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.

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 A Quantitative Discriminant Method of Elbow Point for the Optimal Number of Clusters in Clustering Algorithm

2021 ◽  
Author(s):  
Congming Shi ◽  
Bingtao Wei ◽  
Shoulin Wei ◽  
Wen Wang ◽  
Hai Liu ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Machine Learning Method ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Public Dataset ◽  
Optimal Cluster ◽  
Better Than ◽  
Optimal Number Of Clusters

Abstract Clustering, a traditional machine learning method, plays a significant role in data analysis. Most clustering algorithms depend on a predetermined exact number of clusters, whereas, in practice, clusters are usually unpredictable. Although the Elbow method is one of the most commonly used methods to discriminate the optimal cluster number, the discriminant of the number of clusters depends on the manual identification of the elbow points on the visualization curve. Thus, experienced analysts cannot clearly identify the elbow point from the plotted curve when the plotted curve is fairly smooth. To solve this problem, a new elbow point discriminant method is proposed to yield a statistical metric that estimates an optimal cluster number when clustering on a dataset. First, the average degree of distortion obtained by the Elbow method is normalized to the range of 0 to 10. Second, the normalized results are used to calculate the cosine of intersection angles between elbow points. Third, this calculated cosine of intersection angles and the arccosine theorem are used to compute the intersection angles between elbow points. Finally, the index of the above computed minimal intersection angles between elbow points is used as the estimated potential optimal cluster number. The experimental results based on simulated datasets and a well-known public dataset (Iris Dataset) demonstrated that the estimated optimal cluster number obtained by our newly proposed method is better than the widely used Silhouette method.

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 Quantitative Discriminant Method of Elbow Point for the Optimal Number of Clusters in Clustering Algorithm

2020 ◽  
Author(s):  
Congming Shi ◽  
Bingtao Wei ◽  
Shoulin Wei ◽  
Wen Wang ◽  
Hai Liu ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Machine Learning Method ◽  
Learning Method ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Optimal Cluster ◽  
Better Than ◽  
Optimal Number Of Clusters

Abstract Clustering, as a traditional machine learning method, is still playing a significant role in data analysis. The most of clustering algorithms depend on a predetermined exact number of clusters, whereas, in practice, clusters are usually unpredictable. Although elbow method is one of the most commonly used methods to discriminate the optimal cluster number, the discriminant of the number of clusters depends on manual identification of the elbow points on the visualization curve, which will lead to the experienced analysts not being able to clearly identify the elbow point from the plotted curve when the plotted curve being fairly smooth. To solve this problem, a new elbow point discriminant method is proposed to work out a statistical metric estimating an optimal cluster number when clustering on a dataset. Firstly, the average degree of distortion obtained by Elbow method is normalized to the range of 0 to10; Secondly, the normalized results are used to calculate Cosine of intersection angles between elbow points; Thirdly, the above calculated Cosine of intersection angles and Arccosine theorem are used to compute the intersection angles between elbow points; Finally, the index of the above computed minimal intersection angles between elbow points is used as the estimated potential optimal cluster number. The experimental results based on simulated datasets and a public well-known dataset demonstrated that the estimated optimal cluster number output by our newly proposed method is better than widely used Silhouette method.

scholarly journals A genetic algorithm using Calinski-Harabasz index for automatic clustering problem

2020 ◽  
Vol 12 (3) ◽  
pp. 97-106
Author(s):  
Suzane Pereira Lima ◽  
Marcelo Dib Cruz
Keyword(s):  
Genetic Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Cluster Validity ◽  
Number Of Clusters ◽  
Correct Number ◽  
Clustering Problem ◽  
Automatic Clustering ◽  
Optimal Number Of Clusters

