Estimating the Optimal Number of Clusters Via Internal Validity Index

2021 ◽  
Author(s):  
Shibing Zhou ◽  
Fei Liu ◽  
Wei Song
Keyword(s):  
Internal Validity ◽  
Optimal Number ◽  
Validity Index ◽  
Number Of Clusters ◽  
Optimal Number Of Clusters

scholarly journals A Validity Index for Fuzzy Clustering Based on Bipartite Modularity

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Yongli Liu ◽  
Xiaoyang Zhang ◽  
Jingli Chen ◽  
Hao Chao
Keyword(s):  
Fuzzy Clustering ◽  
Optimal Number ◽  
Experimental Results ◽  
Validity Index ◽  
Number Of Clusters ◽  
Validity Indices ◽  
Noise Data ◽  
Clustering Validity ◽  
Optimal Number Of Clusters

Because traditional fuzzy clustering validity indices need to specify the number of clusters and are sensitive to noise data, we propose a validity index for fuzzy clustering, named CSBM (compactness separateness bipartite modularity), based on bipartite modularity. CSBM enhances the robustness by combining intraclass compactness and interclass separateness and can automatically determine the optimal number of clusters. In order to estimate the performance of CSBM, we carried out experiments on six real datasets and compared CSBM with other six prominent indices. Experimental results show that the CSBM index performs the best in terms of robustness while accurately detecting the number of clusters.

scholarly journals A Self-Adaptive Fuzzyc-Means Algorithm for Determining the Optimal Number of Clusters

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Min Ren ◽  
Peiyu Liu ◽  
Zhihao Wang ◽  
Jing Yi
Keyword(s):  
Adaptive Method ◽  
Convergence Result ◽  
Decision Function ◽  
Optimal Number ◽  
Validity Index ◽  
Number Of Clusters ◽  
Clustering Validity Index ◽  
Clustering Validity ◽  
Optimal Number Of Clusters ◽  
Self Adaptive

For the shortcoming of fuzzyc-means algorithm (FCM) needing to know the number of clusters in advance, this paper proposed a new self-adaptive method to determine the optimal number of clusters. Firstly, a density-based algorithm was put forward. The algorithm, according to the characteristics of the dataset, automatically determined the possible maximum number of clusters instead of using the empirical rulenand obtained the optimal initial cluster centroids, improving the limitation of FCM that randomly selected cluster centroids lead the convergence result to the local minimum. Secondly, this paper, by introducing a penalty function, proposed a new fuzzy clustering validity index based on fuzzy compactness and separation, which ensured that when the number of clusters verged on that of objects in the dataset, the value of clustering validity index did not monotonically decrease and was close to zero, so that the optimal number of clusters lost robustness and decision function. Then, based on these studies, a self-adaptive FCM algorithm was put forward to estimate the optimal number of clusters by the iterative trial-and-error process. At last, experiments were done on the UCI, KDD Cup 1999, and synthetic datasets, which showed that the method not only effectively determined the optimal number of clusters, but also reduced the iteration of FCM with the stable clustering result.

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.

Clustering Count-based RNA Methylation Data Using a Nonparametric Generative Model

2018 ◽  
Vol 14 (1) ◽  
pp. 11-23 ◽  
Author(s):  
Lin Zhang ◽  
Yanling He ◽  
Huaizhi Wang ◽  
Hui Liu ◽  
Yufei Huang ◽  
...  
Keyword(s):  
Clustering Analysis ◽  
Methylation Level ◽  
Optimal Number ◽  
Generative Model ◽  
Methylation Data ◽  
Sequencing Data ◽  
Number Of Clusters ◽  
Rna Methylation ◽  
Clustering Effect ◽  
Optimal Number Of Clusters

Background: RNA methylome has been discovered as an important layer of gene regulation and can be profiled directly with count-based measurements from high-throughput sequencing data. Although the detailed regulatory circuit of the epitranscriptome remains uncharted, clustering effect in methylation status among different RNA methylation sites can be identified from transcriptome-wide RNA methylation profiles and may reflect the epitranscriptomic regulation. Count-based RNA methylation sequencing data has unique features, such as low reads coverage, which calls for novel clustering approaches. <P><P> Objective: Besides the low reads coverage, it is also necessary to keep the integer property to approach clustering analysis of count-based RNA methylation sequencing data. <P><P> Method: We proposed a nonparametric generative model together with its Gibbs sampling solution for clustering analysis. The proposed approach implements a beta-binomial mixture model to capture the clustering effect in methylation level with the original count-based measurements rather than an estimated continuous methylation level. Besides, it adopts a nonparametric Dirichlet process to automatically determine an optimal number of clusters so as to avoid the common model selection problem in clustering analysis. <P><P> Results: When tested on the simulated system, the method demonstrated improved clustering performance over hierarchical clustering, K-means, MClust, NMF and EMclust. It also revealed on real dataset two novel RNA N6-methyladenosine (m6A) co-methylation patterns that may be induced directly by METTL14 and WTAP, which are two known regulatory components of the RNA m6A methyltransferase complex. <P><P> Conclusion: Our proposed DPBBM method not only properly handles the count-based measurements of RNA methylation data from sites of very low reads coverage, but also learns an optimal number of clusters adaptively from the data analyzed. <P><P> Availability: The source code and documents of DPBBM R package are freely available through the Comprehensive R Archive Network (CRAN): https://cran.r-project.org/web/packages/DPBBM/.

Investigating cluster validation metrics for optimal number of clusters determination

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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