Clustering Validity Evaluation Research Articles

Multi-fuzzy clustering validity index ensemble: A Dempster-Shafer theory-based parallel and series fusion

Clustering validity evaluation is a key part in clustering process. To adapt the complex data structure, the traditional fuzzy clustering validity index (FCVI) is designed more complex. The weighted combined validity evaluation method (WCVEM) is simple in structure but difficult in weight selection. Therefore, this paper proposed an ensemble method based on multi-fuzzy clustering algorithms and multi-FCVI. Firstly, multi-FCVI are calculated by using the multiple sets of cluster centers and membership degrees that obtained by multi-fuzzy clustering algorithms. This can improve the robustness of the multi-FCVI. Secondly, multi-FCVI are ensembled by Dempster-Shafer (DS) theory. The validity index basic probability assignment function can be obtained by calculating the credibility of each validity index with different clusters number. Finally, the decision module is used to output the optimal clusters number. This paper ensembles multi-fuzzy clustering algorithms, multi-FCVI, and the DS theory by using series and parallel structure to verify performance of the proposed model and the degree of information retention of the FCVI. The proposed method is simple in structure and does not need to be select weighted. 6 artificial datasets and 12 UCI datasets were selected to simulate and verify the method. When facing different data, the simulation results show that the parallel structure has the highest accuracy, and the series structure is even worse than the weighted method in some datasets. In addition, the paper changes the value of fuzzy weighted, and experimental results show that the ensemble method has better stability than other methods in the face of different fuzzy weighted strategy.

A survey of fuzzy clustering validity evaluation methods

As an unsupervised learning method, clustering does not need to know prior knowledge of the datasets in advance. How determining the optimal number of clusters becomes an important method to judge the quality of clustering results. For fuzzy clustering algorithms, the introduction to fuzzy partition makes it more consistent with the structure of real datasets than hard clustering algorithms. Therefore, it is necessary to carry out the research on the validity evaluation methods of fuzzy clustering. At present, the research on fuzzy clustering validity mainly focuses on the fuzzy clustering validity index (FCVI) and the combined fuzzy clustering validity evaluation method (CFCVE). From these two aspects, this paper reviews fuzzy clustering validity functions and combined fuzzy clustering validity evaluation methods. Then FCVI and CFCVE are discussed in details from different points on fuzzy clustering validity functions, and the research status and construction strategies of different fuzzy clustering validity evaluation methods are analyzed. The accuracy and stability of each fuzzy clustering validity evaluation method are analyzed through comparative experiments. Finally, the paper summarizes the shortcomings and advantages of the current research on fuzzy clustering validity and looks forward to the research direction and improved methods of the evaluation methods.

Data-Driven Load Pattern Identification Based on R-Vine Copula and Random Forest Method

Massive residential power consumption information provides data support for the mining and analysis of load patterns. This article proposes a complete framework for load pattern identification, which mainly includes the clustering module and the classification module. Considering that the high-dimensional load profiling dataset will bring a heavy computational burden, multiple dimensional scaling is introduced in the process of data preprocessing. Then, an innovative mixture model based on regular vine copula mixture model (RVMM) is adopted for clustering typical load patterns. Finally, a random forest (RF) classifier constructed with certain load characteristic indexes and RVMM clustering results is employed as a supervised classification model to predict the categories of subsequent new customers, and the accuracy is calculated by the 10-fold cross-validation. It is demonstrated in the case study that the proposed RVMM algorithm exhibits better performance in the clustering validity evaluation. Besides, higher accuracy is achieved by the RF classifier.

Incremental fuzzy clustering of time series

Clustering is one of the most popular data mining methods for analyzing the time series, not only due to its exploratory power, but also because it is often a preprocessing step or subroutine for other techniques. In this paper, an incremental fuzzy clustering algorithm of time series (IFCTS) is proposed, in which the clustering is divided into two stages: offline and online clustering. During the offline clustering process, the fuzzy clustering validity evaluation index is introduced to FCM to automatically obtain the optimal number of initial clusters for off-line data. Then, in the online clustering process, IFCTS algorithm can dynamically update the existing clusters in the incremental data snapshot, distinguish outliers and control the creation of new clusters adaptively by combining with the previous clusters. The experimental results show that the proposed algorithm has good clustering accuracy and efficiency for both equal-length and unequal-length time series.

