Logo PTI Logo FedCSIS

Position Papers of the 18th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 36

Large Minded Reasoners for Soft and Hard Cluster Validation -- Some Directions

,

DOI: http://dx.doi.org/10.15439/2023F7902

Citation: Position Papers of the 18th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 36, pages 1–8 ()

Full text

Abstract. In recent research, validation methods for soft and hard clustering through general granular rough clusters are proposed by the first author. Large-minded reasoners are introduced and studied in the context of new concepts of non-stochastic rough randomness in a separate paper by her. In this research, the methodologies are reviewed and new low-cost scalable methodologies and algorithms are invented for computing granular rough approximations of soft clusters for many classes of partially ordered datasets. Specifically, these are applicable to datasets in which attribute values are numeric, vector valued, lattice-ordered or partially ordered. Additionally, new research directions are indicated.

References

  1. C. Hennig, M. Meila, F. Murtagh, and R. Rocci, Handbook of Cluster Analysis, 1st ed. Edited Volume. Chapman and Hall: CRC Press, 2016.
  2. M. Kim and R. S. Ramakrishna, “New Indices For Cluster Validity Assessment Pattern,” Pattern Recognition Letters, vol. 26, pp. 2353–2363, 2005. http://dx.doi.org/10.1016/j.patrec.2005.04.007
  3. C. Hennig and T. F. Liao, “Comparing Latent Class and Dissimilarity Based Clustering for Mixed Type Variables...” Journal of the Royal Statistical Society, pp. 309–369, 2013. http://dx.doi.org/10.1111/j.1467-9876.2012.01066.x
  4. C. Bouveyron, G. Celeux, B. Murphy, and A. Raftery, Model-Based Clustering and Classification for Data Science: With Applications in R. Cambridge University Press, 2019.
  5. A. Mani, “Dialectics of Counting and The Mathematics of Vagueness,” Transactions on Rough Sets, vol. XV, no. LNCS 7255, pp. 122–180, 2012. http://dx.doi.org/10.1007/978-3-642-31903-7 4
  6. ——, “Comparative Approaches to Granularity in General Rough Sets,” in IJCRS 2020, ser. LNAI, R. Bello et al., Eds. Springer, 2020, vol. 12179, pp. 500–518.
  7. ——, “General Rough Modeling of Cluster Analysis,” in Rough Sets: IJCRS-EUSFLAT 2021, ser. LNAI 12872, S. Ramanna et al., Eds. Springer Nature, 2021.
  8. A. Campagner and D. Ciucci, “A formal learning theory for three-way clustering,” in SUM 2020, J. Davis and K. Tabia, Eds. Springer, 2020, vol. LNAI 12322, pp. 128–140.
  9. A. Mani, “Algebraic Methods for Granular Rough Sets,” in Algebraic Methods in General Rough Sets, ser. Trends in Mathematics, A. Mani, I. Düntsch, and G. Cattaneo, Eds. Birkhauser Basel, 2018, pp. 157–336.
  10. ——, “Algebraic Semantics of Similarity-Based Bitten Rough Set Theory,” Fundamenta Informaticae, vol. 97, no. 1-2, pp. 177–197, 2009. http://dx.doi.org/10.3233/FI-2009-196
  11. P. Wasilewski and D. Ślȩzak, “Foundations of Rough Sets from Vagueness Perspective,” in Rough Computing: Theories, Technologies and Applications, A. Hassanien et al., Eds. IGI, Global, 2008, pp. 1–37.
  12. I. Chajda, Algebraic Theory of Tolerance Relations. Olomouc University Press, 1991. [Online]. Available: https://www.researchgate.net/publication/36797871
  13. A. Mani, “Representation, Duality and Beyond,” in Algebraic Methods in General Rough Sets, ser. Trends in Mathematics, A. Mani, I. Düntsch, and G. Cattaneo, Eds. Birkhauser Basel, 2018, pp. 459–552.
  14. H. J. Bandelt, “Tolerance relations of a lattice,” Bulletin Austral.Math. Soc., vol. 23, pp. 367–381, 1981. http://dx.doi.org/10.1017/S0004972700007255
  15. G. Czedli and L. Klukovits, “A note on tolerances of idempotent algebras,” Glasnik Matematicki (Zagreb), vol. 18, pp. 35–38, 1983. [Online]. Available: https://web.math.pmf.unizg.hr/glasnik/18.1/18103.pdf
  16. A. Górnicka, J. Grygiel, and I. Tyrala, “On the lattice of tolerances for a finite chain,” Czestochowa Mathematics, vol. XXI, pp. 25–30, 2016. http://dx.doi.org/10.16926/m.2016.21.03
