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A novel stratification clustering algorithm based on a new local density estimation method and an improved local inter-cluster distance measure

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Abstract

Recently clustering for datasets with different shapes, densities and noises has attracted more and more attention from scholars. However, most current clustering algorithms improve the clustering performance at the expense of the simplicity, and cannot balance well between the clustering quality and the operability for the users. To solve this problem, we propose a new algorithm called stratification clustering based on density, hierarchy and partition (SDHP) by effectively integrating the advantages of the density-based, hierarchical-based and partition-based clustering. First, a new parameter-free local density estimation strategy based on the bidirectional natural neighbor relationship named local density based on natural neighbor (NN-LD) is proposed to identify the core part of each sub-cluster. Then, a new stratification strategy based on the NN-LD Stratification-NN-LD (S-NN-LD) is proposed to divide the entire dataset into two layers, the core layer and the edge layer, to simplify the dataset structure and make the algorithm robust to noises. Next, the hierarchical-based single-linkage algorithm is adopted in the core layer to obtain the initial clustering result since it has advantages on clustering the datasets with various shapes and densities. Finally, to improve the clustering accuracy of samples in the edge layer, a combination of a new local inter-cluster distance measure based on the average of neighbor distances and the partitioning clustering is adopted to match these samples to the sub-clusters in the initial clustering result. The experiments on twenty datasets show that the SDHP has better clustering accuracy, and can be applied in practice well compared with four popular hierarchical clustering algorithms, four recent density-based clustering algorithms, and a state-of-the-art partitioning clustering algorithm. The source code can be downloaded from https://github.com/qi111678/SDHP.

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Data availability

The Aggregation, Compound, Pathbased, Spiral, R15, Flame and D31 are from the clustering basic benchmark (http://cs.uef.fi/sipu/datasets/). The Seeds, Iris, Yeast, Waveform, Wdbc, Breast, Pageblocks, Wine and Glass are the public datasets, they are available in the UCI Machine Learning Repository (http://archive.ics.uci.edu/ml/). The Circles (noise = 0), Moons, Circles (noise = 0.1), five illustrative datasets and the Chinese wine market data are available on request from the corresponding author.

References

  1. Arthur D, Vassilvitskii S (2007) k-Means plus plus: the advantages of careful seeding. In: Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms, pp 1027–1035

  2. Ahmad A, Khan SS (2020) initKmix—a novel initial partition generation algorithm for clustering mixed data using k-means-based clustering. Expert Syst Appl 167(2):114149. https://doi.org/10.1016/j.eswa.2020.114149

    Article  Google Scholar 

  3. Brunner TA, Siegrist M (2011) A consumer-oriented segmentation study in the Swiss wine market. Br Food J 113(3):353–373. https://doi.org/10.1108/00070701111116437

    Article  Google Scholar 

  4. Bruwer J, Roediger B, Herbst F (2017) Domain-specific market segmentation: a wine-related lifestyle (WRL) approach. Asia Pac J Mark Logist 29(1):4–26. https://doi.org/10.1108/apjml-10-2015-0161

    Article  Google Scholar 

  5. Bibi M, Abbasi WA, Aziz W, Khalil S, Uddin M, Iwendi C, Gadekallu TR (2022) A novel unsupervised ensemble framework using concept-based linguistic methods and machine learning for twitter sentiment analysis. Pattern Recogn Lett 158:80–86. https://doi.org/10.1016/j.patrec.2022.04.004

    Article  Google Scholar 

  6. Crespi-Vallbona M, Dimitrovski D (2016) Food markets visitors: a typology proposal. Br Food J 118(4):840–857. https://doi.org/10.1108/bfj-11-2015-0420

    Article  Google Scholar 

  7. Cheng D, Zhu Q, Huang J, Wu Q, Yang L (2019) A local cores-based hierarchical clustering algorithm for data sets with complex structures. Neural Comput Appl 31(11):8051–8068. https://doi.org/10.1007/s00521-018-3641-8

    Article  Google Scholar 

  8. Cheng D, Zhu Q, Huang J, Wu Q, Yang L (2019) A hierarchical clustering algorithm based on noise removal. Int J Mach Learn Cybern 10(7):1591–1602. https://doi.org/10.1007/s13042-018-0836-3

    Article  Google Scholar 

  9. Capo M, Perez A, Lozano J (2020) An efficient split-merge re-start for the K-means algorithm. IEEE Trans Knowl Data Eng. https://doi.org/10.1109/tkde.2020.3002926

    Article  MATH  Google Scholar 

  10. Chen L, Chen F, Liu Z, Lv M, He T, Zhang S (2022) Parallel gravitational clustering based on grid partitioning for large-scale data. Appl Intell. https://doi.org/10.1007/s10489-022-03661-7

    Article  Google Scholar 

  11. 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. https://doi.org/10.1007/s10489-022-03661-7

    Article  Google Scholar 

  12. Du G, Li X, Zhang L, Liu L, Zhao C (2021) Novel automated K-means++ algorithm for financial data sets. Math Probl Eng 2021:1–12. https://doi.org/10.1155/2021/5521119

