Performance Evaluation of Line Symmetry-Based Validity Indices on Clustering Algorithms

2017 ◽  
Vol 26 (3) ◽  
pp. 483-503 ◽  
Author(s):  
Vijay Kumar ◽  
Jitender Kumar Chhabra ◽  
Dinesh Kumar
Keyword(s):  
Clustering Algorithms ◽  
Harmony Search ◽  
Real Life ◽  
Optimal Number ◽  
Distance Measures ◽  
Cluster Validity ◽  
Number Of Clusters ◽  
Cluster Validity Indices ◽  
Validity Indices ◽  
On Line

AbstractFinding the optimal number of clusters and the appropriate partitioning of the given dataset are the two major challenges while dealing with clustering. For both of these, cluster validity indices are used. In this paper, seven widely used cluster validity indices, namely DB index, PS index, I index, XB index, FS index, K index, and SV index, have been developed based on line symmetry distance measures. These indices provide the measure of line symmetry present in the partitioning of the dataset. These are able to detect clusters of any shape or size in a given dataset, as long as they possess the property of line symmetry. The performance of these indices is evaluated on three clustering algorithms: K-means, fuzzy-C means, and modified harmony search-based clustering (MHSC). The efficacy of symmetry-based validity indices on clustering algorithms is demonstrated on artificial and real-life datasets, six each, with the number of clusters varying from 2 to $\sqrt n ,$ where n is the total number of data points existing in the dataset. The experimental results reveal that the incorporation of line symmetry-based distance improves the capabilities of these existing validity indices in finding the appropriate number of clusters. Comparisons of these indices are done with the point symmetric and original versions of these seven validity indices. The results also demonstrate that the MHSC technique performs better as compared to other well-known clustering techniques. For real-life datasets, analysis of variance statistical analysis is also performed.

scholarly journals Role of Cluster Validity Indices in Delineation of Precipitation Regions

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1372
Author(s):  
Nikhil Bhatia ◽  
Jency M. Sojan ◽  
Slobodon Simonovic ◽  
Roshan Srivastav
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Ratio Test ◽  
Cluster Validity ◽  
Number Of Clusters ◽  
Cluster Validity Indices ◽  
Validity Indices ◽  
Point Data ◽  
Optimal Number Of Clusters

The delineation of precipitation regions is to identify homogeneous zones in which the characteristics of the process are statistically similar. The regionalization process has three main components: (i) delineation of regions using clustering algorithms, (ii) determining the optimal number of regions using cluster validity indices (CVIs), and (iii) validation of regions for homogeneity using L-moments ratio test. The identification of the optimal number of clusters will significantly affect the homogeneity of the regions. The objective of this study is to investigate the performance of the various CVIs in identifying the optimal number of clusters, which maximizes the homogeneity of the precipitation regions. The k-means clustering algorithm is adopted to delineate the regions using location-based attributes for two large areas from Canada, namely, the Prairies and the Great Lakes-St Lawrence lowlands (GL-SL) region. The seasonal precipitation data for 55 years (1951–2005) is derived using high-resolution ANUSPLIN gridded point data for Canada. The results indicate that the optimal number of clusters and the regional homogeneity depends on the CVI adopted. Among 42 cluster indices considered, 15 of them outperform in identifying the homogeneous precipitation regions. The Dunn, D e t _ r a t i o and Trace( W − 1 B ) indices found to be the best for all seasons in both the regions.

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.

scholarly journals Towards Expert-Inspired Automatic Criterion to Cut a Dendrogram for Real-Industrial Applications

2021 ◽  
Author(s):  
Shikha Suman ◽  
Ashutosh Karna ◽  
Karina Gibert
Keyword(s):  
Hierarchical Clustering ◽  
Clustering Algorithms ◽  
Computational Cost ◽  
Real Life ◽  
Ground Truth ◽  
Industrial Applications ◽  
Underlying Structure ◽  
Cluster Validity ◽  
Cluster Validity Index ◽  
Number Of Clusters

