# Center-based l₁-clustering method

International Journal of Applied Mathematics and Computer Science (2014)

- Volume: 24, Issue: 1, page 151-163
- ISSN: 1641-876X

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topKristian Sabo. "Center-based l₁-clustering method." International Journal of Applied Mathematics and Computer Science 24.1 (2014): 151-163. <http://eudml.org/doc/271908>.

@article{KristianSabo2014,

abstract = {In this paper, we consider the l₁-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 l₂-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 l₁-clustering algorithm is faster and gives significantly better results than the l₂-clustering algorithm.},

author = {Kristian Sabo},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {l₁-clustering; data mining; optimization; weighted median problem; clustering},

language = {eng},

number = {1},

pages = {151-163},

title = {Center-based l₁-clustering method},

url = {http://eudml.org/doc/271908},

volume = {24},

year = {2014},

}

TY - JOUR

AU - Kristian Sabo

TI - Center-based l₁-clustering method

JO - International Journal of Applied Mathematics and Computer Science

PY - 2014

VL - 24

IS - 1

SP - 151

EP - 163

AB - In this paper, we consider the l₁-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 l₂-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 l₁-clustering algorithm is faster and gives significantly better results than the l₂-clustering algorithm.

LA - eng

KW - l₁-clustering; data mining; optimization; weighted median problem; clustering

UR - http://eudml.org/doc/271908

ER -

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