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Fast density peaks clustering algorithm in polar coordinate system

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Abstract

Density peaks clustering (DPC) algorithm provides an efficient method to quickly find cluster centers with decision graphs. In recent years, due to its unique parameters, no iteration, and good robustness, it has been widely studied and applied. However, it also has some shortcomings, such as no adaptability, inadaptability to high-dimensional data and accuracy is easily affected. For reducing the higher time complexity of DPC, we introduce the polar coordinates to DPC (PC-DPC). Firstly, obtain the distance from every point to third-party point and the cosine value of the angle formed with the third-party vector, and reorder the points by distances and cosine values. Then, select other points in the adjacent sequence number of each point to calculate distances, and build a sparse distance matrix. Finally, the sparse distance matrix is used as the input of DPC to obtain clustering results. Theoretical analysis and experiments show that, compared with DPC and other algorithms, PC-DPC greatly reduces running time of DPC while maintaining clustering precision.

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References

  1. Hilbert M, Lopez P (2011) The World’s technological capacity to store, communicate, and compute information. Since 332(6025):60–65

    Article  Google Scholar 

  2. Chen XQ, Zhou LJ, Liu YZ (2017) A survey of clustering algorithms. Integ Technol 6(003):41–49

    Google Scholar 

  3. MacQueen JB (1967) Some methods for classification and analysis of multivariate observations. Proceed Fifth Berkeley Symposium Math Stat Probability:281–297

  4. Hae-Sang, Park, Chi-Hyuck, et al. A simple and fast algorithm for k-medoids clustering - sciencedirect. Exp Syst Appl, 2009, 36(Part 2): 3336–3341

  5. Karypis G, Han EH, Kumar V (1999) Chameleon: hierarchical clustering using dynamic modeling. Computer 32(8):68–75

    Article  Google Scholar 

  6. Zhang T, Ramakrishnan R, Livny M (1996) BIRCH: an efficient data clustering method for very large databases. ACM SIGMOD Rec 25(2):103–114

    Article  Google Scholar 

  7. Ester M, Kriegel HP, Sander J et al (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. Proceed 2nd Int Conf Knowledge Discovery Data Mining:226–231

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

    Article  Google Scholar 

  9. Wang W, Yang J, Muntz R (1997) STING: A statistical information grid approach to spatial data mining. Proceed 23rd Int Conf Very Large Data Bases:186–195

  10. Agrawal R, Gehrke J, Gunopulos D et al (1998) Automatic subspace clustering of high dimensional data for data mining applications. Proceed 1998 ACM SIGMOD Int Conf Manag Data:94–105

  11. Xing CZ, Zhao QY, Wang X et al (2017) Research on accelerated EM algorithm based on robust Gaussian mixture model. Comput Appl Res 04:1042–1046

    Google Scholar 

  12. Sun YF, Lu YS (2007) A grid based subspace clustering algorithm for high dimensional data streams. Comput Sci (04):199–203+221

  13. et al (2018) A survey of clustering with deep learning: from the perspective of network architecture. IEEE Access 6:39501–39514Min E, Guo X, Liu Qet al A survey of clustering with deep learning: from the perspective of network architecture. IEEE Access, 2018, 6:39501–39514

  14. Luxburg UV (2007) A tutorial on spectral clustering. Stat Comput 17(4):395–416

    Article  MathSciNet  Google Scholar 

  15. Zhao J, Tang J, Fan T, Li C, Xu L (2020) Density peaks clustering based on circular partition and grid similarity. Concurr Comput Pract Exp 32(7):e5567

    Article  Google Scholar 

  16. Yu D, Liu G, Guo M, Liu X, Yao S (2019) Density peaks clustering based on weighted local density sequence and nearest neighbor assignment. IEEE Access 7:34301–34317

    Article  Google Scholar 

  17. 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 

  18. Gong S F, Zhang Y F. EDDPC: an efficient distributed density center clustering algorithm. Comput Res Dev 2016, (06): 1400–1409

  19. Dean J, Ghemawat S (2008) MapReduce: simplified data processing on large clusters. Commun ACM 51(1):107–113

    Article  Google Scholar 

  20. Ji X, Yao S, Zhao P (2020) Density peak clustering algorithm optimized by relative neighborhood and pruning strategy. J Auto 46(3):562–575

