Fuzzy Clustering Model Research Articles

Personalized Recommendation Intelligent Fuzzy Clustering Model for theTourism

Personalized recommendations in tourism have transformed the way travellers explore new destinations, offering tailored experiences that align with individual preferences and interests. As the travel industry increasingly harnesses data analytics and artificial intelligence, tourists can now receive customized suggestions that reflect their unique tastes, whether they seek adventure, relaxation, cultural immersion, or culinary exploration. This paper explores the implementation and effectiveness of intelligent tourism management strategies using fuzzy clustering and personalized recommendations. By analyzing various scenarios, including baseline, personalized recommendations, dynamic pricing, crisis management, and enhanced resource allocation, the study demonstrates how advanced data-driven techniques can significantly improve key performance indicators such as visitor satisfaction, total revenue, repeat visitation rates, and operational efficiency. The simulation results reveal that personalized recommendations and optimized resource allocation are particularly effective in enhancing visitor experiences and economic outcomes. Conversely, the analysis underscores the critical need for robust crisis management strategies to maintain performance during adverse events. This research provides valuable insights into the transformative potential of intelligent systems in modern tourism management, offering a pathway towards more resilient and competitive tourism destinations. For instance,personalized recommendations increased average visitor satisfaction from 7.2 to 8.5, total revenue from $500,000 to $600,000, and the repeat visitation rate from 35% to 45%. The dynamic pricing strategy improved visitor satisfaction to 7.8 and revenue to $550,000, while enhanced resource allocation resulted in a satisfaction rate of 7.9 and revenue of $570,000. Conversely, crisis management showed the importance of preparedness, as satisfaction dropped to 6.5 and revenue to $450,000. These results underscore the critical need for robust management strategies.

Exploring the Link Between Roommate Compatibility and Academic Outcomes: A Systematic Review of Personality-Based Matching Systems

The collegiate experience significantly influences students’ academic, personal, and social development. Roommate relationships, a central part of shared living arrangements, are crucial for students’ psychosocial well-being and academic success. This systematic review aims to evaluate the effectiveness of personality-based roommate matching systems in improving roommate compatibility, fostering personal development, and enhancing academic performance. A comprehensive search of the Google Scholar and Scopus databases was conducted to identify studies on automated and personality-based systems. Selected studies were screened and analyzed to assess the impact on resource allocation, student satisfaction, and housing efficiency. Personality-based systems - such as fuzzy clustering models, genetic algorithms, and rule-based algorithms - significantly outperform traditional methods in enhancing compatibility and resource allocation. Findings highlight the positive impact of roommate compatibility on students’ self-confidence, communication, and independence, with female students facing unique challenges. Positive relationships, especially among students with high extraversion and conscientiousness, correlate with improved academic outcomes, while negative interactions and depressive symptoms are linked to lower performance and well-being. Personality assessments, like the Open Four Temperaments Scales Test, show promise in reducing conflicts and increasing satisfaction. The study suggests that integrating personality profiling with technology can provide supportive living environments in higher education. However, gaps remain in understanding their impact across different institutional and cultural contexts. Further research is needed to explore the long-term efficacy of these systems. This review provides insights for institutions seeking to optimize hostel management practices and support student development.

Fuzzy Clustering Guided by Spectral Rotation and Scaling.

Representing data in different spaces becomes more powerful and suitable for solving downstream learning tasks. The membership degrees obtained through fuzzy C -means (FCM) clustering cannot capture data structures sufficiently, as they represent samples from a single Euclidean geometrical perspective. To address this issue, we propose a novel fuzzy clustering model guided by spectral rotation and scaling (FCSR). In FCSR, both spectral embeddings and membership degrees are considered as new representations of data. They can complement each other from different perspectives which enables the model to engage more structural properties of the data. The process of solving the problem of membership degrees not only inherits the merits of traditional FCM but also preserves data neighborhood structures revealed by the spectral decomposition based on an affinity matrix. Furthermore, to improve the adaptability and extensibility of FCSR, the projected and kernel versions of FCSR (FCSR-P and FCSR-K) are formed. We demonstrate that FCSR-P is suitable for high-dimensional scenarios and FCSR-K can improve the linear separability among data. Extensive experiments conducted on various well-known data sets illustrate the validity of the proposed ideas.

