Skip to main content
Log in

Density peaks clustering using geodesic distances

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Density peaks clustering (DPC) algorithm is a novel clustering algorithm based on density. It needs neither iterative process nor more parameters. However, it cannot effectively group data with arbitrary shapes, or multi-manifold structures. To handle this drawback, we propose a new density peaks clustering, i.e., density peaks clustering using geodesic distances (DPC-GD), which introduces the idea of the geodesic distances into the original DPC method. By experiments on synthetic data sets, we reveal the power of the proposed algorithm. By experiments on image data sets, we compared our algorithm with classical methods (kernel k-means algorithm and spectral clustering algorithm) and the original algorithm in accuracy and NMI. Experimental results show that our algorithm is feasible and effective.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Wen X, Shao L, Xue Y et al (2015) A rapid learning algorithm for vehicle classification. Inf Sci 295:395–406

    Article  Google Scholar 

  2. 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 

  3. Jia H, Ding S, Du M et al (2016) Approximate normalized cuts without Eigen-decomposition. Inf Sci 374:135–150

    Article  Google Scholar 

  4. Zheng Y, Jeon B, Xu D et al (2015) Image segmentation by generalized hierarchical fuzzy C-means algorithm. J Intell Fuzzy Syst 28(2):961–973

    Google Scholar 

  5. Han J, Kamber M (2000) Data mining: concepts and techniques. Morgan Kaufman, San Francisco

    MATH  Google Scholar 

  6. Zhang Y, Sun X, Wang B (2016) Efficient algorithm for k-barrier coverage based on integer linear programming. China Commun 13(7):16–23

    Article  Google Scholar 

  7. Li X, Liang Y, Cai Y (2016) CC-K-means: a candidate centres-based K-means algorithm for text data. Int J Collab Intell 1(3):189–204

    Google Scholar 

  8. Dong CR, Ng WWY, Wang XZ et al (2014) An improved differential evolution and its application to determining feature weights in similarity-based clustering. Neurocomputing 146:95–103

    Article  Google Scholar 

  9. Xu L, Ding S, Xu X et al (2016) Self-adaptive extreme learning machine optimized by rough set theory and affinity propagation clustering. Cognit Comput 8(4):720–728

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. Chen GJ, Zhang XY, 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 

  12. Lu KY, Xia SY, Xia C (2015) Clustering based road detection method. In: Proceedings of the 34th Chinese Control Conference (CCC). pp 3874–3879

  13. Xie K, Wu J, Yang W, Sun CY (2015) K-means clustering based on density for scene image classification. In: Proceedings of the 2015 Chinese Intelligent Automation Conference. pp 379–386

  14. Du M, Ding S, Xue Y (2017) A robust density peaks clustering algorithm using fuzzy neighborhood. Int J Mach Learn Cybern. doi:10.1007/s13042-017-0636-1

    Google Scholar 

  15. 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

  16. Tang GH, Jia S, Li J (2015) An enhanced density peak-based clustering approach for hyperspectral band selection. In: Proceedings of the international geoscience and remote sensing symposium. pp 1116–1119

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

  18. Wang XF, Xu YF (2015) Fast clustering using adaptive density peak detection. Stat Methods Med Res. doi:10.1177/0962280215609948

    Google Scholar 

  19. 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 

  20. Tenenbaum JB, Silva VD, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Sci 290(5500):2319–2323

    Article  Google Scholar 

  21. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Sci 290(5500):2323–2326

    Article  Google Scholar 

  22. Liu Z, Wang W, Jin Q et al (2016) Manifold alignment using discrete surface Ricci flow. CAAI Trans Intell Technol 1(3):285–292

    Article  Google Scholar 

  23. Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15(6):1373–1396

    Article  MATH  Google Scholar 

  24. Sampat MP, Wang Z, Gupta S et al (2009) Complex wavelet structural similarity: a new image similarity index. IEEE Trans Image Process 18(11):2385–2401

    Article  MathSciNet  MATH  Google Scholar 

  25. Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 7:2399–2434

    MathSciNet  MATH  Google Scholar 

  26. Ding SF, Hua XP (2014) Recursive least squares projection twin support vector machines for nonlinear classification. Neurocomputing 130:3–9

    Article  Google Scholar 

  27. 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 

  28. 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 

  29. Ng AY, Jordan MI, Weiss Y (2002) On spectral clustering: analysis and an algorithm. Proc Adv Neural Inf Process Syst 2:849–856

    Google Scholar 

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

    Google Scholar 

  31. Zelnik-Manor L, Perona P (2004) Self-tuning spectral clustering. Proc Adv Neural Inf Process Syst 1601–1608

  32. Nene SA, Nayar SK, Murase H (1996) Columbia object image library (COIL-20). Technical Report CUCS-005-96. Columbia University, USA

    Google Scholar 

  33. Graham DB, Allinson NM (1998) Characterising virtual eigensignatures for general purpose face recognition. Face recognition. Springer, Berlin Heidelberg, pp 446–456

    Google Scholar 

  34. Friedman J, Hastie T, Tibshirani R (2001) The elements of statistical learning. Springer, Berlin

    MATH  Google Scholar 

  35. Ma Z, Liu Q, Sun K et al (2016) A syncretic representation for image classification and face recognition. CAAI Trans Intell Technol 1(2):173–178

    Article  Google Scholar 

  36. Zeng S, Yang X, Gou J et al (2016) Integrating absolute distances in collaborative representation for robust image classification. CAAI Trans Intell Technol 1(2):189–196

    Article  Google Scholar 

  37. Xia Z, Wang X, Sun X et al (2016) Steganalysis of LSB matching using differences between nonadjacent pixels. Multimed Tools Appl 75(4):1947–1962

    Article  Google Scholar 

  38. Gu B, Sheng VS, Wang Z et al (2015) Incremental learning for ν-support vector regression. Neural Netw 67:140–150

    Article  Google Scholar 

  39. Jia HJ, Ding SF, Meng LH et al (2014) A density-adaptive affinity propagation clustering algorithm based on spectral dimension reduction. Neural Comput Applic 25(7–8):1557–1567

    Article  Google Scholar 

  40. Wang XZ, He YL, Wang DD (2014) Non-naive bayesian classifiers for classification problems with continuous attributes. IEEE Trans Cybern 44(1):21–39

    Article  Google Scholar 

  41. Chen WY, Song YQ, Bai HJ et al (2011) Parallel spectral clustering in distributed systems. IEEE Trans Pattern Anal Mach Intell 33(3):568–586

    Article  Google Scholar 

  42. Papadimitriou CH, Steiglitz K (1998) Combinatorial optimization: algorithms and complexity. Courier Dover Publications, Mineola

    MATH  Google Scholar 

  43. Strehl A, Ghosh J (2003) Cluster ensembles- knowledge reuse framework for combining multiple partitions. J Mach Learn Res 3:583–617

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 61379101 and 61672522), the National Key Basic Research Program of China (No. 2013CB329502). The Priority Academic Program Development of Jiangsu Higer Education Institutions (PAPD), and the Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology (CICAEET).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shifei Ding.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, M., Ding, S., Xu, X. et al. Density peaks clustering using geodesic distances. Int. J. Mach. Learn. & Cyber. 9, 1335–1349 (2018). https://doi.org/10.1007/s13042-017-0648-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-017-0648-x

Keywords

Navigation