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Journal ArticleDOI

A New Cluster Validity Index for Fuzzy Clustering

TL;DR: A new “Graded Distance index” (GD_index) is proposed for computing optimal number of fuzzy clusters for a given data set and the efficiency of this index is compared with well-known existing indices and tested on several data sets.
About: This article is published in IFAC Proceedings Volumes.The article was published on 2013-12-01. It has received 21 citations till now. The article focuses on the topics: Fuzzy clustering & Cluster analysis.
Citations
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Journal ArticleDOI
TL;DR: This review examines the various clustering algorithms applicable to the gene expression data in order to discover and provide useful knowledge of the appropriate clustering technique that will guarantee stability and high degree of accuracy in its analysis procedure.
Abstract: Gene expression data hide vital information required to understand the biological process that takes place in a particular organism in relation to its environment. Deciphering the hidden patterns in gene expression data proffers a prodigious preference to strengthen the understanding of functional genomics. The complexity of biological networks and the volume of genes present increase the challenges of comprehending and interpretation of the resulting mass of data, which consists of millions of measurements; these data also inhibit vagueness, imprecision, and noise. Therefore, the use of clustering techniques is a first step toward addressing these challenges, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. The clustering of gene expression data has been proven to be useful in making known the natural structure inherent in gene expression data, understanding gene functions, cellular processes, and subtypes of cells, mining useful information from noisy data, and understanding gene regulation. The other benefit of clustering gene expression data is the identification of homology, which is very important in vaccine design. This review examines the various clustering algorithms applicable to the gene expression data in order to discover and provide useful knowledge of the appropriate clustering technique that will guarantee stability and high degree of accuracy in its analysis procedure.

134 citations

Journal ArticleDOI
TL;DR: A Neuro-Fuzzy C-Means Clustering algorithm (NFCM) is presented to resolve the issues mentioned above by adopting a novel Artificial Neural Network (ANN) based clustering approach.

33 citations

Journal ArticleDOI
08 Feb 2021-Energies
TL;DR: In this paper, the authors classified the Central and Eastern European (CEE) countries from the point of view of green energy transformation (original indicator) and to predict new threats to Romania, Poland, and Bulgaria.
Abstract: In the conditions of climate change and the scarcity of natural resources, the future of energy is increasingly associated with the development of the so-called green energy. Its development is reflected in the European Commission strategic vision to transition to a climate-neutral economy. This is a challenge that the Central and Eastern European (CEE) countries, members of the EU, are also trying to meet. In recent years, these countries have seen an increase in the share of renewable energy and a reduction in greenhouse gas emissions (GGE). On the other hand, basing the energy sector on unstable energy sources (photovoltaics and wind technologies) may imply new challenges on the way to sustainable development. These are old problems in a new version (ecology, diversification of supplies) and new ones related to the features of renewable energy sources (RES; instability, dispersion). The aim of the article was to classify, on the basis of taxonomic methods, the CEE countries from the point of view of green energy transformation (original indicator) and to predict new threats to Romania, Poland, and Bulgaria, the countries representing different groups according to the applied classification. The issues presented are part of a holistic view of RES and can be useful in energy policy.

27 citations


Cites background from "A New Cluster Validity Index for Fu..."

  • ...They are applicable (also in social sciences) in assessing the similarities and differences between the studied objects (countries) [12,13]....

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Journal ArticleDOI
13 Aug 2019-Genes
TL;DR: A multi-objective optimization-based fuzzy clustering approach for detecting cell clusters from scRNA-seq data that obtained differentially expressed genes (DEGs) using Limma through the comparison of expression of the samples between each resultant cluster and the remaining clusters.
Abstract: Rapid advance in single-cell RNA sequencing (scRNA-seq) allows measurement of the expression of genes at single-cell resolution in complex disease or tissue. While many methods have been developed to detect cell clusters from the scRNA-seq data, this task currently remains a main challenge. We proposed a multi-objective optimization-based fuzzy clustering approach for detecting cell clusters from scRNA-seq data. First, we conducted initial filtering and SCnorm normalization. We considered various case studies by selecting different cluster numbers ( c l = 2 to a user-defined number), and applied fuzzy c-means clustering algorithm individually. From each case, we evaluated the scores of four cluster validity index measures, Partition Entropy ( P E ), Partition Coefficient ( P C ), Modified Partition Coefficient ( M P C ), and Fuzzy Silhouette Index ( F S I ). Next, we set the first measure as minimization objective (↓) and the remaining three as maximization objectives (↑), and then applied a multi-objective decision-making technique, TOPSIS, to identify the best optimal solution. The best optimal solution (case study) that had the highest TOPSIS score was selected as the final optimal clustering. Finally, we obtained differentially expressed genes (DEGs) using Limma through the comparison of expression of the samples between each resultant cluster and the remaining clusters. We applied our approach to a scRNA-seq dataset for the rare intestinal cell type in mice [GEO ID: GSE62270, 23,630 features (genes) and 288 cells]. The optimal cluster result (TOPSIS optimal score= 0.858) comprised two clusters, one with 115 cells and the other 91 cells. The evaluated scores of the four cluster validity indices, F S I , P E , P C , and M P C for the optimized fuzzy clustering were 0.482, 0.578, 0.607, and 0.215, respectively. The Limma analysis identified 1240 DEGs (cluster 1 vs. cluster 2). The top ten gene markers were Rps21, Slc5a1, Crip1, Rpl15, Rpl3, Rpl27a, Khk, Rps3a1, Aldob and Rps17. In this list, Khk (encoding ketohexokinase) is a novel marker for the rare intestinal cell type. In summary, this method is useful to detect cell clusters from scRNA-seq data.

19 citations

References
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Book
01 Jan 1973

810 citations

Journal ArticleDOI
TL;DR: A solution obtained without prior knowledge of labelled pattern structure is offered in support of contention that the fuzzy clustering technique proposed affords a comparatively reliable criterion for a posteriori evaluation of cluster validity.
Abstract: A recently developed fuzzy clustering technique is utilized to analyze the substructure of a well known set of 4-dimensional botanical data. A solution obtained without prior knowledge of labelled pattern structure is offered in support of our contention that the technique proposed affords a comparatively reliable criterion for a posteriori evaluation of cluster validity.

579 citations

Journal ArticleDOI
TL;DR: The fundamental concepts of cluster validity are introduced, and a review of fuzzy cluster validity indices available in the literature are presented, and extensive comparisons of the mentioned indices are conducted in conjunction with the Fuzzy C-Means clustering algorithm.

489 citations

Journal ArticleDOI
TL;DR: Validation of fuzzy partitions induced through c-shells clustering is considered, and a new set of indices are shown to be capable of validating the structure characterized by the shell clustering algorithms.

264 citations

Journal ArticleDOI
Soon-H. Kwon1
TL;DR: A new cluster validation index is presented which can be used to eliminate the montonically decreasing tendency when the number of clusters becomes very large and close to thenumber of data points.
Abstract: A new cluster validation index is presented which can be used to eliminate the montonically decreasing tendency when the number of clusters becomes very large and close to the number of data points The limiting behaviour is described and numerical examples presented to show the effectiveness of the proposed cluster validity index

264 citations