Minimum spanning tree‐based cluster analysis: A new algorithm for determining inconsistent edges

2021 ◽  
Author(s):  
Fadi Şaar ◽  
Ahmet E. Topcu
Keyword(s):  
Cluster Analysis ◽  
Spanning Tree ◽  
Minimum Spanning Tree

Application of optimization tasks in cluster analysis

10.12737/7483 ◽  
2014 ◽  
Vol 8 (7) ◽  
pp. 0-0
Author(s):  
Олег Сдвижков ◽  
Oleg Sdvizhkov
Keyword(s):  
Cluster Analysis ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Clustering Algorithms ◽  
Clustering Methods ◽  
Number Of Clusters ◽  
Homogeneous Groups ◽  
Finite Set ◽  
Minimum Number

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.

scholarly journals Converting MST to TSP Path by Branch Elimination

2020 ◽  
Vol 11 (1) ◽  
pp. 177
Author(s):  
Pasi Fränti ◽  
Teemu Nenonen ◽  
Mingchuan Yuan
Keyword(s):  
Spanning Tree ◽  
Closed Loop ◽  
Minimum Spanning Tree ◽  
Travelling Salesman Problem ◽  
Open Loop ◽  
Travelling Salesman ◽  
Elimination Algorithm ◽  
Number Of Iterations ◽  
Number Of Branches

Travelling salesman problem (TSP) has been widely studied for the classical closed loop variant but less attention has been paid to the open loop variant. Open loop solution has property of being also a spanning tree, although not necessarily the minimum spanning tree (MST). In this paper, we present a simple branch elimination algorithm that removes the branches from MST by cutting one link and then reconnecting the resulting subtrees via selected leaf nodes. The number of iterations equals to the number of branches (b) in the MST. Typically, b << n where n is the number of nodes. With O-Mopsi and Dots datasets, the algorithm reaches gap of 1.69% and 0.61 %, respectively. The algorithm is suitable especially for educational purposes by showing the connection between MST and TSP, but it can also serve as a quick approximation for more complex metaheuristics whose efficiency relies on quality of the initial solution.

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