Original scientific paper

DATA CLUSTERING: APPLICATIONS IN ENGINEERING

Zdravko Krpić ; Faculty of Electrical Engineering, University of Osijek, Osijek, Croatia
Goran Martinović orcid.org/0000-0002-7469-6018 ; Faculty of Electrical Engineering, University of Osijek, Osijek, Croatia
Ivan Vazler ; Department of Mathematics, University of Osijek, Osijek, Croatia

Abstract

Dividing a set S $\mathcal{S} = \{x_i=(x_1^{(i)}+\dots+x_n^{(i)})^T \in \mathbb{R}^n:i=1,\dots,m\}$ (a set of vectors from a vector space $\mathbb{R}^n$) into disjunct subsets $\pi_1,\dots,\pi_k, 1\leq k\leq m$, such that
$\cup_{i=1}^k \pi_i=S,
\pi_i \cap \pi_j=0, i \ne j,
|\pi_j|\geq 1, j=1,\dots,k$,
determines a partition of the set $\mathcal{S}$. The elements of such partition $\pi_1,\dots,\pi_k$ are called clusters.
For practical clustering applications the number of all clusters is too big and the problem of determining the optimal partition in the least-squares sense is an NP-hard problem.
In this paper we will consider some well-known algorithms for searching for an optimal LS-partition, list some of the numerous applications of cluster analysis in engineering and give some practical applications.

Keywords

data clustering; engineering; least squares

Hrčak ID:

94967

URI

https://hrcak.srce.hr/94967

Publication date:

22.12.2010.

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