APPLICATION OF OPTIMIZATION TASKS IN CLUSTER ANALYSIS
Rubrics: EDUCATION
Authors:
Type:
Article
Pages:
from 0
to 0
Status:
Published
Received:
12.01.2015
Accepted:
12.01.2015
Published:
12.01.2015
Language:
Russian
Keywords:
cluster, linear programming, the shortest cycle, the minimum spanning tree
Abstract (English):
Cluster analysis [3] is a relatively new branch of mathematics that studies the methods partitioning a set of objects, given a finite set of attributes into homogeneous groups (clusters). Cluster analysis is widely used in psychology, sociology, economics (market segmentation), and many other areas in which there is a problem of classification of objects according to their characteristics. Clustering methods implemented in a package STATISTICA [1] and SPSS [2], they return the partitioning into clusters, clustering and dispersion statistics dendrogram of hierarchical clustering algorithms. MS Excel Macros for main clustering methods and application examples are given in the monograph [5]. One of the central problems of cluster analysis is to define some criteria for the number of clusters, we denote this number by K, into which separated are a given set of objects. There are several dozen approaches [4] to determine the number K. In particular, according to [6], the number of clusters K - minimum number which satisfies where - the minimum value of total dispersion for partitioning into K clusters, N - number of objects. Among the clusters automatically causes the consistent application of abnormal clusters [4]. In 2010, proposed and experimentally validated was a method for obtaining the number of K by applying the density function [4]. The article offers two simple approaches to determining K, where each cluster has at least two objects. In the first number K is determined by the shortest Hamiltonian cycles in the second - through the minimum spanning tree. The examples of clustering with detailed step by step solutions and graphic illustrations are suggested. Shown is the use of macro VBA Excel, which returns the minimum spanning tree to the problems of clustering. The article contains a macro code, with commentaries to the main unit.
Cluster analysis [3] is a relatively new branch of mathematics that studies the methods partitioning a set of objects, given a finite set of attributes into homogeneous groups (clusters). Cluster analysis is widely used in psychology, sociology, economics (market segmentation), and many other areas in which there is a problem of classification of objects according to their characteristics. Clustering methods implemented in a package STATISTICA [1] and SPSS [2], they return the partitioning into clusters, clustering and dispersion statistics dendrogram of hierarchical clustering algorithms. MS Excel Macros for main clustering methods and application examples are given in the monograph [5]. One of the central problems of cluster analysis is to define some criteria for the number of clusters, we denote this number by K, into which separated are a given set of objects. There are several dozen approaches [4] to determine the number K. In particular, according to [6], the number of clusters K - minimum number which satisfies where - the minimum value of total dispersion for partitioning into K clusters, N - number of objects. Among the clusters automatically causes the consistent application of abnormal clusters [4]. In 2010, proposed and experimentally validated was a method for obtaining the number of K by applying the density function [4]. The article offers two simple approaches to determining K, where each cluster has at least two objects. In the first number K is determined by the shortest Hamiltonian cycles in the second - through the minimum spanning tree. The examples of clustering with detailed step by step solutions and graphic illustrations are suggested. Shown is the use of macro VBA Excel, which returns the minimum spanning tree to the problems of clustering. The article contains a macro code, with commentaries to the main unit.
Keywords:
cluster, linear programming, the shortest cycle, the minimum spanning tree
cluster, linear programming, the shortest cycle, the minimum spanning tree
1. Vukolov, E.A. Osnovy statisticheskogo analiza: praktikum po statisticheskim metodam i issledovaniyu operatsiy s ispol´zovaniem paketov STATISTICA i EXCEL. - M.: INFRA-M, 2004.
2. Dubov, I.Yu. Obrabotka statisticheskoy informatsii s pomoshch´yu SPSS. - M.: NT Press, 2004.
3. Mandel´, I.D. Klasternyy analiz. - M.: Finansy i statistika, 1988.
4. Mirkin, B.G. Metody klaster-analiza dlya podderzhki prinyatiya resheniy. - M.: izd. dom «Vysshaya shkola ekonomiki», 2011.
5. Sdvizhkov, O. A. Diskretnaya matematika i matematicheskie metody ekonomiki s primeneniem VBA Excel. - M.: DMK Press, 2012.
6. Hartigan J. A. Clustering Algorithms. N.Y.: J. Wiley & Sons, 1975.
