scholarly journals Double-Valued Neutrosophic Sets, their Minimum Spanning Trees, and Clustering Algorithm

2018 ◽  
Vol 27 (2) ◽  
pp. 163-182 ◽  
Author(s):  
Ilanthenral Kandasamy
Keyword(s):  
Fuzzy Sets ◽  
Spanning Tree ◽  
Clustering Algorithm ◽  
Minimum Spanning Tree ◽  
Distance Measure ◽  
Clustering Algorithms ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Inconsistent Information ◽  
Intuitionistic Fuzzy

AbstractNeutrosophy (neutrosophic logic) is used to represent uncertain, indeterminate, and inconsistent information available in the real world. This article proposes a method to provide more sensitivity and precision to indeterminacy, by classifying the indeterminate concept/value into two based on membership: one as indeterminacy leaning towards truth membership and the other as indeterminacy leaning towards false membership. This paper introduces a modified form of a neutrosophic set, called Double-Valued Neutrosophic Set (DVNS), which has these two distinct indeterminate values. Its related properties and axioms are defined and illustrated in this paper. An important role is played by clustering in several fields of research in the form of data mining, pattern recognition, and machine learning. DVNS is better equipped at dealing with indeterminate and inconsistent information, with more accuracy, than the Single-Valued Neutrosophic Set, which fuzzy sets and intuitionistic fuzzy sets are incapable of. A generalised distance measure between DVNSs and the related distance matrix is defined, based on which a clustering algorithm is constructed. This article proposes a Double-Valued Neutrosophic Minimum Spanning Tree (DVN-MST) clustering algorithm, to cluster the data represented by double-valued neutrosophic information. Illustrative examples are given to demonstrate the applications and effectiveness of this clustering algorithm. A comparative study of the DVN-MST clustering algorithm with other clustering algorithms like Single-Valued Neutrosophic Minimum Spanning Tree, Intuitionistic Fuzzy Minimum Spanning Tree, and Fuzzy Minimum Spanning Tree is carried out.

scholarly journals A Novel Hybrid Clustering Algorithm Based on Minimum Spanning Tree of Natural Core Points

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 43707-43720 ◽  
Author(s):  
Jinlong Huang ◽  
Ru Xu ◽  
Dongdong Cheng ◽  
Sulan Zhang ◽  
Keke Shang
Keyword(s):  
Spanning Tree ◽  
Clustering Algorithm ◽  
Minimum Spanning Tree ◽  
Hybrid Clustering ◽  
Core Points

scholarly journals Does Determination of Initial Cluster Centroids Improve the Performance of K-Means Clustering Algorithm? Comparison of Three Hybrid Methods by Genetic Algorithm, Minimum Spanning Tree, and Hierarchical Clustering in an Applied Study

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Saeedeh Pourahmad ◽  
Atefeh Basirat ◽  
Amir Rahimi ◽  
Marziyeh Doostfatemeh
Keyword(s):  
Genetic Algorithm ◽  
Hierarchical Clustering ◽  
Spanning Tree ◽  
Clustering Algorithm ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Hybrid Methods ◽  
Optimal Solution ◽  
Initial Cluster ◽  
Algorithm Comparison

Random selection of initial centroids (centers) for clusters is a fundamental defect in K-means clustering algorithm as the algorithm’s performance depends on initial centroids and may end up in local optimizations. Various hybrid methods have been introduced to resolve this defect in K-means clustering algorithm. As regards, there are no comparative studies comparing these methods in various aspects, the present paper compared three hybrid methods with K-means clustering algorithm using concepts of genetic algorithm, minimum spanning tree, and hierarchical clustering method. Although these three hybrid methods have received more attention in previous researches, fewer studies have compared their results. Hence, seven quantitative datasets with different characteristics in terms of sample size, number of features, and number of different classes are utilized in present study. Eleven indices of external and internal evaluating index were also considered for comparing the methods. Data indicated that the hybrid methods resulted in higher convergence rate in obtaining the final solution than the ordinary K-means method. Furthermore, the hybrid method with hierarchical clustering algorithm converges to the optimal solution with less iteration than the other two hybrid methods. However, hybrid methods with minimal spanning trees and genetic algorithms may not always or often be more effective than the ordinary K-means method. Therefore, despite the computational complexity, these three hybrid methods have not led to much improvement in the K-means method. However, a simulation study is required to compare the methods and complete the conclusion.

CLUSTERING WITH MINIMUM SPANNING TREES

2011 ◽  
Vol 20 (01) ◽  
pp. 139-177 ◽  
Author(s):  
YAN ZHOU ◽  
OLEKSANDR GRYGORASH ◽  
THOMAS F. HAIN
Keyword(s):  
Spanning Tree ◽  
Clustering Algorithm ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Clustering Algorithms ◽  
Predefined Criterion ◽  
Point Set ◽  
Color Clustering ◽  
Representative Points ◽  
Set Of Points

We propose two Euclidean minimum spanning tree based clustering algorithms — one a k-constrained, and the other an unconstrained algorithm. Our k-constrained clustering algorithm produces a k-partition of a set of points for any given k. The algorithm constructs a minimum spanning tree of a set of representative points and removes edges that satisfy a predefined criterion. The process is repeated until k clusters are produced. Our unconstrained clustering algorithm partitions a point set into a group of clusters by maximally reducing the overall standard deviation of the edges in the Euclidean minimum spanning tree constructed from a given point set, without prescribing the number of clusters. We present our experimental results comparing our proposed algorithms with k-means, X-means, CURE, Chameleon, and the Expectation-Maximization (EM) algorithm on both artificial data and benchmark data from the UCI repository. We also apply our algorithms to image color clustering and compare them with the standard minimum spanning tree clustering algorithm as well as CURE, Chameleon, and X-means.

The Application of Minimum Spanning Tree Clustering in the Ontology Mapping Pretreatment

2014 ◽  
Vol 644-650 ◽  
pp. 2151-2154
Author(s):  
Jin Hui Cheng ◽  
Wan Long Li ◽  
Shan Hong Zheng ◽  
Dong Han
Keyword(s):  
Objective Function ◽  
Information Entropy ◽  
Spanning Tree ◽  
Clustering Algorithm ◽  
Minimum Spanning Tree ◽  
Graph Clustering ◽  
Ontology Mapping ◽  
System Information

Screening candidates is the key step to improve the efficiency of ontology mapping. Minimum spanning tree clustering is one of the important ways of graph clustering algorithm. Defining the related concepts and methods first, according to the characteristics of the ontology file itself, Select graph clustering of minimum spanning tree clustering algorithm, To screening candidates of participate in the concept of mapping, Aiming at the deficiency and improvement of objective function in the algorithm, based on the system information entropy instead of the complicated calculation of similarity to supervise the clustering. To reduce the computational scale and improve the efficiency.

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