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A novel density peaks clustering with sensitivity of local density and density-adaptive metric

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Abstract

The density peaks (DP) clustering approach is a novel density-based clustering algorithm. On the basis of the prior assumption of consistency for semi-supervised learning problems, we further make the assumptions of consistency for density-based clustering. The first one is the assumption of the local consistency, which means nearby points are likely to have the similar local density; the second one is the assumption of the global consistency, which means points on the same high-density area (or the same structure, i.e., the same cluster) are likely to have the same label. According to the first assumption, we provide a new option based on the sensitivity of the local density for the local density. In addition, we redefine \( \delta \) and redesign the assignation strategy based on a new density-adaptive metric according to the second assumption. We compare the performance of our algorithm with traditional clustering schemes, including DP, K-means, fuzzy C-means, Gaussian mixture model, and self-organizing maps. Experiments on different benchmark data sets demonstrate the effectiveness of the proposed algorithm.

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References

  1. Ankerst M, Breunig MM, Kriegel HP et al (1999) OPTICS: ordering points to identify the clustering structure. In: Proceedings of the ACM international conference on management of data, pp 49–60

  2. Backer E, Jain AK (1981) A clustering performance measure based on fuzzy set decomposition. IEEE Trans Pattern Anal Mach Intell 3(1):66–75

    Article  MATH  Google Scholar 

  3. Chen G, Zhang X, Wang ZJ et al (2015) Robust support vector data description for outlier detection with noise or uncertain data. Knowl-Based Syst 90:129–137

    Article  Google Scholar 

  4. Chen WJ, Shao YH, Hong N (2014) Laplacian smooth twin support vector machine for semi-supervised classification. Int J Mach Learn Cybern 5(3):459–468

    Article  Google Scholar 

  5. Chen Z, Qi Z, Meng F et al (2015) Image segmentation via improving clustering algorithms with density and distance. Proc Comput Sci 55:1015–1022

    Article  Google Scholar 

  6. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B (Methodological) 39(1):1–38

    MathSciNet  MATH  Google Scholar 

  7. Du M, Ding S, Jia H (2016) Study on density peaks clustering based on k-nearest neighbors and principal component analysis. Knowl-Based Syst 99:135–145

    Article  Google Scholar 

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

  9. Fernández A, García S, del Jesus MJ et al (2008) A study of the behaviour of linguistic fuzzy rule based classification systems in the framework of imbalanced data-sets. Fuzzy Sets Syst 159(18):2378–2398

    Article  MathSciNet  Google Scholar 

  10. Güvenir HA, Demiröz G, Ilter N (1998) Learning differential diagnosis of erythemato-squamous diseases using voting feature intervals. Artif Intell Med 13(3):147–165

    Article  Google Scholar 

  11. He Q, Jin X, Du C et al (2014) Clustering in extreme learning machine feature space. Neurocomputing 128:88–95

    Article  Google Scholar 

  12. Iam-On N, Boongoen T, Kongkotchawan N (2014) A new link-based method to ensemble clustering and cancer microarray data analysis. Int J Collab Intell 1(1):45–67

    Google Scholar 

  13. Jain AK, Law MC (2005) Data clustering: a user’s Dilemma. In: Proceedings of first international conference of the pattern recognition and machine intelligence, pp 20–22

  14. Jia H, Ding S, Meng L et al (2014) A density-adaptive affinity propagation clustering algorithm based on spectral dimension reduction. Neural Comput Appl 25(7–8):1557–1567

    Article  Google Scholar 

  15. Jiang X, Zhang W (2016) Structure learning for weighted networks based on Bayesian nonparametric models. Int J Mach Learn Cybern 7(3):479–489

    Article  Google Scholar 

  16. Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43(1):59–69

    Article  MATH  Google Scholar 

  17. Liang Z, Chen P (2016) Delta-density based clustering with a divide-and-conquer strategy: 3DC clustering. Pattern Recogn Lett 73:52–59

    Article  Google Scholar 

  18. Lu K, Xia S, Xia C (2015) Clustering based road detection method. In: Proceedings of the 34th Chinese control conference, pp 3874–3879

  19. Ma T, Wang Y, Tang M et al (2016) LED: a fast overlapping communities detection algorithm based on structural clustering. Neurocomputing 207:488–500

