Skip to main content

Generalized Median Computation for Consensus Learning: A Brief Survey

  • Conference paper
  • First Online:
Computer Analysis of Images and Patterns (CAIP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14184))

Included in the following conference series:

  • 574 Accesses

Abstract

Computing a consensus object from a set of given objects is a core problem in machine learning and pattern recognition. A popular approach is the formulation of generalized median as an optimization problem. The concept of generalized median has been studied for numerous problem domains with a broad range of applications. Currently, the research is widely scattered in the literature and no comprehensive survey is available. This brief survey contributes to closing this gap and systematically discusses the relevant issues of generalized median computation. In particular, we present a taxonomy of computation frameworks and methods. We also outline a number of future research directions.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Bader, M.: The transposition median problem is NP-complete. Theoret. Comput. Sci. 412(12–14), 1099–1110 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beck, A., Sabach, S.: Weiszfeld’s method: old and new results. J. Optim. Theory Appl. 164(1), 1–40 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Boongoen, T., Iam-On, N.: Cluster ensembles: a survey of approaches with recent extensions and applications. Comput. Sci. Rev. 28, 1–25 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cohen-Boulakia, S., Denise, A., Hamel, S.: Using medians to generate consensus rankings for biological data. In: Bayard Cushing, J., French, J., Bowers, S. (eds.) SSDBM 2011. LNCS, vol. 6809, pp. 73–90. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22351-8_5

    Chapter  Google Scholar 

  5. Chakraborty, R., et al.: Intrinsic Grassmann averages for online linear, robust and nonlinear subspace learning. IEEE-TPAMI 43(11), 3904–3917 (2021)

    Article  Google Scholar 

  6. Chakraborty, R., et al.: ManifoldNet: a deep neural network for manifold-valued data with applications. IEEE-TPAMI 44(2), 799–810 (2022)

    Article  Google Scholar 

  7. Chatterjee, S., Mukhopadhyay, A.: Clustering ensemble: a multiobjective genetic algorithm based approach. In: Proceedings of International Conference on Computational Intelligence: Modeling, Techniques and Applications, pp. 443–449 (2013)

    Google Scholar 

  8. Ferrer, M., et al.: Generalized median graph computation by means of graph embedding in vector spaces. Pattern Recogn. 43(4), 1642–1655 (2010)

    Article  MATH  Google Scholar 

  9. Ferrer, M., et al.: A generic framework for median graph computation based on a recursive embedding approach. Comput. Vis. Image Underst. 115(7), 919–928 (2011)

    Article  Google Scholar 

  10. Fletcher, P.T., et al.: The geometric median on Riemannian manifolds with application to robust atlas estimation. Neuroimage 45(1), S143–S152 (2009)

    Article  Google Scholar 

  11. Franek, L., Jiang, X.: Evolutionary weighted mean based framework for generalized median computation with application to strings. In: Gimel’farb, G., et al. (eds.) SSPR /SPR 2012. LNCS, vol. 7626, pp. 70–78. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34166-3_8

    Chapter  Google Scholar 

  12. Fred, A.L.N., Jain, A.K.: Combining multiple clusterings using evidence accumulation. IEEE-TPAMI 27(6), 835–850 (2005)

    Article  Google Scholar 

  13. Gionis, A., et al.: Clustering aggregation. ACM Trans. Knowl. Discov. Data 1(1), 4 (2007)

    Article  Google Scholar 

  14. Goder, A., Filkov, V.: Consensus clustering algorithms: comparison and refinement. In: Proceedings of 10th Workshop on Algorithm Engineering and Experiments, pp. 109–117 (2008)

    Google Scholar 

  15. Hartley, R., et al.: Rotation averaging. Int. J. Comput. Vision 103(3), 267–305 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hayashida, M., Koyano, H.: Finding median and center strings for a probability distribution on a set of strings under Levenshtein distance based on integer linear programming. In: Fred, A., Gamboa, H. (eds.) BIOSTEC 2016. CCIS, vol. 690, pp. 108–121. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-54717-6_7

    Chapter  Google Scholar 

  17. de la Higuera, C., Casacuberta, F.: Topology of strings: median string is np-complete. Theoret. Comput. Sci. 230(1–2), 39–48 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Honeine, P., Richard, C.: Preimage problem in kernel-based machine learning. IEEE Signal Process. Mag. 28(2), 77–88 (2011)

    Article  Google Scholar 

  19. Jiang, X., Bunke, H.: Optimal lower bound for generalized median problems in metric space. In: Caelli, T., Amin, A., Duin, R.P.W., de Ridder, D., Kamel, M. (eds.) SSPR /SPR 2002. LNCS, vol. 2396, pp. 143–151. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-70659-3_14

    Chapter  Google Scholar 

  20. Jiang, X., Münger, A., Bunke, H.: On median graphs: properties, algorithms, and applications. IEEE-TPAMI 23(10), 1144–1151 (2001)

    Article  Google Scholar 

  21. Juan, A., Vidal, E.: Fast median search in metric spaces. In: Amin, A., Dori, D., Pudil, P., Freeman, H. (eds.) SSPR /SPR 1998. LNCS, vol. 1451, pp. 905–912. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0033318

    Chapter  Google Scholar 

  22. Khelifi, L., Mignotte, M.: A novel fusion approach based on the global consistency criterion to fusing multiple segmentations. IEEE Trans. Syst. Man Cybern. Syst. 47(9), 2489–2502 (2017)

