomputing 235:59–70

    Article  Google Scholar 

  • Yao H, Hamilton H (2006) Mining itemset utilities from transaction databases. Data Knowl Eng 59(3):603–626

    Article  Google Scholar 

  • Yi J, Jin R, Jain A, Yang T, Jain S (2012) Semi-crowdsourced clustering: generalizing crowd labeling by robust distance metric learning. In: Proceedings of the international conference on neural information processing systems, pp 1772–1780

    Google Scholar 

  • Yu ZW, Wongb HS, You J, Yang QM, Liao HY (2011) Knowledge based cluster ensemble for cancer discovery from biomolecular data. IEEE Trans NanoBiosci 10(2):76–85

    Article  Google Scholar 

  • Zha H, He X, Ding CHQ, Gu M, Simon HD (2001) Spectral relaxation for k-means clustering. In: Proceedings of the international conference on neural information processing systems, pp 1057–1064

    Google Scholar 

  • Zhang T, Ando R (2006) Analysis of spectral kernel design based semi-supervised learning. In: Proceedings of the international conference on neural information processing systems, pp 1601–1608

    Google Scholar 

  • Zhi W, Wang X, Qian B, Butler P, Ramakrishnan N, Davidson I (2013) Clustering with complex constraints - algorithms and applications. In: Proceedings of the AAAI conference on artificial intelligence, pp 1056–1062

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pierre Gançarski .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Gançarski, P., Dao, TBH., Crémilleux, B., Forestier, G., Lampert, T. (2020). Constrained Clustering: Current and New Trends. In: Marquis, P., Papini, O., Prade, H. (eds) A Guided Tour of Artificial Intelligence Research. Springer, Cham. https://doi.org/10.1007/978-3-030-06167-8_14

Download citation

Publish with us

Policies and ethics