  17. J. Niederle, “A note on tolerance lattices of products of lattices,” Casop. Pest. Matem., vol. 107, pp. 114–115, 1982. http://dx.doi.org/10.21136/CPM.1982.118112
  18. S. Mitra, “An Evolutionary Rough Partitive Clustering,” Pattern Recognition Letters, vol. 25, no. 12, pp. 1439–1449, 2004. http://dx.doi.org/10.1016/j.patrec.2004.05.007
  19. G. Peters, “Rough Clustering Utilizing the Principle of Indifference,” Information Sciences, vol. 277, pp. 358–374, 2014. http://dx.doi.org/10.1016/j.ins.2014.02.073
  20. J. Vermunt and J. Magidson, “Latent Class Cluster Analysis,” in Applied Latent Class Analysis. Cambridge: Cambridge University Press, 2002, pp. 89–106.
  21. I. Düntsch and G. Gediga, “Rough Set Clustering,” in Handbook of Cluster Analysis, C. Hennig, M. Meila, and F. Murtagh, Eds. CRC Press, 2016, ch. 25, pp. 575–594.
  22. A. D. Concilio, C. Guadagni, J. Peters, and S. Ramanna, “Descriptive Proximities. Properties and Interplay Between Classical Proximities and Overlap,” Mathematics in Computer Science, vol. 12, no. 1, pp. 91–106, 2018. http://dx.doi.org/10.1007/s11786-017-0328-y
  23. A. N. Kolmogorov, “On the logical foundations of probability theory,” in Selected Works of A. N. Kolmogorov, A. N. Shiryayev, Ed. Kluwer Academic, Nauka, 1986, vol. 2, ch. 53, pp. 515–519.
  24. B. Liu, Uncertainty Theory, ser. Studies in Fuzziness and Soft Comput- ing. Springer, 2004, vol. 154.
  25. T. Steifer, “A note on learning theoretic characterizations of randomness and convergence,” Review of Symbolic Logic, vol. 15, no. 3, pp. 807–822, 2022. http://dx.doi.org/10.1017/S1755020321000125
  26. L. Beach and G. Braun, “Laboratory studies of subjective probability: a status report,” in Subjective Probability, G. Wright and P. Ayton, Eds. John Wiley, 1994, pp. 107–128.
  27. A. Mani, I. Düntsch, and G. Cattaneo, Eds., Algebraic Methods in General Rough Sets, ser. Trends in Mathematics. Birkhauser Basel, 2018. ISBN 978-3-030-01161-1
  28. P. Pagliani and M. Chakraborty, A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns. Berlin: Springer, 2008.
  29. A. Mani, “Rough randomness and its application,” Journal of the Calcutta Mathematical Society, pp. 1–15, 2023. http://dx.doi.org/10.5281/zen-odo.7762335. [Online]. Available: https://zenodo.org/record/7762335
  30. J. Stepaniuk, Rough-Granular Computing in Knowledge Discovery and Data Mining, ser. Studies in Computational Intelligence,Volume 152. Springer-Verlag, 2009. ISBN 978-3-540-70800-1
  31. A. Gomolinska, “Rough Approximation Based on Weak q-RIFs,” Transactions on Rough Sets, vol. X, pp. 117–135, 2009. http://dx.doi.org/10.1007/978-3-642-03281-3_4
  32. M. Gagrat and S. Naimpally, “Proximity approach to semi-metric and developable spaces,” Pacific Journal of Mathematics, vol. 44, no. 1, pp. 93–105, 1973. http://dx.doi.org/10.2140/pjm.1973.44-1
  33. O. Cheong et al., Eds., Listing All Maximal Cliques in Sparse Graphs in Near-Optimal Time, ser. LNCS 6506. Berlin: Springer, 2010. doi: 10.1007/978-3-642-17517-6 36
  34. R. Freese, J. Jezek, J. Jipsen, P. Markovic, M. Maroti, and R. Mckenzie, “The Variety Generated by Order Algebras,” Algebra Universalis, vol. 47, pp. 103–138, 2002. http://dx.doi.org/10.1007/s00012-002-8178-z
  35. A. Mani, “Granularity and Rational Approximation: Rethinking Graded Rough Sets,” Transactions on Rough Sets, vol. XXIII, no. LNCS 13610, pp. 33–59, 2022. http://dx.doi.org/10.1007/978-3-662-66544-2 4
  36. M. Meila, “Spectral Clustering,” in Handbook of Cluster Analysis, C. Hennig, M. Meila, and F. Murtagh, Eds. CRC Press, 2016, ch. 7, pp. 125–144.
  37. S. Roy and P. Maji, “Tumor delineation from 3-d mr brain images,” Signal, Image and Video Processing, pp. 1–9, 2023. http://dx.doi.org/10.1007/s11760-023-02565-4
  38. P. Dutta and S. Mitra, “Composite deep network with feature weighting for improved delineation of covid infection in lung ct,” MedRxiv, pp. 1–22, 2023. http://dx.doi.org/10.1101/2023.01.17.23284673