    Google Scholar 

  23. Krivánek, M., Morávek, J.: NP-hard problems in hierarchical-tree clustering. Acta Inform. 23(3), 311–323 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kruskal, J.B.: An overview of sequence comparison: time warps, string edits, and macromolecules. SIAM Rev. 25(2), 201–237 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kruzslicz, F.: Improved greedy algorithm for computing approximate median strings. Acta Cybern. 14(2), 331–339 (1999)

    MathSciNet  MATH  Google Scholar 

  26. Lopresti, D.P., Zhou, J.: Using consensus sequence voting to correct OCR errors. Comput. Vis. Image Underst. 67(1), 39–47 (1997)

    Article  Google Scholar 

  27. Ma, T., et al.: Ensembling low precision models for binary biomedical image segmentation. In: IEEE Winter Conference on Applications of Computer Vision, pp. 325–334 (2021)

    Google Scholar 

  28. Markley, F.L., et al.: Averaging quaternions. J. Guid. Control. Dyn. 30(4), 1193–1197 (2007)

    Article  Google Scholar 

  29. Maronna, R.A., et al.: Robust Statistics: Theory and Methods (with R), 2nd edn. Wiley, Hoboken (2019)

    MATH  Google Scholar 

  30. Márquez, D.G., Félix, P., García, C.A., Tejedor, J., Fred, A.L.N., Otero, A.: Positive and negative evidence accumulation clustering for sensor fusion: an application to heartbeat clustering. Sensors 19(21), 4635 (2019)

    Article  Google Scholar 

  31. Micó, L., Oncina, J.: An approximate median search algorithm in non-metric spaces. Pattern Recogn. Lett. 22(10), 1145–1151 (2001)

    Article  MATH  Google Scholar 

  32. Mirabal, P., et al.: Assessing the best edit in perturbation-based iterative refinement algorithms to compute the median string. Pattern Recogn. Lett. 120, 104–111 (2019)

    Article  Google Scholar 

  33. Nienkötter, A., Jiang, X.: Distance-preserving vector space embedding for the closest string problem. In: Proceedings of 23rd ICPR, pp. 1530–1535 (2016)

    Google Scholar 

  34. Nienkötter, A., Jiang, X.: Consensus learning for sequence data. In: Data Mining in Time Series and Streaming Databases, pp. 69–91. World Scientific (2018)

    Google Scholar 

  35. Nienkötter, A., Jiang, X.: Distance-preserving vector space embedding for consensus learning. IEEE Trans. Syst. Man Cybern. Syst 51(2), 1244–1257 (2021)

    Article  Google Scholar 

  36. Nienkötter, A., Jiang, X.: Kernel-based generalized median computation for consensus learning. IEEE-TPAMI 45(5), 5872–5888 (2023)

    Google Scholar 

  37. de Oliveira, J.V., et al.: Particle swarm clustering in clustering ensembles: exploiting pruning and alignment free consensus. Appl. Soft Comput. 55, 141–153 (2017)

    Article  Google Scholar 

  38. Petitjean, F., et al.: A global averaging method for dynamic time warping, with applications to clustering. Pattern Recogn. 44(3), 678–693 (2011)

    Article  MATH  Google Scholar 

  39. Pósfai, M., et al.: Consensus ranking for multi-objective interventions in multiplex networks. N. J. Phys. 21, 055001 (2019)

    Google Scholar 

  40. Storath, M., Weinmann, A.: Fast median filtering for phase or orientation data. IEEE-TPAMI 40(3), 639–652 (2018)

    Article  Google Scholar 

  41. Topchy, A.P., et al.: Clustering ensembles: models of consensus and weak partitions. IEEE-TPAMI 27(12), 1866–1881 (2005)

    Article  Google Scholar 

  42. Tu, P., et al.: Ultrasound image guided and mixed reality-based surgical system with real-time soft tissue deformation computing for robotic cervical pedicle screw placement. IEEE Trans. Biomed. Eng. 69(8), 2593–2603 (2022)

    Article  Google Scholar 

  43. Vega-Pons, S., et al.: Weighted partition consensus via kernels. Pattern Recogn. 43(8), 2712–2724 (2010)

    Article  MATH  Google Scholar 

  44. Wazarkar, S., Keshavamurthy, B.N.: A survey on image data analysis through clustering techniques for real world applications. J. Vis. Commun. Image Represent. 55, 596–626 (2018)

    Article  Google Scholar 

  45. Xie, Y., et al.: Multiple atlas construction from a heterogeneous brain MR image collection. IEEE Trans. Med. Imaging 32(3), 628–635 (2013)

    Article  Google Scholar 

  46. Yin, L., Liu, Y.: Ensemble biclustering gene expression data based on the spectral clustering. Neural Comput. Appl. 30(8), 2403–2416 (2018)

    Article  Google Scholar 

  47. Zhang, M.: Weighted clustering ensemble: a review. Pattern Recogn. 124, 108428 (2022)

    Google Scholar 

Download references

Acknowledgments

This work was partly supported by the Deutsche Forschungsgemeinschaft (DFG) - CRC 1450 - 431460824 and the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant 778602 ULTRACEPT.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaoyi Jiang .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jiang, X., Nienkötter, A. (2023). Generalized Median Computation for Consensus Learning: A Brief Survey. In: Tsapatsoulis, N., et al. Computer Analysis of Images and Patterns. CAIP 2023. Lecture Notes in Computer Science, vol 14184. Springer, Cham. https://doi.org/10.1007/978-3-031-44237-7_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-44237-7_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-44236-0

  • Online ISBN: 978-3-031-44237-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics