scholarly journals Automatic Domain Decomposition in Finite Element Method – A Comparative Study

2021 ◽  
Author(s):  
Ali Kaveh ◽  
Mohammad Reza Seddighian ◽  
Pouya Hassani
Keyword(s):  
Finite Element ◽  
Heuristic Algorithms ◽  
Three Dimensional ◽  
Optimal Number ◽  
Cluster Validity ◽  
Cluster Validity Index ◽  
Automatic Data ◽  
Decomposition Problem ◽  
Clustering Approach ◽  
Optimal Number Of Clusters

In this paper, an automatic data clustering approach is presented using some concepts of the graph theory. Some Cluster Validity Index (CVI) is mentioned, and DB Index is defined as the objective function of meta-heuristic algorithms. Six Finite Element meshes are decomposed containing two- and three- dimensional types that comprise simple and complex meshes. Six meta-heuristic algorithms are utilized to determine the optimal number of clusters and minimize the decomposition problem. Finally, corresponding statistical results are compared.

A classification approach based on variable precision rough sets and cluster validity index function

2014 ◽  
Vol 31 (8) ◽  
pp. 1778-1789
Author(s):  
Hongkang Lin
Keyword(s):  
Optimal Number ◽  
Data Sets ◽  
Cluster Validity ◽  
Cluster Validity Index ◽  
Index Method ◽  
Data Set ◽  
Content Type ◽  
The Individual ◽  
Variable Precision Rough Sets ◽  
Optimal Number Of Clusters

Purpose – The clustering/classification method proposed in this study, designated as the PFV-index method, provides the means to solve the following problems for a data set characterized by imprecision and uncertainty: first, discretizing the continuous values of all the individual attributes within a data set; second, evaluating the optimality of the discretization results; third, determining the optimal number of clusters per attribute; and fourth, improving the classification accuracy (CA) of data sets characterized by uncertainty. The paper aims to discuss these issues. Design/methodology/approach – The proposed method for the solution of the clustering/classifying problem, designated as PFV-index method, combines a particle swarm optimization algorithm, fuzzy C-means method, variable precision rough sets theory, and a new cluster validity index function. Findings – This method could cluster the values of the individual attributes within the data set and achieves both the optimal number of clusters and the optimal CA. Originality/value – The validity of the proposed approach is investigated by comparing the classification results obtained for UCI data sets with those obtained by supervised classification BPNN, decision-tree methods.

A new cluster validity index using maximum cluster spread based compactness measure

2016 ◽  
Vol 9 (2) ◽  
pp. 179-204 ◽  
Author(s):  
M. Arif Wani ◽  
Romana Riyaz
Keyword(s):  
Optimal Number ◽  
Data Sets ◽  
Cluster Validity ◽  
Cluster Validity Index ◽  
Validity Index ◽  
Data Set ◽  
Number Of Clusters ◽  
Content Type ◽  
Validity Indices ◽  
Optimal Number Of Clusters

Purpose – The most commonly used approaches for cluster validation are based on indices but the majority of the existing cluster validity indices do not work well on data sets of different complexities. The purpose of this paper is to propose a new cluster validity index (ARSD index) that works well on all types of data sets. Design/methodology/approach – The authors introduce a new compactness measure that depicts the typical behaviour of a cluster where more points are located around the centre and lesser points towards the outer edge of the cluster. A novel penalty function is proposed for determining the distinctness measure of clusters. Random linear search-algorithm is employed to evaluate and compare the performance of the five commonly known validity indices and the proposed validity index. The values of the six indices are computed for all nc ranging from (nc min, nc max) to obtain the optimal number of clusters present in a data set. The data sets used in the experiments include shaped, Gaussian-like and real data sets. Findings – Through extensive experimental study, it is observed that the proposed validity index is found to be more consistent and reliable in indicating the correct number of clusters compared to other validity indices. This is experimentally demonstrated on 11 data sets where the proposed index has achieved better results. Originality/value – The originality of the research paper includes proposing a novel cluster validity index which is used to determine the optimal number of clusters present in data sets of different complexities.

scholarly journals A Hybrid Clustering Approach for Bag-of-Words Image Categorization

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Hui Huang ◽  
Yan Ma
Keyword(s):  
Hierarchical Clustering ◽  
Optimal Number ◽  
Bag Of Words ◽  
Image Categorization ◽  
Vocabulary Size ◽  
Number Of Clusters ◽  
Visual Words ◽  
Initial Cluster ◽  
Clustering Approach ◽  
Optimal Number Of Clusters

The Bag-of-Words (BoW) model is a well-known image categorization technique. However, in conventional BoW, neither the vocabulary size nor the visual words can be determined automatically. To overcome these problems, a hybrid clustering approach that combines improved hierarchical clustering with a K-means algorithm is proposed. We present a cluster validity index for the hierarchical clustering algorithm to adaptively determine when the algorithm should terminate and the optimal number of clusters. Furthermore, we improve the max-min distance method to optimize the initial cluster centers. The optimal number of clusters and initial cluster centers are fed into K-means, and finally the vocabulary size and visual words are obtained. The proposed approach is extensively evaluated on two visual datasets. The experimental results show that the proposed method outperforms the conventional BoW model in terms of categorization and demonstrate the feasibility and effectiveness of our approach.

scholarly journals A novel fuzzy clustering approach to regionalise watersheds with an automatic determination of optimal number of clusters

