Two Novel Clustering Performance Measures Based on Coherence and Relative Assignments of Clusters

  • H. J. Areiza-Laverde
  • A. E. Castro-OspinaEmail author
  • P. Rosero-Montalvo
  • D. H. Peluffo-Ordóñez
  • J. L. Rodríguez-Sotelo
  • M. A. Becerra-Botero
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 735)


This work proposes two novel alternatives for dealing with the highly important issue of the clustering performance estimation. One of the measures is the cluster coherence aimed to quantifying the normalized ratio of cuts within a graph-partitioning framework, and therefore it uses a graph-driven approach to explore the nature of data regarding the cluster assignment. The another one is the probability-based-performance quantifier, which calculates a probability value for each cluster through relative frequencies. Proposed measures are tested on some clustering representative techniques applied to real and artificial data sets. Experimental results probe the readability and robustness to noisy labels of our measures.


Cluster coherence Clustering Graph-partitioning Probabilities Relative frequencies 


  1. 1.
    Agarwal, A., Triggs, B.: Monocular human motion capture with a mixture of regressors. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition-Workshops, 2005, CVPR Workshops, p. 72. IEEE (2005)Google Scholar
  2. 2.
    Truong Cong, D., Khoudour, L., Achard, C., Meurie, C., Lezoray, O.: People re-identification by spectral classification of silhouettes. Signal Process. 90(8), 2362–2374 (2010)CrossRefzbMATHGoogle Scholar
  3. 3.
    You, L., Zhou, S., Gao, G., Leng, M.: Scalable spectral clustering combined with adjacencies merging for image segmentation. In: Wu, Y. (ed.) Advances in Computer, Communication, Control and Automation. LNEE, vol. 121. Springer, Heidelberg (2012)Google Scholar
  4. 4.
    Wang, L., Dong, M.: Multi-level low-rank approximation-based spectral clustering for image segmentation. Pattern Recogn. Lett. 33(16), 2206–2215 (2012)CrossRefGoogle Scholar
  5. 5.
    Molina-Giraldo, S., Álvarez-Meza, A., Peluffo-Ordoñez, D., Castellanos-Domínguez, G.: Image segmentation based on multi-kernel learning and feature relevance analysis. In: Advances in Artificial Intelligence-IBERAMIA 2012, pp. 501–510 (2012)Google Scholar
  6. 6.
    Ekin, A., Pankanti, S., Hampapur, A.: Initialization-independent spectral clustering with applications to automatic video analysis. In: IEEE International Conference on Acoustics, Speech, and Signal Processing, 2004, Proceedings ICASSP 2004, vol. 3, pp. 3–641. IEEE (2004)Google Scholar
  7. 7.
    Zhang, D., Lin, C., Chang, S., Smith, J.: Semantic video clustering across sources using bipartite spectral clustering. In: 2004 IEEE International Conference on Multimedia and Expo, ICME 2004, vol. 1, pp. 117–120. IEEE (2004)Google Scholar
  8. 8.
    Stella, X.Y., Shi, J.: Multiclass spectral clustering. In: ICCV, pp. 313–319 (2003)Google Scholar
  9. 9.
    Wolf, L., Shashua, A.: Feature selection for unsupervised and supervised inference: the emergence of sparsity in a weight-based approach. J. Mach. Learn. 6, 1855–1887 (2005)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Stella, X.Y., Jianbo, S.: Multiclass spectral clustering. In: ICCV 2003: Proceedings of the Ninth IEEE International Conference on Computer Vision, p. 313. IEEE Computer Society, Washington (2003)Google Scholar
  11. 11.
    MacQueen, J., et al.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, Oakland, CA, USA, pp. 281–297 (1967)Google Scholar
  12. 12.
    Bezdek, J.C., Ehrlich, R., Full, W.: Fcm: The fuzzy c-means clustering algorithm. Comput. Geosci. 10(2–3), 191–203 (1984)CrossRefGoogle Scholar
  13. 13.
    Ng, A.Y., Jordan, M.I., Weiss, Y., et al.: On spectral clustering: analysis and an algorithm. In: NIPS, vol. 14, pp. 849–856 (2001)Google Scholar
  14. 14.
    Zelnik-Manor, L., Perona, P.: Self-tuning spectral clustering. In: NIPS, vol. 17, p. 16 (2004)Google Scholar
  15. 15.
    Halkidi, M., Batistakis, Y., Vazirgiannis, M.: Cluster validity methods: part i. ACM Sigmod Rec. 31(2), 40–45 (2002)CrossRefGoogle Scholar
  16. 16.
    Amigó, E., Gonzalo, J., Artiles, J., Verdejo, F.: A comparison of extrinsic clustering evaluation metrics based on formal constraints. Inf. Retrieval 12(4), 461–486 (2009)CrossRefGoogle Scholar
  17. 17.
    Beauchemin, M.: A density-based similarity matrix construction for spectral clustering. Neurocomputing 151, 835–844 (2015)CrossRefGoogle Scholar
  18. 18.
    Chen, G., Jaradat, S.A., Banerjee, N., Tanaka, T.S., Ko, M.S., Zhang, M.Q.: Evaluation and comparison of clustering algorithms in analyzing es cell gene expression data. Statistica Sinica 12, 241–262 (2002). MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • H. J. Areiza-Laverde
    • 1
  • A. E. Castro-Ospina
    • 1
    Email author
  • P. Rosero-Montalvo
    • 2
  • D. H. Peluffo-Ordóñez
    • 2
  • J. L. Rodríguez-Sotelo
    • 3
  • M. A. Becerra-Botero
    • 4
  1. 1.Instituto Tecnológico Metropolitano - ITMMedellínColombia
  2. 2.Universidad Técnica del NorteIbarraEcuador
  3. 3.Universidad Autónoma de ManizalesManizalesColombia
  4. 4.Institución Universitaria Salazar y HerreraMedellínColombia

Personalised recommendations