期刊
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE
卷 24, 期 1, 页码 151-163出版社
SCIENDO
DOI: 10.2478/amcs-2014-0012
关键词
l(1)-clustering; data mining; optimization; weighted median problem
资金
- Ministry of Science, Education and Sport, Republic of Croatia [235-2352818-1034]
In this paper, we consider the l(1)-clustering problem for a finite data-point set which should be partitioned into k disjoint nonempty subsets. In that case, the objective function does not have to be either convex or differentiable, and generally it may have many local or global minima. Therefore, it becomes a complex global optimization problem. A method of searching for a locally optimal solution is proposed in the paper, the convergence of the corresponding iterative process is proved and the corresponding algorithm is given. The method is illustrated by and compared with some other clustering methods, especially with the l(2)-clustering method, which is also known in the literature as a smooth k-means method, on a few typical situations, such as the presence of outliers among the data and the clustering of incomplete data. Numerical experiments show in this case that the proposed l(1)-clustering algorithm is faster and gives significantly better results than the l(2)-clustering algorithm.
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