Papers on Cluster Analysis


  1. C. Lenart, A generalized distance in graphs and centered partitions, SIAM J. Discrete Math. 11 (1998), 293-304 (MR 99g:05067).
  2. C. Lenart, Defining separability of two fuzzy clusters by a fuzzy decision hyperplane, Pattern Recognition 26 no. 9 (1993), 1351-1356.
  3. C. Lenart, Clustering and Learning in Pattern Recognition, Ph.D. thesis, University of Cluj, 1992.
  4. I. Haidu, I. Lazar, C. Lenart, and A. Imbroane, Modelling of natural hydroenergy organization of the small basins, in Proceedings of World Renewable Energy Congress, Reading, UK, 3159-3167, 1990.
  5. L. Ghergari, C. Lenart, I. Mârza, and D. Pop, Anorthitic composition of plagioclases, criterion for parallelizing tuff horizons in the Transylvanian basin, Studia Univ. "Babes-Bolyai", Geologia 37 no. 1 (1992), 31-40.
  6. C. Lenart, Method for improving the results of certain clustering procedures, Studia Univ. "Babes-Bolyai", Mathematica 35 no. 3 (1990), 55-63 (MR 94a:68115).
  7. C. Lenart, A classification algorithm for ellipsoid form clusters, Univ. of Cluj-Napoca Research Seminars, Preprint no. 9 (1989), 93-102.
  8. C. Lenart, Classification with fuzzy relations II, Studia Univ. "Babes-Bolyai", Mathematica 34 no. 3 (1989), 63-67 (MR 91i:04009).
  9. C. Lenart, Classification with fuzzy relations I, Studia Univ. "Babes-Bolyai", Mathematica 33 no. 3 (1988), 52-55 (MR 90j:03103).
  10. D. Dumitrescu and C. Lenart, Divisive hierarchical classification for linear clusters, Studia Univ. "Babes-Bolyai", Mathematica 33 no. 3 (1988), 48-51 (CMP 1 027 357).
  11. C. Lenart and D. Dumitrescu, Convex decomposition of fuzzy partitions, Univ. of Cluj-Napoca Research Seminars, Preprint no. 5 (1987), 46-54 (MR 90i:05006).


The main aim of my research in this area was to develop efficient clustering algorithms, based on fuzzy sets and non-linear optimization [2, 7, 10], fuzzy relations and Boolean optimization [8, 9, 11], graphs [1, 6], and graph grammars [3]. In the process of doing this, I addressed several mathematical problems, and I investigated notions having mainly a theoretical interest, such as the generalized distance in graphs defined in [1]. I also developed a package for clustering by implementing several classical algorithms and some of my own; this package was used to process geological, geographical, and biological data [4, 5].
Cristian Lenart, Department of Mathematics, ES 118, SUNY at Albany