Fuzzy Cluster Pitch Synthesis System for the Violin Sound with Machine Learning

Pitch synthesis with violin sound involves the generation of musical pitches using technology to mimic the distinctive tonal characteristics of a violin. This process typically employs digital signal processing techniques to recreate the timbre, articulation, and nuances of a real violin. Advanced algorithms analyze and model the acoustic properties of a violin sound, allowing for the synthesis of realistic pitch variations and expressive qualities. Whether utilized in electronic music production, virtual instruments, or sound design, pitch synthesis with violin sound aims to emulate the rich and complex sonic palette of the violin, offering musicians and composers versatile tools for creative expression and sonic exploration. In this paper proposed Fuzzy Pitch Clustering Machine Learning (FPC-ML) for the violin Music Pitch Synthesis using Machine Learning. The proposed FPC-ML model uses the Fuzzy Clustering model for the estimation of pitches in the violin music signal. Based on the Fuzzy clustering model membership degree is computed for the proposed FPC-ML for the estimation of the pitch in the violin music. With the estimation of linguistic variables, clustering is performed in the Music signal for the computation of pitches. With the estimated pitches in the violin music, the features are trained in the machine learning model for the classification and estimation of features in the Violin Music. Simulation analysis demonstrated that the proposed FPC-ML model computes the features of the Violin Music Pitch values based on the estimated clustering values synthesis performed for the classification of the Violin Music signal. The proposed FPC-ML technique achieves an accuracy value of 0.98 for the violin signal with an iteration of 20. With the increase in several iterations and epoch, the accuracy of the FPC-ML model is further increased for the synthesis of the Violin Music.

Generation of Graphic Design Color Schemes Based on CMYK Color Model and Corrosion Algorithms

Graphic design colour schemes play a fundamental role in shaping the visual identity and impact of a design. This paper proposed an efficient Feature Extraction Madhami Fuzzy Clustering Probabilistic Corrosion (FEMFcPC) for the graphic design. The proposed FEMFcPC model comprises the CMYK color scheme for the estimation of the features in the images. With the estimation of the FEMFcPC model corrosion algorithm is implemented for the computation of the graphic design features. Once the features are estimated the related features for the graphic design are designed with the mamdhami fuzzy clustering model. The estimated features are clustered with the CMYK color schemes. The proposed FEMFcPC model estimates the patterns and relationships among graphic designs to provide valuable insights for design categorization and recommendation systems. A dataset comprising various graphic design examples with their corresponding CMYK color schemes is utilized for analysis. Through the application of the FEMFcPC algorithm, clustering results are obtained, revealing distinct grouping patterns and similarities among the designs. The simulation results stated that the proposed FEMFcPC model achieves a significant color scheme for the graphic design. Through the clustering process, the proposed FEMFcPC model with the values of the probabilistic features for the graphic design. The Key findings include the identification of dominant clusters, even distribution of designs across multiple clusters, detection of outliers, and assessment of cluster density. These insights offer significant implications for design categorization, recommendation systems, and targeted marketing strategies within the graphic design domain. The study contributes to advancing our understanding of graphic design analysis and provides a foundation for future research in this field.

A Novel Grey Fuzzy Clustering Model and its Application on Students’ Performance Evaluation

Aiming to address the issues of traditional student evaluation methods, which tend to be overly subjective and overlook the intrinsic data structure, this paper introduces a novel grey fuzzy clustering model named the grey entropy game-weighted fuzzy c-means (GEG-WFCM) model. Firstly, subjective weights are calculated using the subjective-objective relationship analysis method, while objective weights are determined through the entropy weight method. Then, a comprehensive approach is adopted, leveraging game theory to calculate the final weights. Based on these comprehensive weights, the relative grey correlation coefficient and fuzzy weighted c-mean algorithm are incorporated to yield the ultimate evaluation results. The proposed model was applied to evaluate student performance, and the experiments show that it can obtain scientific and reasonable results. The model not only acknowledges the expertise of experts but also respects the objectivity of the data, thus circumventing the limitations of purely subjective judgments, and surpassing traditional evaluation methods.

IFKMHC: Implicit Fuzzy K-Means Model for High-Dimensional Data Clustering.

The graph-information-based fuzzy clustering has shown promising results in various datasets. However, its performance is hindered when dealing with high-dimensional data due to challenges related to redundant information and sensitivity to the similarity matrix design. To address these limitations, this article proposes an implicit fuzzy k-means (FKMs) model that enhances graph-based fuzzy clustering for high-dimensional data. Instead of explicitly designing a similarity matrix, our approach leverages the fuzzy partition result obtained from the implicit FKMs model to generate an effective similarity matrix. We employ a projection-based technique to handle redundant information, eliminating the need for specific feature extraction methods. By formulating the fuzzy clustering model solely based on the similarity matrix derived from the membership matrix, we mitigate issues, such as dependence on initial values and random fluctuations in clustering results. This innovative approach significantly improves the competitiveness of graph-enhanced fuzzy clustering for high-dimensional data. We present an efficient iterative optimization algorithm for our model and demonstrate its effectiveness through theoretical analysis and experimental comparisons with other state-of-the-art methods, showcasing its superior performance.

