Tri-partition cost-sensitive active learning through kNN

  • Fan MinEmail author
  • Fu-Lun Liu
  • Liu-Ying Wen
  • Zhi-Heng Zhang
Methodologies and Application


Active learning differs from the training–testing scenario in that class labels can be obtained upon request. It is widely employed in applications where the labeling of instances incurs a heavy manual cost. In this paper, we propose a new algorithm called tri-partition active learning through k-nearest neighbors (TALK). The optimization objective is to minimize the total teacher and misclassification costs. First, a k-nearest neighbors classifier is employed to divide unlabeled instances into three disjoint regions. Region I contains instances for which the expected misclassification cost is lower than the teacher cost, Region II contains instances to be labeled by human experts, and Region III contains the remaining instances. Various strategies are designed to determine which instances are in Region II. Second, instances in Regions I and II are labeled and added to the training set, and the tri-partition process is repeated until all instances have been labeled. Experiments are undertaken on eight University of California, Irvine, datasets using different cost settings. Compared with the state-of-the-art cost-sensitive classification and active learning algorithms, our new algorithm generally exhibits a lower total cost.


Active learning Classification Cost k-Nearest neighbors Tri-partition 



This work is supported in part by National Natural Science Foundation of China (Grant No. 61379089) and the Natural Science Foundation of Department of Education of Sichuan Province (Grant No. 16ZA0060).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.