    Article  Google Scholar 

  13. Ester M, Kriegel HP, Sander S, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: KDD’96: Proceedings of the second international conference on knowledge discovery and data mining, pp 226–231

  14. Emmendorfer LR, Canuto AMDP (2021) A generalized average linkage criterion for hierarchical agglomerative clustering. Appl Soft Comput 100:106990. https://doi.org/10.1016/j.asoc.2020.106990

    Article  Google Scholar 

  15. Fan J (2019) OPE-HCA: an optimal probabilistic estimation approach for hierarchical clustering algorithm. Neural Comput Appl 31(7):2095–2105. https://doi.org/10.1007/s00521-015-1998-5

    Article  Google Scholar 

  16. Güzel İ, Kaygun A (2020) A new non-Archimedan metric on persistent homology. Comput Stat. https://doi.org/10.1007/s00180-021-01187-z

    Article  MATH  Google Scholar 

  17. Huang T, Wang S, Zhu W (2020) An adaptive kernelized rank-order distance for clustering non-spherical data with high noise. Int J Mach Learn Cybern 11(8):1735–1747. https://doi.org/10.1007/s13042-020-01068-9

    Article  Google Scholar 

  18. Hou H, Ding S, Xu X (2022) A deep clustering by multi-level feature fusion. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-022-01557-z

    Article  Google Scholar 

  19. Jahan M, Hasan M (2021) A robust fuzzy approach for gene expression data clustering. Soft Comput 25(23):14583–14596. https://doi.org/10.1007/s00500-021-06397-7

    Article  Google Scholar 

  20. Köse E, Hocaoğlu AK (2022) Clustering with density based initialization and Bhattacharyya based merging. Turk J Electr Eng Comput Sci 30(3):502–517. https://doi.org/10.55730/1300-0632.3794

    Article  Google Scholar 

  21. Kaliji SA, Imami D, Canavari M, Gjonbalaj M, Gjokaj E (2022) Fruit-related lifestyles as a segmentation tool for fruit consumers. Br Food J 124(13):126–142. https://doi.org/10.1108/bfj-09-2021-1001

    Article  Google Scholar 

  22. Liu Y, Ma Z, Yu F (2017) Adaptive density peak clustering based on K-nearest neighbors with aggregating strategy. Knowl Based Syst 133:208–220. https://doi.org/10.1016/j.knosys.2017.07.010

    Article  Google Scholar 

  23. López-Rosas CA, Espinoza-Ortega A (2018) Understanding the motives of consumers of Mezcal in Mexico. Br Food J 120(7):1643–1656. https://doi.org/10.1108/bfj-07-2017-0381

    Article  Google Scholar 

  24. Li Y, Chu X, Tian D, Feng J, Mu W (2021) Customer segmentation using K-means clustering and the adaptive particle swarm optimization algorithm. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2021.107924

    Article  Google Scholar 

  25. Li C, Wang H, Jiang F, Zhang Y, Peng Y (2022) A new clustering mining algorithm for multi-source imbalanced location data. Inf Sci 584:50–64. https://doi.org/10.1016/j.ins.2021.10.029

    Article  Google Scholar 

  26. Mu W, Zhu H, Tian D, Feng J (2017) Profiling wine consumers by price segment: a case study in Beijing, China. Ital J Food Sci 29(3):377–397

    Google Scholar 

  27. Maciejewski G, Mokrysz S, Wróblewski Ł (2019) Segmentation of coffee consumers using sustainable values: cluster analysis on the polish coffee market. Sustainability 11(3):613. https://doi.org/10.3390/su11030613

    Article  Google Scholar 

  28. Naderipour M, Zarandi MHF, Bastani S (2022) A fuzzy cluster-validity index based on the topology structure and node attribute in complex networks. Expert Syst Appl 187:115913. https://doi.org/10.1016/j.eswa.2021.115913

    Article  Google Scholar 

  29. Paschen J, Paschen U, Kietzmann JH (2016) À votre santé-conceptualizing the AO typology for luxury wine and spirits. Int J Wine Bus Res 28(2):170–186

    Article  Google Scholar 

  30. Prabhagar MV, Punniyamoorthy M (2020) Development of new agglomerative and performance evaluation models for classification. Neural Comput Appl 32(7):2589–2600. https://doi.org/10.1007/s00521-019-04297-4

    Article  MATH  Google Scholar 

  31. Qaddoura R, Faris H, Aljarah I (2020) An efficient clustering algorithm based on the k-nearest neighbors with an indexing ratio. Int J Mach Learn Cybern 11(3):675–714. https://doi.org/10.1007/s13042-019-01027-z

    Article  Google Scholar 

  32. Qi J, Li Y, Jin H, Feng J, Mu W (2022) User value identification based on an improved consumer value segmentation algorithm. Kybernetes. https://doi.org/10.1108/K-01-2022-0049

    Article  Google Scholar 

  33. Rodriguez A, Laio A (2014) Clustering by fast search and find of density peaks. Science 344(6191):1492–1496. https://doi.org/10.1126/science.1242072