Deep Adaptive Fuzzy Clustering for Evolutionary Unsupervised Representation Learning.

Cluster assignment of large and complex datasets is a crucial but challenging task in pattern recognition and computer vision. In this study, we explore the possibility of employing fuzzy clustering in a deep neural network framework. Thus, we present a novel evolutionary unsupervised learning representation model with iterative optimization. It implements the deep adaptive fuzzy clustering (DAFC) strategy that learns a convolutional neural network classifier from given only unlabeled data samples. DAFC consists of a deep feature quality-verifying model and a fuzzy clustering model, where deep feature representation learning loss function and embedded fuzzy clustering with the weighted adaptive entropy is implemented. We joint fuzzy clustering to the deep reconstruction model, in which fuzzy membership is utilized to represent a clear structure of deep cluster assignments and jointly optimize for the deep representation learning and clustering. Also, the joint model evaluates current clustering performance by inspecting whether the resampled data from estimated bottleneck space have consistent clustering properties to improve the deep clustering model progressively. Experiments on various datasets show that the proposed method obtains a substantially better performance for both reconstruction and clustering quality compared to the other state-of-the-art deep clustering methods, as demonstrated with the in-depth analysis in the extensive experiments.

Decoding Emotions: Intelligent visual perception for movie image classification using sustainable AI in entertainment computing

Affective computing researchers have been studying emotion recognition (ER) based on real-world facial photos and videos for a while now, and it’s a very popular area. With the sounds produced by head posture, facial deformation, and lighting fluctuation, ER is still difficult to execute in the wild. This research employs a machine learning model for sustainable artificial intelligence (AI) in entertainment computing to perform emotion decoding for movie picture categorization. Emotion labels are produced for every video sample by the suggested model, which takes video data as input. First, we employ a face identification and selection process based on the video data to identify the most consequential face areas. Here, facial expressions from films have been gathered as input pictures, which have then been processed for noise reduction and normalisation. Then, in order to analyse the facial expressions in this image, it was segmented using the fuzzy K-means equalisation clustering model. Convolutional adversarial U-net graph neural networks have been used to classify the studied pictures for emotion decoding. Several movie-based emotion datasets are subjected to experimental analysis in order to determine accuracy, precision, recall, F-1 score, RMSE, and AUC. With excellent classification accuracy, the suggested deep learning paradigm shows promise in identifying the emotional shifts in gamers. The suggested method achieved 97% accuracy, 96% precision, 92% recall, 85% F-1 score, 79% RMSE, and 86% AUC.

Network and attribute-based clustering of tennis players and tournaments

AbstractThis paper aims at targeting some relevant issues for clustering tennis players and tournaments: (i) it considers players, tournaments and the relation between them; (ii) the relation is taken into account in the fuzzy clustering model based on the Partitioning Around Medoids (PAM) algorithm through spatial constraints; (iii) the attributes of the players and of the tournaments are of different nature, qualitative and quantitative. The proposal is novel for the methodology used, a spatial Fuzzy clustering model for players and for tournaments (based on related attributes), where the spatial penalty term in each clustering model depends on the relation between players and tournaments described in the adjacency matrix. The proposed model is compared with a bipartite players-tournament complex network model (the Degree-Corrected Stochastic Blockmodel) that considers only the relation between players and tournaments, described in the adjacency matrix, to obtain communities on each side of the bipartite network. An application on data taken from the ATP official website with regards to the draws of the tournaments, and from the sport statistics website Wheelo ratings for the performance data of players and tournaments, shows the performances of the proposed clustering model.

Reconstruction-Aware Kernelized Fuzzy Clustering Framework Incorporating Local Information for Image Segmentation

Kernelized fuzzy C-means clustering with weighted local information is an extensively applied robust segmentation algorithm for noisy image. However, it is difficult to effectively solve the problem of segmenting image polluted by strong noise. To address this issue, a reconstruction-aware kernel fuzzy C-mean clustering with rich local information is proposed in this paper. Firstly, the optimization modeling of guided bilateral filtering is given for noisy image; Secondly, this filtering model is embedded into kernelized fuzzy C-means clustering with local information, and a novel reconstruction-filtering information driven fuzzy clustering model for noise-corrupted image segmentation is presented; Finally, a tri-level alternative and iterative algorithm is derived from optimizing model using optimization theory and its convergence is strictly analyzed. Many Experimental results on noisy synthetic images and actual images indicate that compared with the latest advanced fuzzy clustering-related algorithms, the algorithm presented in this paper has better segmentation performance and stronger robustness to noise, and its PSNR and ACC values increase by about 0.16–3.28 and 0.01–0.08 respectively.

