Naslov
One-dimensional center-based $l_1$-clustering method

Autori
Sabo, Kristian ; Scitovski, Rudolf ; Vazler, Ivan

Izvornik
Optimization Letters (1862-4472) 7 (2013), 1; 5-22

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
clustering; data mining; optimization; weighted median problem

Sažetak
Motivated by the method for solving center-based Least Squares - clustering problem (Kogan(2007), Teboulle(2007)), we construct a very efficient iterative process for solving a one-dimensional center-based $l_1$ -clustering problem, on the basis of which it is possible to determine the optimal partition. We analyze the basic properties and convergence of our iterative process, which converges to a stationary point of the corresponding objective function for each choice of the initial approximation. Given is also a corresponding algorithm, which in only few steps gives a stationary point and the corresponding partition. The method is illustrated and visualized on the example of looking for an optimal partition with two clusters, where we check all stationary points of the corresponding minimizing functional. Also, the method is tested on the basis of large numbers of data points and clusters and compared with the method for solving the center-based Least Squares - clustering problem described in Kogan(2007) and Teboulle (2007).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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