One-dimensional center-based l 1-clustering method

Sabo, Kristian; Scitovski, Rudolf; Vazler, Ivan

doi:10.1007/s11590-011-0389-9

Cited by 38 publications

(18 citation statements)

References 27 publications

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“…In this way, it is also possible to modify the Mahalanobis k-means algorithm in the LAD sense. As expected, application of the LAD-distance function will show better behaviour when outliers are anticipated among the data (see [16]). …”

Section: Construction Of a Good Initial Approximationsupporting

confidence: 71%

Multiple ellipse fitting by center-based clustering

Marošević

Scitovski

2015

Croat. Oper. Res. Rev.

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Abstract. This paper deals with the multiple ellipse fitting problem based on a given set of data points in a plane. The presumption is that all data points are derived from k ellipses that should be fitted. The problem is solved by means of center-based clustering, where cluster centers are ellipses. If the Mahalanobis distance-like function is introduced in each cluster, then the cluster center is represented by the corresponding Mahalanobis circle-center. The distance from a point a ∈ R 2 to the Mahalanobis circle is based on the algebraic criterion. The well-known k-means algorithm has been adapted to search for a locally optimal partition of the Mahalanobis circle-centers. Several numerical examples are used to illustrate the proposed algorithm.

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Section: Construction Of a Good Initial Approximationsupporting

confidence: 71%

Multiple ellipse fitting by center-based clustering

Marošević

Scitovski

2015

Croat. Oper. Res. Rev.

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“…Clustering or grouping a data set into conceptually meaningful clusters is a well-studied problem in recent literature, and it has practical importance in a wide variety of applications such as medicine, biology, pattern recognition, facility location problem, text classification, information retrieval, earthquake investigation, understanding the Earth's climate, psychology, ranking of municipalities for financial support, business, etc. (Kogan, 2007;Liao et al, 2012;Mostafa, 2013;Pintér, 1996;Reyes et al, 2013;Sabo et al, 2011;Sabo et al, 2013;Scitovski and Scitovski, 2013). If we introduce the distance from the point T ¼ ðn; gÞ 2 A to a line p j ða j ; b j ; c j Þ given by (1) as orthogonal squared distance (Chernov, 2010;Nievergelt, 1994) …”

Section: Cluster-based Line Detectionmentioning

confidence: 99%

“…It does not have to be either convex or differentiable, but it is a Lipschitz continuous function (Grbić et al, 2013a;Pintér, 1996;Sabo et al, 2013). The objective function F can also be considered as a symmetric function U :…”

Section: Cluster-based Line Detectionmentioning

confidence: 99%

Center-based clustering for line detection and application to crop rows detection

Vidović

Scitovski

2014

Computers and Electronics in Agriculture

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“…(c) locally optimal dkm/smoka partition Figure 3. Locally optimal partitions for randomly generated points with σ 2 = 2.0 For the purpose of illustrating the efficiency of the dkm algorithm in relation to smoka, we will carry out the following simple numerical experiment motivated by the example from [19]. E x a m p l e 4.2.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…[1], [21]). A global optimization problem (1.5) can also be found in literature as a center-based clustering problem or k-means/k-median problem [9], [15], [19], [23]. Thereby, the objective function F is a symmetric Lipschitz continuous function which can have a large number of independent variables (the number of clusters in the partition multiplied by the dimension of data points (k · n)), it has to be neither convex nor differentiable, and generally it may have at least k!…”

Section: Introductionmentioning

confidence: 99%

Interpretation and optimization of the k-means algorithm

Sabo

Scitovski

2014

Appl Math

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Interpretation and optimization of the k-means algorithmApplications of Mathematics, Vol. 59 (2014) Abstract. The paper gives a new interpretation and a possible optimization of the wellknown k-means algorithm for searching for a locally optimal partition of the set A = {a i ∈ R n : i = 1, . . . , m} which consists of k disjoint nonempty subsets π 1 , . . . , π k , 1 k m. For this purpose, a new divided k-means algorithm was constructed as a limit case of the known smoothed k-means algorithm. It is shown that the algorithm constructed in this way coincides with the k-means algorithm if during the iterative procedure no data points appear in the Voronoi diagram. If in the partition obtained by applying the divided k-means algorithm there are data points lying in the Voronoi diagram, it is shown that the obtained result can be improved further.,

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One-dimensional center-based l 1-clustering method

Cited by 38 publications

References 27 publications

Multiple ellipse fitting by center-based clustering

Multiple ellipse fitting by center-based clustering

Center-based clustering for line detection and application to crop rows detection

Interpretation and optimization of the k-means algorithm

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