    Article  Google Scholar 

  20. MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, pp 281–297

  21. Mangasarian OL, Street WN, Wolberg WH (1995) Breast cancer diagnosis and prognosis via linear programming. Oper Res 43(4):570–577

    Article  MathSciNet  MATH  Google Scholar 

  22. Mohamad IB, Usman D (2013) Standardization and its effects on k-means clustering algorithm. Res J Appl Sci Eng Technol 6(17):3299–3303

    Article  Google Scholar 

  23. Ng AY, Jordan MI, Weiss Y (2002) On spectral clustering: analysis and an algorithm. In: Proceedings of advances in neural information processing systems, pp 849–856

  24. Pan Z, Lei J, Zhang Y et al (2016) Fast motion estimation based on content property for low-complexity H.265/HEVC encoder. IEEE Trans Broadcast 62(3):675–684

    Article  Google Scholar 

  25. Rodriguez A, Laio A (2014) Clustering by fast search and find of density peaks. Science 344(6191):1492–1496

    Article  Google Scholar 

  26. Sigillito VG, Wing SP, Hutton LV et al (1989) Classification of radar returns from the ionosphere using neural networks. Johns Hopkins APL Tech Dig 10(3):262–266

    Google Scholar 

  27. Wang B, Zhang J, Liu Y et al (2017) Density peaks clustering based integrate framework for multi-document summarization. CAAI Trans Intell Technol 2(1):26–30

    Article  Google Scholar 

  28. Wang L, Bo LF, Jiao LC (2007) Density-sensitive spectral clustering. Acta Electron Sin 35(8):1577–1581

    Google Scholar 

  29. Wolberg WH, Street WN, Heisey DM et al (1995) Computerized breast cancer diagnosis and prognosis from fine-needle aspirates. Arch Surg 130(5):511–516

    Article  Google Scholar 

  30. Xu X, Ding S, Du M et al (2016) DPCG: an efficient density peaks clustering algorithm based on grid. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-016-0603-2

    Google Scholar 

  31. Xu X, Law R, Chen W et al (2016) Forecasting tourism demand by extracting fuzzy Takagi–Sugeno rules from trained SVMs. CAAI Trans Intell Technol 1(1):30–42

    Article  Google Scholar 

  32. Yang P, Zhu Q, Huang B (2011) Spectral clustering with density sensitive similarity function. Knowl-Based Syst 24(5):621–628

    Article  Google Scholar 

  33. Zelnik-Manor L, Perona P (2004) Self-tuning spectral clustering. In: Proceedings of advances in neural information processing systems, pp 1601–1608

  34. Zhang W, Li J (2015) Extended fast search clustering algorithm: widely density clusters, no density peaks. https://doi.org/10.5121/csit.2015.50701. arXiv preprint arXiv:1505.05610

  35. Zhang Y, Xia Y, Liu Y et al (2015) Clustering sentences with density peaks for multi-document summarization. In: Proceedings of human language technologies: the 2015 annual conference of the North American Chapter of the ACL, pp 1262–1267

  36. Zhong Q, Chen F (2016) Trajectory planning for biped robot walking on uneven terrain–Taking stepping as an example. CAAI Trans Intell Technol 1(3):197–209

    Article  MathSciNet  Google Scholar 

  37. Zhou D, Bousquet O, Lal TN et al (2004) Learning with local and global consistency. In: Proceedings of advances in neural information processing systems, pp 321–328

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 61672522 and 61379101), and the National Key Basic Research Program of China (No. 2013CB329502).

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Authors and Affiliations

  1. School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, 221116, China

    Mingjing Du & Shifei Ding

  2. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100090, China

    Shifei Ding & Zhongzhi Shi

  3. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Yu Xue

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  1. Mingjing Du
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  2. Shifei Ding
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Correspondence to Shifei Ding.

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Du, M., Ding, S., Xue, Y. et al. A novel density peaks clustering with sensitivity of local density and density-adaptive metric. Knowl Inf Syst 59, 285–309 (2019). https://doi.org/10.1007/s10115-018-1189-7

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  • DOI: https://doi.org/10.1007/s10115-018-1189-7

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