    Article  Google Scholar 

  34. Ros F, Guillaume S (2018) Protras: a probabilistic traversing sampling algorithm. Expert Syst Appl 105:65–76. https://doi.org/10.1016/j.eswa.2018.03.052

    Article  Google Scholar 

  35. Ros F, Guillaume S (2019) A hierarchical clustering algorithm and an improvement of the single linkage criterion to deal with noise. Expert Syst Appl 128:96–108. https://doi.org/10.1016/j.eswa.2019.03.031

    Article  Google Scholar 

  36. Shi J, Ye L, Li Z, Zhan D (2022) Unsupervised binary protocol clustering based on maximum sequential patterns. CMES Comput Model Eng Sci 130(1):483–498. https://doi.org/10.32604/cmes.2022.017467

    Article  Google Scholar 

  37. Turkoglu B, Uymaz SA, Kaya E (2022) Clustering analysis through artificial algae algorithm. Int J Mach Learn Cybern 13(4):1179–1196. https://doi.org/10.1007/s13042-022-01518-6

    Article  Google Scholar 

  38. Tellaroli P (2022) SingleCross-clustering: an algorithm for finding elongated clusters with automatic estimation of outliers and number of clusters. Commun Stat Simul Comput 51(5):2412–2428. https://doi.org/10.1080/03610918.2019.1697449

    Article  MathSciNet  MATH  Google Scholar 

  39. Ventorimr IM, Luchi D, Rodrigues AL, Varejão FM (2021) BIRCHSCAN: a sampling method for applying DBSCAN to large datasets. Expert Syst Appl 184(1):115518. https://doi.org/10.1016/j.eswa.2021.115518

    Article  Google Scholar 

  40. Wang G, Song Q (2016) Automatic clustering via outward statistical testing on density metrics. IEEE Trans Knowl Data Eng 28(8):1971–1985. https://doi.org/10.1109/tkde.2016.2535209

    Article  Google Scholar 

  41. Xie J, Gao H, Xie W, Liu X, Grant PW (2016) Robust clustering by detecting density peaks and assigning points based on fuzzy weighted K-nearest neighbors. Inf Sci 354:19–40. https://doi.org/10.1016/j.ins.2016.03.011

    Article  Google Scholar 

  42. Yuan X, Yu H, Liang J, Xu B (2021) A novel density peaks clustering algorithm based on K nearest neighbors with adaptive merging strategy. Int J Mach Learn Cybern 12(10):2825–2841. https://doi.org/10.1007/s13042-021-01369-7

    Article  Google Scholar 

  43. Yan J, Chen J, Zhan J, Song S, Zhang Y, Zhao M, Liu Y, Xu W (2022) Automatic identification of rock discontinuity sets using modified agglomerative nesting algorithm. Bull Eng Geol Environ. https://doi.org/10.1007/s10064-022-02724-w

    Article  Google Scholar 

  44. Yang Q, Gao W, Han G, Li Z, Tian M, Zhu S, Deng Y (2023) HCDC: a novel hierarchical clustering algorithm based on density-distance cores for data sets with varying density. Inf Syst 114:102159. https://doi.org/10.1016/j.is.2022.102159

    Article  Google Scholar 

  45. Zhu Q, Feng J, Huang J (2016) Natural neighbor: A self-adaptive neighborhood method without parameter K. Pattern Recogn Lett 80:30–36. https://doi.org/10.1016/j.patrec.2016.05.007

    Article  Google Scholar 

  46. Zhou S, Liu F (2020) A novel internal cluster validity index. J Intell Fuzzy Syst 38(4):4559–4571. https://doi.org/10.3233/jifs-191361

    Article  Google Scholar 

  47. Zhou J, Zhai L, Pantelous AA (2020) Market segmentation using high-dimensional sparse consumers data. Expert Syst Appl 145:113136. https://doi.org/10.1016/j.eswa.2019.113136

    Article  Google Scholar 

  48. Zhou Z, Si G, Sun H, Qu K, Hou W (2022) A robust clustering algorithm based on the identification of core points and KNN kernel density estimation. Expert Syst Appl 195:116573. https://doi.org/10.1016/j.eswa.2022.116573

    Article  Google Scholar 

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Acknowledgements

This study was supported by the earmarked fund for CARS-29 and the open funds of the Key Laboratory of Viticulture and Enology, Ministry of Agriculture, PR China.

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Authors and Affiliations

  1. College of Information and Electrical Engineering, China Agricultural University, 537#, No. 17, Qinghua East Road, Haidian District, Beijing, 100083, People’s Republic of China

    Jianfang Qi, Yue Li, Haibin Jin, Jianying Feng, Dong Tian & Weisong Mu

  2. Key Laboratory of Viticulture and Enology, Ministry of Agriculture, Beijing, 100083, People’s Republic of China

    Weisong Mu

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  1. Jianfang Qi
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Qi, J., Li, Y., Jin, H. et al. A novel stratification clustering algorithm based on a new local density estimation method and an improved local inter-cluster distance measure. Int. J. Mach. Learn. & Cyber. 14, 4251–4283 (2023). https://doi.org/10.1007/s13042-023-01893-8

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