Data clustering is a technique that aims to represent a dataset in clusters according to their similarities. In clustering algorithms, it is usually assumed that the number of clusters is known. Unfortunately, the optimal number of clusters is unknown for many applications. This kind of problem is called Automatic Clustering. There are several cluster validity indexes for evaluating solutions, it is known that the quality of a result is influenced by the chosen function. From this, a genetic algorithm is described in this article for the resolution of the automatic clustering using the Calinski-Harabasz Index as a form of evaluation. Comparisons of the results with other algorithms in the literature are also presented. In a first analysis, fitness values equivalent or higher are found in at least 58% of cases for each comparison. Our algorithm can also find the correct number of clusters or close values in 33 cases out of 48. In another comparison, some fitness values are lower, even with the correct number of clusters, but graphically the partitioning are adequate. Thus, it is observed that our proposal is justified and improvements can be studied for cases where the correct number of clusters is not found.

scholarly journals A Quantitative Discriminant Method of Elbow Point for the Optimal Number of Clusters in Clustering Algorithm

2020 ◽  
Author(s):  
Congming Shi ◽  
Bingtao Wei ◽  
Shoulin Wei ◽  
Wen Wang ◽  
Hai Liu ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Machine Learning Method ◽  
Learning Method ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Optimal Cluster ◽  
Better Than ◽  
Optimal Number Of Clusters

Abstract Clustering, as a traditional machine learning method, is still playing a significant role in data analysis. The most of clustering algorithms depend on a predetermined exact number of clusters, whereas, in practice, clusters are usually unpredictable. Although elbow method is one of the most commonly used methods to discriminate the optimal cluster number, the discriminant of the number of clusters depends on manual identification of the elbow points on the visualization curve, which will lead to the experienced analysts not being able to clearly identify the elbow point from the plotted curve when the plotted curve being fairly smooth. To solve this problem, a new elbow point discriminant method is proposed to work out a statistical metric estimating an optimal cluster number when clustering on a dataset. Firstly, the average degree of distortion obtained by Elbow method is normalized to the range of 0 to10; Secondly, the normalized results are used to calculate Cosine of intersection angles between elbow points; Thirdly, the above calculated Cosine of intersection angles and Arccosine theorem are used to compute the intersection angles between elbow points; Finally, the index of the above computed minimal intersection angles between elbow points is used as the estimated potential optimal cluster number. The experimental results based on simulated datasets and a public well-known dataset (Iris Dataset) demonstrated that the estimated optimal cluster number output by our newly proposed method is better than widely used Silhouette method.

scholarly journals A quantitative discriminant method of elbow point for the optimal number of clusters in clustering algorithm

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Congming Shi ◽  
Bingtao Wei ◽  
Shoulin Wei ◽  
Wen Wang ◽  
Hai Liu ◽  
...  
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Machine Learning Method ◽  
Cluster Number ◽  
Number Of Clusters ◽  
Public Dataset ◽  
Optimal Cluster ◽  
Better Than ◽  
Optimal Number Of Clusters

AbstractClustering, a traditional machine learning method, plays a significant role in data analysis. Most clustering algorithms depend on a predetermined exact number of clusters, whereas, in practice, clusters are usually unpredictable. Although the Elbow method is one of the most commonly used methods to discriminate the optimal cluster number, the discriminant of the number of clusters depends on the manual identification of the elbow points on the visualization curve. Thus, experienced analysts cannot clearly identify the elbow point from the plotted curve when the plotted curve is fairly smooth. To solve this problem, a new elbow point discriminant method is proposed to yield a statistical metric that estimates an optimal cluster number when clustering on a dataset. First, the average degree of distortion obtained by the Elbow method is normalized to the range of 0 to 10. Second, the normalized results are used to calculate the cosine of intersection angles between elbow points. Third, this calculated cosine of intersection angles and the arccosine theorem are used to compute the intersection angles between elbow points. Finally, the index of the above-computed minimal intersection angles between elbow points is used as the estimated potential optimal cluster number. The experimental results based on simulated datasets and a well-known public dataset (Iris Dataset) demonstrated that the estimated optimal cluster number obtained by our newly proposed method is better than the widely used Silhouette method.

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.

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