Hierarchical clustering is one of the most preferred choices to understand the underlying structure of a dataset and defining typologies, with multiple applications in real life. Among the existing clustering algorithms, the hierarchical family is one of the most popular, as it permits to understand the inner structure of the dataset and find the number of clusters as an output, unlike popular methods, like k-means. One can adjust the granularity of final clustering to the goals of the analysis themselves. The number of clusters in a hierarchical method relies on the analysis of the resulting dendrogram itself. Experts have criteria to visually inspect the dendrogram and determine the number of clusters. Finding automatic criteria to imitate experts in this task is still an open problem. But, dependence on the expert to cut the tree represents a limitation in real applications like the fields industry 4.0 and additive manufacturing. This paper analyses several cluster validity indexes in the context of determining the suitable number of clusters in hierarchical clustering. A new Cluster Validity Index (CVI) is proposed such that it properly catches the implicit criteria used by experts when analyzing dendrograms. The proposal has been applied on a range of datasets and validated against experts ground-truth overcoming the results obtained by the State of the Art and also significantly reduces the computational cost.

scholarly journals Number of Clusters and the Quality of Hybrid Predictive Models in Analytical CRM

2014 ◽  
Vol 37 (1) ◽  
pp. 141-157 ◽  
Author(s):  
Mariusz Łapczyński ◽  
Bartłomiej Jefmański
Keyword(s):  
Predictive Models ◽  
Cluster Validity ◽  
Number Of Clusters ◽  
Model Combining ◽  
Cluster Validity Indices ◽  
Validity Indices ◽  
And Cluster Analysis ◽  
Analytical Tools ◽  
F Measure

Abstract Making more accurate marketing decisions by managers requires building effective predictive models. Typically, these models specify the probability of customer belonging to a particular category, group or segment. The analytical CRM categories refer to customers interested in starting cooperation with the company (acquisition models), customers who purchase additional products (cross- and up-sell models) or customers intending to resign from the cooperation (churn models). During building predictive models researchers use analytical tools from various disciplines with an emphasis on their best performance. This article attempts to build a hybrid predictive model combining decision trees (C&RT algorithm) and cluster analysis (k-means). During experiments five different cluster validity indices and eight datasets were used. The performance of models was evaluated by using popular measures such as: accuracy, precision, recall, G-mean, F-measure and lift in the first and in the second decile. The authors tried to find a connection between the number of clusters and models' quality.

scholarly journals Assessment of some combinations of hard and fuzzy clustering techniques for regionalisation of catchments in Sefidroud basin

2016 ◽  
Vol 18 (6) ◽  
pp. 1033-1054 ◽  
Author(s):  
Ali Ahani ◽  
S. Saeid Mousavi Nadoushani
Keyword(s):  
Objective Function ◽  
Clustering Algorithms ◽  
Hybrid Approach ◽  
Hybrid Algorithms ◽  
Flood Frequency Analysis ◽  
Cluster Validity ◽  
Fcm Algorithm ◽  
Cluster Validity Indices ◽  
Validity Indices ◽  
Regional Flood Frequency Analysis

Cluster analysis methods are a type of well-known technique for regionalisation of catchments to perform regional flood frequency analysis. In this study, a fuzzy extension of hybrid clustering algorithms is evaluated. Self-organizing feature maps and four hierarchical clustering algorithms were used to provide the initial cluster centres for fuzzy c-means (FCM) algorithm. The hybrid approach was used for regionalisation of catchments in Sefidroud basin based on feature vectors including five catchment attributes: longitude and latitude, drainage area, runoff coefficient and mean annual precipitation. The results showed that according to the values of both the objective function and the cluster validity indices, the performances of FCM algorithm often was improved by using the proposed hybrid approach. Also, it was evident from the results that in the case of minimizing the objective function, the combination of Ward's algorithm and FCM provided best results, but according to the cluster validity indices, other hybrid algorithms such as combinations of single linkage or complete linkage and FCM algorithm presented the most desirable results. In addition, according to the results, there are two well-defined homogeneous regions in Sefidroud basin identified by all the examined hybrid algorithms.