    MATH  Google Scholar 

  21. Xu X, Ding S, Du M et al (2018) DPCG: an efficient density peaks clustering algorithm based on grid. Int J Mach Learn Cybern 9(5):743–754

    Article  Google Scholar 

  22. Xu X, Ding S, Sun T (2018) A fast density peaks clustering algorithm based on pre-screening. 2018 IEEE Int Conf Big Data and Smart Comput (BigComp):513–516

  23. Chen Y, Hu X, Fan W, Shen L, Zhang Z, Liu X, du J, Li H, Chen Y, Li H (2020) Fast density peak clustering for large scale data based on kNN. Knowl-Based Syst 187:104824

    Article  Google Scholar 

  24. Xu X, Ding S, Wang Y, Wang L, Jia W (2021) A fast density peaks clustering algorithm with sparse search. Inf Sci 554:61–83

    Article  MathSciNet  Google Scholar 

  25. Xu X, Ding S, Shi Z (2018) An improved density peaks clustering algorithm with fast finding cluster centers. Knowl-Based Syst 158:65–74

    Article  Google Scholar 

  26. Vinh NX, Epps J, Bailey J (2010) Information theoretic measures for clusterings comparison: variants, properties, normalization and correction for chance. J Mach Learn Res 11:2837–2854

    MathSciNet  MATH  Google Scholar 

  27. Yang Y, Jin F, Kamel M (2008) A survey of clustering validity evaluation. Comput Appl Res (06, 1630):–1632+1638

  28. 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. Inform Sci An Int J 354:19–40

    Google Scholar 

  29. Gionis A, Mannila H, Tsaparas P (2007) Clustering aggregation. ACM Trans Knowl Discov Data 1(1):4

    Article  Google Scholar 

  30. Tu B, Zhang X, Kang X, Zhang G, Li S (2019) Density peak-based Noisy label detection for hyperspectral image classification. IEEE Trans Geosci Remote Sens 57(3):1573–1584

    Article  Google Scholar 

  31. Zeng X, Chen A, Zhou M (2019) Color perception algorithm of medical images using density peak based hierarchical clustering. Biomed Signal Process Control 48:69–79

    Article  Google Scholar 

  32. Yan H, Wang L, Lu Y (2019) Identifying cluster centroids from decision graph automatically using a statistical outlier detection method. Neurocomputing 329:348–358

    Article  Google Scholar 

  33. Xu X, Ding S, Wang Y (2020) Optimized density peaks clustering algorithm based on dissimilarity measure. J Software 31(12):1–13

    MATH  Google Scholar 

  34. Xu X, Ding S, Sun T et al (2018) Large-scale density peaks clustering algorithm based on grid screening. J Comput Res Dev 55(11):2419–2429

    Google Scholar 

  35. Chen JY, He HH (2016) A fast density-based data stream clustering algorithm with cluster centers self-determined for mixed data. Inf Sci 345:271–293

    Article  Google Scholar 

  36. Wang M, Min F, Zhang ZH, Wu YX (2017) Active learning through density clustering. Expert Syst Appl 85:305–317

    Article  Google Scholar 

  37. Abdul MM, Huang JZ, Wei C et al (2018) I-nice: a new approach for identifying the number of clusters and initial cluster Centres. Inform Ences 466:129–151

    Google Scholar 

  38. Du J, Ma Y, Huang H (2021) Clustering algorithm based on local gravity and distance. Comput Appl:1–9

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant no.61976216 and no.61672522.

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Authors and Affiliations

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

    Chao Li, Shifei Ding, Xiao Xu, Shuying Du & Tianhao Shi

  2. Mine Digitization Engineering Research Center of Ministry of Education of the People’s Republic of China, Xuzhou, 221116, China

    Shifei Ding

Authors
  1. Chao Li
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  2. Shifei Ding
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  3. Xiao Xu
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  4. Shuying Du
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  5. Tianhao Shi
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Correspondence to Shifei Ding or Xiao Xu.

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Li, C., Ding, S., Xu, X. et al. Fast density peaks clustering algorithm in polar coordinate system. Appl Intell 52, 14478–14490 (2022). https://doi.org/10.1007/s10489-022-03360-3

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