Combination Evaluation Method of Fuzzy C-Mean Clustering Validity Based on Hybrid Weighted Strategy

Clustering validity function is an index used to judge the accuracy of clustering results. At present, most studies on clustering validity are based on single clustering validity function. Research shows that no clustering validity function can handle any data and always perform better than other indexes. Therefore, a hybrid weighted combination evaluation method based on fuzzy C-means (FCM) clustering validity functions was proposed. The weighting method combines expert weighting with information entropy weighting to improve the subjective factor influence of expert weighting and the shortcoming of information entropy weighting in the value judgment of each clustering validity function. Four clustering validity function combination methods of linear, exponential, logarithm and proportion was studied. Finally, the proposed fuzzy clustering validity evaluation method is verified by experiments on artificial data sets and UCI data sets. The experimental results show that the proposed fuzzy clustering validity evaluation method can overcome the shortcoming of single clustering validity function, and can get the optimal clustering number more accurately for different data sets.

Study on Regional Division of Air Traffic Management in Mainland China in the Future

With the problems of poor coordination and frequent flight delays among major air traffic control regions in mainland China becoming increasingly prominent, a series of air traffic control reform measures are imperative. In order to meet the development need of the transition from a large civil aviation country to power one in the future, it is necessary to divide the air traffic management regions reasonably in advance. Therefore, based on the flights between the airports from 2011 to 2017, this paper combines the grey prediction algorithm with the gravity model and considers the impact of high-speed rail on the flights of civil aviation, then constructs the grey gravity prediction model. According to the forecast result of the future airport flow by the grey gravity prediction model, the flight plans of each airport are generated by using the equal proportion enlargement method. On the basis of the flight plans of each airport, the flight situation in mainland China at a certain time is simulated. According to the simulated aircraft longitude and latitude data, the optimal clustering results are obtained by using the fuzzy C-means clustering algorithm and clustering validity evaluation index. Finally, the clustering results are processed by clustering boundary recognition algorithm, the future air traffic management regional division results in mainland China are obtained. The experimental results show that the prediction accuracy of the grey gravity prediction model considering the influence of high-speed rail is better than the traditional grey prediction algorithm, and the original seven major air traffic control zones in mainland China are re-divided into three major air traffic control zones: North China, South Central China and Northwest China, which can provide reference for future air traffic control reform and development.

A cluster validity evaluation method for dynamically determining the near-optimal number of clusters

Cluster validity evaluation is a hot issue in clustering algorithm research. Aiming at determining the optimal number of clusters in cluster validity evaluation, this paper proposes a new cluster validity index Ratio of Deviation of Sum-of-squares and Euclid distance (RDSED), and designs a cluster validity evaluation method based on RDSED which is suitable to dynamically determine the near-optimal number of clusters. Firstly, based on the analysis of the relationships of the intra-class and inter-class, the concepts of sum-of-squares of within-cluster, sum-of-squares of between-cluster, total sum-of-squares, sum of intra-cluster distance and average distance between clusters are proposed, and then a cluster validity index RDSED based on these concepts is constructed. Secondly, a cluster validity evaluation method based on RDSED for dynamically determining the near-optimal number of clusters is designed. In this method, RDSED value is calculated from large to small in the range of clustering number and this index value is used to dynamically terminate the clustering validity verification process, and finally the near-optimal number of clusters and clustering partition results are obtained. Experiment results of artificial datasets and real datasets show that, compared with some classical clustering validity evaluation method, the proposed cluster validity evaluation method can obtain the near-optimal number of clusters that is closest to the real cluster number in most cases and can effectively evaluate clustering partition results.

Generalized trajectory fuzzy clustering based on the multi-objective mixed function

Spatio-temporal trajectory clustering can extract behavior and moving pattern of object with the change of time and space by exploring similar trajectories. Most of trajectory clustering method can be achieved by expanding the traditional clustering algorithms. Considering the limitations of fitness and optimization of most clustering algorithms, especially for spatio-temporal trajectory data sets, this paper proposes a trajectory fuzzy clustering method based on multi-objective mixed function, which can simultaneously optimize multiple objective function such as FCM and XB when perform particle swarm optimization method. And we also propose a new coarse-grained DTW based on interpolation point for generalization trajectory data and improvement the performance of measure the similarity between trajectories. The experimental results, which implement on the synthetized trajectory data and real vehicle history data by employing the new clustering algorithm, and clustering validity evaluation and hot spots analysis show that the proposed method, which combines different objective functions with different optimization criteria and particle swarm algorithm, can effectively solve the clustering problem and produce better clustering results than the traditional clustering method.

