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Center-based l1-clustering method

Sabo K.

International Journal of Applied Mathematics and Computer Science

2014

Vol. 24, no. 1

151--163

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.

Wpływ metody grupowania na wynik klasyfikowania drgań podłoża wywołanych ruchem pojazdu

Jackowski J., Prochowski L.

Archiwum Motoryzacji

2004

Vol. 7, nr 1

43-52

W pracy przedstawiono wyniki klasyfikowania sygnałów drgań podłoża, wywołanych ruchem pojazdów o różnej masie I konstrukcji. Analizę przedstawionych wyników obliczeń przeprowadzono w celu wskazania najkorzystniejszej metody grupowania sygnałów, którą można wykorzystać w procesie identyfikowania pojazdu.

This paper presents result of initial calculations of classifying ground vibration signals caused by vehicle movement. Analysis of presented calculations results was performed in order to show the most profitable grouping method, which could be use in process of identification.

An varepsilon-Insensitive Approach to Fuzzy Clustering

Łęski J.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 4

993-1007

Fuzzy clustering can be helpful in finding natural vague boundaries in data. The fuzzy c-means method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in the data. The present paper introduces a new varepsilon-insensitive Fuzzy C-Means (varepsilonFCM) clustering algorithm. As a special case, this algorithm includes the well-known Fuzzy C-Medians method (FCMED). The performance of the new clustering algorithm is experimentally compared with the Fuzzy C-Means (FCM) method using synthetic data with outliers and heavy-tailed, overlapped groups of the data.