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

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.

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Role of Cluster Validity Indices in Delineation of Precipitation Regions

Water ◽

10.3390/w12051372 ◽

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.

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Fast Search Algorithm for Determining the Optimal Number of Clusters using Cluster Validity Index

The Journal of the Korea Contents Association ◽

10.5392/jkca.2009.9.9.080 ◽

2009 ◽

Vol 9 (9) ◽

pp. 80-89 ◽

Cited By ~ 1

Author(s):

Sang-Wook Lee

Keyword(s):

Search Algorithm ◽

Optimal Number ◽

Cluster Validity ◽

Cluster Validity Index ◽

Validity Index ◽

Number Of Clusters ◽

Fast Search ◽

Fast Search Algorithm ◽

Optimal Number Of Clusters

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Investigating cluster validation metrics for optimal number of clusters determination

Intelligent Decision Technologies ◽

10.3233/idt-210187 ◽

2021 ◽

pp. 1-16

Author(s):

Aikaterini Karanikola ◽

Charalampos M. Liapis ◽

Sotiris Kotsiantis

Keyword(s):

Real World ◽

Optimal Number ◽

Cluster Validation ◽

Clustering Methods ◽

Number Of Clusters ◽

Validity Indices ◽

Selection Of ◽

Specific Distance ◽

Optimal Number Of Clusters

In short, clustering is the process of partitioning a given set of objects into groups containing highly related instances. This relation is determined by a specific distance metric with which the intra-cluster similarity is estimated. Finding an optimal number of such partitions is usually the key step in the entire process, yet a rather difficult one. Selecting an unsuitable number of clusters might lead to incorrect conclusions and, consequently, to wrong decisions: the term “optimal” is quite ambiguous. Furthermore, various inherent characteristics of the datasets, such as clusters that overlap or clusters containing subclusters, will most often increase the level of difficulty of the task. Thus, the methods used to detect similarities and the parameter selection of the partition algorithm have a major impact on the quality of the groups and the identification of their optimal number. Given that each dataset constitutes a rather distinct case, validity indices are indicators introduced to address the problem of selecting such an optimal number of clusters. In this work, an extensive set of well-known validity indices, based on the approach of the so-called relative criteria, are examined comparatively. A total of 26 cluster validation measures were investigated in two distinct case studies: one in real-world and one in artificially generated data. To ensure a certain degree of difficulty, both real-world and generated data were selected to exhibit variations and inhomogeneity. Each of the indices is being deployed under the schemes of 9 different clustering methods, which incorporate 5 different distance metrics. All results are presented in various explanatory forms.

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Multi-Objective Genetic Algorithm for Robust Clustering with Unknown Number of Clusters

International Journal of Applied Evolutionary Computation ◽

10.4018/jaec.2012010101 ◽

2012 ◽

Vol 3 (1) ◽

pp. 1-20

Author(s):

Amit Banerjee

Keyword(s):

Genetic Algorithm ◽

Data Clustering ◽

Optimal Number ◽

Least Trimmed Squares ◽

Cluster Assignment ◽

Objective Criterion ◽

Number Of Clusters ◽

Multi Objective ◽

Multi Objective Genetic Algorithm ◽

Optimal Number Of Clusters

In this paper, a multi-objective genetic algorithm for data clustering based on the robust fuzzy least trimmed squares estimator is presented. The proposed clustering methodology addresses two critical issues in unsupervised data clustering – the ability to produce meaningful partition in noisy data, and the requirement that the number of clusters be known a priori. The multi-objective genetic algorithm-driven clustering technique optimizes the number of clusters as well as cluster assignment, and cluster prototypes. A two-parameter, mapped, fixed point coding scheme is used to represent assignment of data into the true retained set and the noisy trimmed set, and the optimal number of clusters in the retained set. A three-objective criterion is also used as the minimization functional for the multi-objective genetic algorithm. Results on well-known data sets from literature suggest that the proposed methodology is superior to conventional fuzzy clustering algorithms that assume a known value for optimal number of clusters.

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

Journal of Hydrology and Hydromechanics ◽

10.1515/johh-2017-0024 ◽

2017 ◽

Vol 65 (4) ◽

pp. 359-365 ◽

Cited By ~ 1

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.

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

10.21203/rs.3.rs-58011/v3 ◽

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.

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Internal evaluation criteria for categorical data in hierarchical clustering

Advances in Methodology and Statistics ◽

10.51936/lxut1974 ◽

2018 ◽

Vol 15 (2) ◽

Author(s):

Zdeněk Šulc ◽

Jana Cibulková ◽

Jiří Procházka ◽

Hana Řezanková

Keyword(s):

Hierarchical Clustering ◽

Categorical Data ◽

Likelihood Function ◽

Evaluation Criteria ◽

Optimal Number ◽

Number Of Clusters ◽

Internal Evaluation ◽

Correct Number ◽

Cluster Quality ◽

Optimal Number Of Clusters

The paper compares 11 internal evaluation criteria for hierarchical clustering of categorical data regarding a correct number of clusters determination. The criteria are divided into three groups based on a way of treating the cluster quality. The variability-based criteria use the within-cluster variability, the likelihood-based criteria maximize the likelihood function, and the distance-based criteria use distances within and between clusters. The aim is to determine which evaluation criteria perform well and under what conditions. Different analysis settings, such as the used method of hierarchical clustering, and various dataset properties, such as the number of variables or the minimal between-cluster distances, are examined. The experiment is conducted on 810 generated datasets, where the evaluation criteria are assessed regarding the optimal number of clusters determination and mean absolute errors. The results indicate that the likelihood-based BIC1 and variability-based BK criteria perform relatively well in determining the optimal number of clusters and that some criteria, usually the distance-based ones, should be avoided.

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GIVING FUZZINESS TO SPATIAL CLUSTERS: A NEW INDEX FOR CHOOSING THE OPTIMAL NUMBER OF CLUSTERS

International Journal of Artificial Intelligence Tools ◽

10.1142/s0218213013500097 ◽

2013 ◽

Vol 22 (03) ◽

pp. 1350009 ◽

Cited By ~ 2

Author(s):

GEORGE GREKOUSIS

Keyword(s):

Fuzzy Clustering ◽

Spatial Clustering ◽

Clustering Algorithms ◽

Optimal Number ◽

Fuzzy Cluster ◽

Cluster Validation ◽

Number Of Clusters ◽

A Value ◽

Membership Value ◽

Optimal Number Of Clusters

Choosing the optimal number of clusters is a key issue in cluster analysis. Especially when dealing with more spatial clustering, things tend to be more complicated. Cluster validation helps to determine the appropriate number of clusters present in a dataset. Furthermore, cluster validation evaluates and assesses the results of clustering algorithms. There are numerous methods and techniques for choosing the optimal number of clusters via crisp and fuzzy clustering. In this paper, we introduce a new index for fuzzy clustering to determine the optimal number of clusters. This index is not another metric for calculating compactness or separation among partitions. Instead, the index uses several existing indices to give a degree, or fuzziness, to the optimal number of clusters. In this way, not only do the objects in a fuzzy cluster get a membership value, but the number of clusters to be partitioned is given a value as well. The new index is used in the fuzzy c-means algorithm for the geodemographic segmentation of 285 postal codes.

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