An efficient clustering ensemble selection algorithm

Clustering ensemble selection has been confirmed that it can always achieve better result than traditional clustering ensemble algorithms. However, many selective clustering ensemble algorithms cannot eliminate the inferior quality partitions' influence and the accuracy of clustering is not high. In order to solve the problems, the paper proposes a new selective clustering ensemble algorithm. The algorithm, firstly, uses clustering validity evaluation to evaluate all available clustering ensemble partitions and selects the best quality as reference partition; secondly, the paper defines selection strategy via the quality and diversity; lastly, the paper proposes the adaptive weight strategy of ensemble members. The experimental results show that the new algorithm is effective and clustering performance could be significantly improved.

An automatic method to determine the number of clusters using decision-theoretic rough set

Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. Determining the number of clusters in a data set is one of the most challenging and difficult problems in cluster analysis. To combat the problem, this paper proposes an efficient automatic method by extending the decision-theoretic rough set model to clustering. A new clustering validity evaluation function is designed based on the risk calculated by loss functions and possibilities. Then a hierarchical clustering algorithm, ACA-DTRS algorithm, is proposed, which is proved to stop automatically at the perfect number of clusters without manual interference. Furthermore, a novel fast algorithm, FACA-DTRS, is devised based on the conclusion obtained in the validation of the ACA-DTRS algorithm. The performance of algorithms has been studied on some synthetic and real world data sets. The algorithm analysis and the results of comparison experiments show that the new method, without manual parameter specified in advance, is more valid to determine the number of clusters and more efficient in terms of time cost.

Research on Fuzzy Clustering Validity

The evaluation of clustering validity is important for clustering analysis, and is one of the hottest spots of cluster analysis. The quality of the evaluation of clustering is that optimal number of clusters is reasonable. For fuzzy clustering, the paper surveys the widely known fuzzy clustering validity evaluation based on the methods of fuzzy partition, geometry structure and statistics.

Transcriptome Classification of B-Cell Non-Hodgkins Lymphoma.

B-cell lymphomas are presently diagnosed according to the WHO criteria based on morphologic, immunophenotype and cytogenetic findings. However, the precise distinction among common lymphoma types is frequently a difficult task, and there are areas of overlapping and heterogeneity between them. Here we have analyzed whether gene expression profiling (GEP) data, solely considered, could be used to validate the currently used B-cell lymphoma classification, or proposing new lymphoma types, and for identifying functional signatures or genes defining these GEP-based lymphoma classification.To this aim, we collected Gene Expression Profiling (GEP) for 173 cases of B-cell NHL, including BL (9), DLBCL (36), MALT (3), MCL (20), CLL (38), FL (33), MZL (6) and SMZL (29). The gene expression data for lymphoma cases was normalized against an average gene expression of reactive lymph nodes, except the SMZL which was normalized against normal spleen (3 cases). The analysis of the cases was done using Cluster Accuracy Analysis Tool (CAAT) (Cunningham P., 2005), that enabled us not only to compare gene expression between each node starting from root but also to identify new classes within existing lymphoma diagnosis defined by an internal validation method called Silhouette Width index (Julia Handl. et al, 2005). Using this approach each cluster could be represented by so called silhouette, which is based on the comparison of its tightness and separation. The average silhouette width could be applied for evaluation of clustering validity and can also be used to decide how good the number of selected clusters is.Using this approach, we obtained the following categorization of lymphoma cases: [Display omitted] Using T-Rex (Herrero J & Dopazo J., 2005) to compare differential expression between the categories obtained by CAAT, and FatiScan analysis (Al-Shahrour, F., 2006), we identified genes that were differentially expressed between molecular categories of lymphoma types, assigning them to Gene Ontology (GO) and KEGG (Kyoto Encyclopedia of Genes and Genomes)-defined pathways. The functional signatures that were identified as distinguishing between these lymphoma types were defining cell cycle, cytokine-cytokine receptor interaction, T-cell receptor, B-cell receptor, cell adhesion, NF-kB activation, and other significant interactions. Comparison between these lymphoma clusters following this definition yielded large number of genes distinguishing them, this list including already known genes and a large number of new potential markers.

Silhouettes: A graphical aid to the interpretation and validation of cluster analysis

A new graphical display is proposed for partitioning techniques. Each cluster is represented by a so-called silhouette, which is based on the comparison of its tightness and separation. This silhouette shows which objects lie well within their cluster, and which ones are merely somewhere in between clusters. The entire clustering is displayed by combining the silhouettes into a single plot, allowing an appreciation of the relative quality of the clusters and an overview of the data configuration. The average silhouette width provides an evaluation of clustering validity, and might be used to select an ‘appropriate’ number of clusters.