2017 ◽  
Vol 65 (4) ◽  
pp. 359-365 ◽  
Author(s):  
Javier Senent-Aparicio ◽  
Jesús Soto ◽  
Julio Pérez-Sánchez ◽  
Jorge Garrido
Keyword(s):  
Frequency Analysis ◽  
Fuzzy Clustering ◽  
Optimal Number ◽  
Regional Frequency Analysis ◽  
Cluster Validity ◽  
Number Of Clusters ◽  
Cluster Validity Indices ◽  
Validity Indices ◽  
Homogeneous Regions ◽  
Optimal Number Of Clusters

AbstractOne of the most important problems faced in hydrology is the estimation of flood magnitudes and frequencies in ungauged basins. Hydrological regionalisation is used to transfer information from gauged watersheds to ungauged watersheds. However, to obtain reliable results, the watersheds involved must have a similar hydrological behaviour. In this study, two different clustering approaches are used and compared to identify the hydrologically homogeneous regions. Fuzzy C-Means algorithm (FCM), which is widely used for regionalisation studies, needs the calculation of cluster validity indices in order to determine the optimal number of clusters. Fuzzy Minimals algorithm (FM), which presents an advantage compared with others fuzzy clustering algorithms, does not need to know a priori the number of clusters, so cluster validity indices are not used. Regional homogeneity test based on L-moments approach is used to check homogeneity of regions identified by both cluster analysis approaches. The validation of the FM algorithm in deriving homogeneous regions for flood frequency analysis is illustrated through its application to data from the watersheds in Alto Genil (South Spain). According to the results, FM algorithm is recommended for identifying the hydrologically homogeneous regions for regional frequency analysis.

Cluster Validity Measures Based Agglomerative Hierarchical Clustering for Network Data

2019 ◽  
Vol 23 (3) ◽  
pp. 577-583
Author(s):  
Yukihiro Hamasuna ◽  
Shusuke Nakano ◽  
Ryo Ozaki ◽  
and Yasunori Endo ◽  
◽  
...  
Keyword(s):  
Hierarchical Clustering ◽  
Optimal Number ◽  
Network Data ◽  
Network Clustering ◽  
Agglomerative Hierarchical Clustering ◽  
Cluster Validity ◽  
Validity Measures ◽  
Evaluation Measure ◽  
Network Partitions ◽  
Optimal Number Of Clusters

The Louvain method is a method of agglomerative hierarchical clustering (AHC) that uses modularity as the merging criterion. Modularity is an evaluation measure for network partitions. Cluster validity measures are also used to evaluate cluster partitions and to determine the optimal number of clusters. Several cluster validity measures are constructed considering the geometric features of clusters. These measures and modularity are considered to be the same concept in the viewpoint of evaluating cluster partitions. In this paper, cluster validity measures based agglomerative hierarchical clustering (CVAHC) is proposed as a novel clustering method for network data. The cluster validity measures are used as a merging criterion and an evaluation measure for network data in the proposed method. Numerical experiments show that Dunn’s and Xie-Beni’s indices for network partitions are useful for network clustering.

A NOVEL VALIDITY INDEX FOR THE SUBTRACTIVE CLUSTERING ALGORITHM

2011 ◽  
Vol 25 (04) ◽  
pp. 547-563 ◽  
Author(s):  
HORNG-LIN SHIEH ◽  
CHENG-CHIEN KUO
Keyword(s):  
Clustering Algorithm ◽  
Optimal Number ◽  
Subtractive Clustering ◽  
Cluster Validity ◽  
Cluster Validity Index ◽  
Validity Index ◽  
Simple Method ◽  
Data Points ◽  
Few Data ◽  
Performance Results

This paper proposes a new validity index for the subtractive clustering (SC) algorithm. The subtractive clustering algorithm proposed by Chiu is an effective and simple method for identifying the cluster centers of sampling data based on the concept of a density function. The SC algorithm continually produces the cluster centers until the final potential compared with the original is less than a predefined threshold. The procedure is terminated when there are only a few data points around the most recent cluster. The choice of the threshold is an important factor affecting the clustering results: if it is too large, then too few data points will be accepted as cluster centers; if it is too small, then too many cluster centers will be generated. In this paper, a modified SC algorithm for data clustering based on a cluster validity index is proposed to obtain the optimal number of clusters. Six examples show that the proposed index achieves better performance results than other cluster validities do.

scholarly journals Cluster Validity Index to Determine the Optimal Number Clusters of Fuzzy Clustering for Classify Customer Buying Behavior

2021 ◽  
Vol 5 (1) ◽  
pp. 7-12
Author(s):  
Salnan Ratih Asrriningtias
Keyword(s):  
Fuzzy Clustering ◽  
Optimal Number ◽  
Buying Behavior ◽  
Cluster Validity ◽  
Cluster Validity Index ◽  
Validity Index ◽  
Number Of Clusters ◽  
Best Value ◽  
Fuzzy Clustering Method ◽  
The Right

One of the strategies in order to compete in Batik  MSMEs  is to look at the characteristics of the customer. To make it easier to see the characteristics of  customer buying behavior, it is necessary to classify customers based on similarity of characteristics using fuzzy clustering. One of the parameters that must be determined at the beginning of the fuzzy clustering method is the number of clusters. Increasing the number of clusters does not guarantee the best performance, but the right number of clusters greatly affects the performance of fuzzy clustering. So to get optimal number cluster, we can measured the result of clustering in each number cluster using the cluster validity index. From several types of cluster validity index,  NPC give the best value. Optimal number cluster that obtained by the validity index is 2 and this number cluster give classify result with small variance value

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