Automatic Data Clustering Using Parameter Adaptive Harmony Search Algorithm and Its Application to Image Segmentation

2016 ◽  
Vol 25 (4) ◽  
pp. 595-610 ◽  
Author(s):  
Vijay Kumar ◽  
Jitender Kumar Chhabra ◽  
Dinesh Kumar
Keyword(s):  
Data Clustering ◽  
Euclidean Distance ◽  
Search Algorithm ◽  
Harmony Search ◽  
Real Life ◽  
Optimal Number ◽  
Optimization Strategy ◽  
Number Of Clusters ◽  
Automatic Data ◽  
Parameter Adaptive

AbstractIn this paper, the problem of automatic data clustering is treated as the searching of optimal number of clusters so that the obtained partitions should be optimized. The automatic data clustering technique utilizes a recently developed parameter adaptive harmony search (PAHS) as an underlying optimization strategy. It uses real-coded variable length harmony vector, which is able to detect the number of clusters automatically. The newly developed concepts regarding “threshold setting” and “cutoff” are used to refine the optimization strategy. The assignment of data points to different cluster centers is done based on the newly developed weighted Euclidean distance instead of Euclidean distance. The developed approach is able to detect any type of cluster irrespective of their geometric shape. It is compared with four well-established clustering techniques. It is further applied for automatic segmentation of grayscale and color images, and its performance is compared with other existing techniques. For real-life datasets, statistical analysis is done. The technique shows its effectiveness and the usefulness.

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.

Automatic Genetic Fuzzy c-Means

2018 ◽  
Vol 29 (1) ◽  
pp. 529-539
Author(s):  
Khalid Jebari ◽  
Abdelaziz Elmoujahid ◽  
Aziz Ettouhami
Keyword(s):  
Fitness Function ◽  
Real Data ◽  
Optimal Number ◽  
Data Sets ◽  
Number Of Clusters ◽  
Fuzzy C Means ◽  
Cluster Validity Indices ◽  
Validity Indices ◽  
Tournament Selection

Abstract Fuzzy c-means is an efficient algorithm that is amply used for data clustering. Nonetheless, when using this algorithm, the designer faces two crucial choices: choosing the optimal number of clusters and initializing the cluster centers. The two choices have a direct impact on the clustering outcome. This paper presents an improved algorithm called automatic genetic fuzzy c-means that evolves the number of clusters and provides the initial centroids. The proposed algorithm uses a genetic algorithm with a new crossover operator, a new mutation operator, and modified tournament selection; further, it defines a new fitness function based on three cluster validity indices. Real data sets are used to demonstrate the effectiveness, in terms of quality, of the proposed algorithm.

scholarly journals Comparison of Cluster Validity Index and Distance Measures Using Integrated Cluster Analysis and Structural Equation Modeling the Warp-PLS Approach

2021 ◽  
Vol 56 (3) ◽  
pp. 157-168
Author(s):  
Adji Achmad Rinaldo Fernandes ◽  
Solimun ◽  
Nurjannah ◽  
Usfi Al Imama Billah ◽  
Ni Made Ayu Astari Badung
Keyword(s):  
Cluster Analysis ◽  
Service Quality ◽  
Willingness To Pay ◽  
Distance Measures ◽  
Primary Data ◽  
Equation Modeling ◽  
Average Score ◽  
Cluster Validity ◽  
Cluster Validity Indices ◽  
Validity Indices

This study wants to compare the Integrated Cluster Analysis and SEM model of the Warp-PLS approach with various cluster validity indices and distance measures on Service Quality, Environment, Fashions, Willingness to Pay, and Compliant Paying Behavior of Bank X Customers. The data used in this study are primary. The variables used in this study are service quality, environment, fashion, willingness to pay, and compliance with paying behavior at Bank X. The data were obtained through a questionnaire with a Likert scale — measurement of variables in primary data using the average score of each item. The sampling technique used was purposive sampling. The object of observation is the customer as many as 100 respondents. Data analysis was carried out quantitatively, and a descriptive analysis was carried out first. An Integrated Cluster Analysis and SEM analysis of the Warp-PLS approach was carried out with the average linkage method on various cluster validity indices and three distance measures. The Warp-PLS approach's integrated cluster and SEM model with the Gap Index, Index C, Global Sillhouette, and Goodman-Kruskal with the Manhattan Distance are better than the Gap, Index C, Global Sillhouette, and Goodman-Kruskal with the Euclidean and Minkowski Distance. The novelty in this research is the application of Integrated Cluster Analysis and SEM of the Warp-PLS approach to compare 4 cluster validity indices, namely Gap Index, C Index, Global Sillhouette, and Goodman-Kruskal, and three distance measures, namely Euclidean, Manhattan, and Minkowski distances simultaneously.

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