  1. Aha DW (1997) Lazy learning. Artif Intell Rev 11:7–10CrossRefzbMATHGoogle Scholar
  2. Basu S (2010) Semi-supervised learning. J Roy Stat Soc 6493(10):2465–2472Google Scholar
  3. Blake C, Merz CJ (1998) UCI repository of machine learning databasesGoogle Scholar
  4. Bradford JP, Kunz C, Kohavi R, Brunk C, Brodley CE (2006) Pruning decision trees with misclassification costs. Lect Notes Comput Sci 51(1398):131–136Google Scholar
  5. Brighton H, Mellish C (2001) Identifying competence-critical instances for instance-based learners. Springer 608:77–94Google Scholar
  6. Cai D, He X (2012) Manifold adaptive experimental design for text categorization. IEEE Trans Knowl Data Eng 24(4):707–719CrossRefGoogle Scholar
  7. Dasgupta S, Hsu D (2008) Hierarchical sampling for active learning. In: International conference on machine learning, pp 208–215Google Scholar
  8. Guo G, Wang H, Bell D, Bi Y, Greer K (2004) KNN model-based approach in classification. Springer, BerlinGoogle Scholar
  9. Harpale AS, Yang Y (2008) Personalized active learning for collaborative filtering. In: International ACM SIGIR conference on research and development in information retrieval, pp 91–98Google Scholar
  10. He YW, Zhang HR, Min F (2015) A teacher-cost-sensitive decision-theoretic rough set model. Springer, New YorkCrossRefGoogle Scholar
  11. Jin R, Si L (2004) A bayesian approach toward active learning for collaborative filtering, pp 278–285Google Scholar
  12. Lesot MJ, Rifqi M, Benhadda H (2009) Similarity measures for binary and numerical data: a survey. Int J Knowl Eng Soft Data Paradig 1(1):63–84CrossRefGoogle Scholar
  13. Li HX, Zhang LB, Huang B, Zhou XZ (2016) Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl Based Syst 91:241–251CrossRefGoogle Scholar
  14. Li JH, Ren Y, Mei CL, Qian YH, Yang XB (2016) A comparative study of multigranulation rough sets and concept lattices via rule acquisition. Knowl Based Syst 91:152–164CrossRefGoogle Scholar
  15. Li XN, Yi HJ, She YH, Sun BZ (2017) Generalized three-way decision models based on subset evaluation. Int J Approximate Reasoning 83:142–159MathSciNetCrossRefzbMATHGoogle Scholar
  16. Liu D, Li TR, Ruan D (2011) Probabilistic model criteria with decision-theoretic rough sets. Inf Sci 181:3709–3722MathSciNetCrossRefGoogle Scholar
  17. Liu D, Li TR, Liang DC (2014) Incorporating logistic regression to decision-theoretic rough sets for classifications. Int J Approx Reason 55:197–210MathSciNetCrossRefzbMATHGoogle Scholar
  18. Liu D, Liang D, Wang C (2016) A novel three-way decision model based on incomplete information system. Knowl-Based Syst 91:32–45CrossRefGoogle Scholar
  19. Long B, Bian J, Chapelle O, Zhang Y (2015) Active learning for ranking through expected loss optimization. IEEE Trans Knowl Data Eng 27(5):1180–1191CrossRefGoogle Scholar
  20. Long B, Chapelle O, Zhang Y, Chang Y, Zheng Z, Tseng B (2010) Active learning for ranking through expected loss optimization. In: Proceeding of the international ACM SIGIR conference on research and development in information retrieval, SIGIR 2010, Geneva, Switzerland, pp 267–274Google Scholar
  21. Mccallum A, Nigam K (1998) Employing EM and pool-based active learning for text classification. In: Fifteenth international conference on machine learning, pp 350–358Google Scholar
  22. Min F, Liu QH (2009) A hierarchical model for test-cost-sensitive decision systems. Inf Sci 179:2442–2452MathSciNetCrossRefzbMATHGoogle Scholar
  23. Quinlan JR (1986) Induction of decision trees. Mach Learn 1(1):81–106Google Scholar
  24. Quinlan JR (2014) C.45: programs for machine learning. Elsevier, AmsterdamGoogle Scholar
  25. Rand GK (1979) Decision systems for inventory management and production planning. Wiley, New YorkGoogle Scholar
  26. Saartsechansky M, Provost F (2004) Active sampling for class probability estimation and ranking. Mach Learn 54(2):153–178CrossRefzbMATHGoogle Scholar
  27. Settles B (2012) Active learning. Synth Lect Artif Intell Mach Learn 6(1):1–114MathSciNetCrossRefzbMATHGoogle Scholar
  28. Seung HS, Opper M, Sompolinsky H (1992) Query by committee. In: Proceedings of the fifth workshop on computational learning theory, vol 284, pp 287–294Google Scholar
  29. Sheng VS (2012) Studying active learning in the cost-sensitive framework. In: Hawaii international conference on system sciences, pp 1097–1106Google Scholar
  30. Tong S, Koller D (2001) Support vector machine active learning with applications to text classification. J Mach Learn Res 2(1):45–66zbMATHGoogle Scholar
  31. Turney PD (2000) Types of cost in inductive concept learning. In: Proceedings of the workshop on cost-sensitive learning at the 17th ICML, pp 1–7Google Scholar
  32. Wang M, Min F, Zhang ZH, Wu YX (2017) Active learning through density clustering. Expert Syst Appl 85:305–317CrossRefGoogle Scholar
  33. Yao YY (2012) An outline of a theory of three-way decisions. In: International conference on rough sets and current trends in computing, Springer, New York, pp 1–17Google Scholar
  34. Yao YY (2016) Three-way decisions and cognitive computing. Cognit Comput 8(4):543–554Google Scholar
  35. Yao YY (2010) Three-way decisions with probabilistic rough sets. Inf Sci 180(3):341–353MathSciNetCrossRefGoogle Scholar
  36. Zhang HR, Min F, Shi B (2016) Regression-based three-way recommendation. Inf SciGoogle Scholar
  37. Zhang HR, Min F (2016) Three-way recommender systems based on random forests. Knowl Based Syst 91:275–286CrossRefGoogle Scholar
  38. Zhang BW, Min F, Ciucci D (2015) Representative-based classification through covering-based neighborhood rough sets. Appl Intell 43(4):840–854CrossRefGoogle Scholar
  39. Zhang Y, Zhou ZH (2008) Cost-sensitive face recognition. In: IEEE conference on computer vision and pattern recognition, pp 1–8Google Scholar
  40. Zhao H, Zhu W (2014) Optimal cost-sensitive granularization based on rough sets for variable costs. Knowl Based Syst 65:72–82CrossRefGoogle Scholar
  41. Zhao Y, Yao Y, Luo F (2007) Data analysis based on discernibility and indiscernibility. Inf Sci 177(22):4959–4976CrossRefzbMATHGoogle Scholar
  42. Zhao H, Wang P, Hu QH (2016) Cost-sensitive feature selection based on adaptive neighborhood granularity with multi-level confidence. Inf Sci 366:134–149MathSciNetCrossRefGoogle Scholar
  43. Zhou ZH, Liu XY (2006) Training cost-sensitive neural networks with methods addressing the class imbalance problem. IEEE Trans Knowl Data Eng 18(1):63–77CrossRefGoogle Scholar
  44. Zhou B, Yao Y, Luo J (2014) Cost-sensitive three-way email spam filtering. J Intell Inf Syst 42(1):19–45CrossRefGoogle Scholar
  45. Zhu XQ, Wu XD (2005) Cost-constrained data acquisition for intelligent data preparation. IEEE Trans Knowl Data Eng 17(11):1542–1556CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Computer ScienceSouthwest Petroleum UniversityChengduChina

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