Papers on Cluster Analysis
- C. Lenart, A generalized distance in graphs and centered partitions, SIAM J. Discrete Math. 11 (1998), 293-304 (MR 99g:05067).
- C. Lenart, Defining separability of two fuzzy clusters by a fuzzy decision hyperplane, Pattern Recognition 26 no. 9 (1993), 1351-1356.
- C. Lenart, Clustering and Learning in Pattern Recognition, Ph.D. thesis, University of Cluj, 1992.
- 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.
- 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.
- 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).
- C. Lenart, A classification algorithm for ellipsoid form clusters, Univ. of Cluj-Napoca Research Seminars, Preprint no. 9 (1989), 93-102.
- C. Lenart, Classification with fuzzy relations II, Studia Univ. "Babes-Bolyai", Mathematica 34 no. 3 (1989), 63-67 (MR 91i:04009).
- C. Lenart, Classification with fuzzy relations I, Studia Univ. "Babes-Bolyai", Mathematica 33 no. 3 (1988), 52-55 (MR 90j:03103).
- 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).
- 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 . 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 . 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,
SUNY at Albany