DATA CLUSTERING: APPLICATIONS IN ENGINEERING

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