An auto-weighted enhanced horizontal collaborative fuzzy clustering algorithm with knowledge adaption mechanism

Among the multi-source data clustering tasks, there is a kind of frequently encountered tasks where only one of the multi-source datasets is available for sake of privacy and other reasons. The only available dataset is called local dataset, and the other are called external datasets. The horizontal collaborative fuzzy clustering (HCFC) model is a typical one that can deal with such clustering tasks. In HCFC, each external dataset is used through the knowledge mined from it rather than itself. The knowledge expressed as a knowledge partition matrix is fused into the clustering process of the local dataset. Reviewing the existing HCFC models, we can find three issues that need improvement. Firstly, the existing HCFC models quantify the collaboration contribution of each external knowledge by a hyperparameter at dataset-level, and moreover, do not distinguish the collaboration contributions of objects in the same external dataset. This may lead to counterintuitive clustering results. Focused on this issue, this paper proposes an enhanced HCFC (EHCFC) algorithm that extends the collaboration from dataset-level to object-level, and assigns different weights to objects based on the information amount provided by objects. Through EHCFC, a more flexible collaboration and a more intuitive clustering result can be reached. Secondly, the collaboration mechanisms of the existing HCFC models require that the dimensionalities of the partition matrices of external datasets and local dataset are the same, which makes the HCFC algorithms unable to work in many real situations. Focused on this limitation, a knowledge adaption mechanism based on relative entropy and spectral clustering is proposed resulting in a further refined EHCFC-KA algorithm, i.e., EHCFC with knowledge adaption. The proposed knowledge adaption mechanism makes both the HCFC algorithms and the EHCFC algorithm effective and successful in more application scenarios. Finally, we define two indexes in terms of consistency (the consistency of the clustering result with external knowledge) to evaluate the performance of collaborative clustering. Experiments on synthetic datasets and UCI public datasets demonstrate that the proposed EHCFC and EHCFC-KA algorithms outperform the existing HCFC algorithms and achieve significantly better intuitive collaborative clustering performance.

Analysing the Hidden Relationship between Long-Distance Transport and Information and Communication Technology Use through a Fuzzy Clustering Eco-Extended Apostle Model

The study analyses the hidden relationship between transport and ICT use for an extensive sample of 26,500 EU citizens. To that aim, a fuzzy clustering Eco-extended apostle model is applied to both latent variables: interurban transport trips and ICT use. The interurban long-distance trip (LDT) latent variable is measured by four different indicators (long- and medium-distance trips for work and leisure in the past twelve months), and the ICT use is based on a ten-item scale that provides information on different transport modes. The fuzzy Eco-extended apostle model is compared with the classical apostle model, translating the satisfaction and loyalty dimensions to our case. The fuzzy clustering model shows that most EU citizens are similar to the representative citizen who moved and used ICT at very low rates (56.5 and 50.4 per cent, respectively). The classical apostle model shows that the quadrants low LDT–high ICT and low LDT–low ICT are more represented by 38.5 and 35.2 per cent, respectively. However, the Eco-extended apostle model reinforces the results of the quadrant of low LDT–low ICT (40.22%) but softens those obtained in the quadrant of low LDT–high ICT (21.01%). Interesting insights of the effects of gender, age, education, and employment status are discussed.

The Impact of Big Data Analytics Capabilities on the Diversification of E-Commerce Firms

Abstract With the arrival of the big data era, e-commerce enterprises are facing more and more competition and market changes. A fuzzy clustering model is created by combining fuzzy set theory and fuzzy logic with a clustering algorithm in this paper. Then, for the shortcomings of the fuzzy C-mean clustering algorithm, the genetic simulated annealing algorithm is used to weight the data points, the fuzzy C-mean clustering model is improved, and a fuzzy clustering algorithm based on the genetic simulated annealing optimization is proposed. By using this algorithm, e-commerce enterprises’ diversification is being analyzed. The results show that the mean and standard deviation of each supply chain inventory, production orders, supplier ordering, and platform ordering quantity after optimization are reduced to different degrees, some of which reach more than 60%. Stabilizing the development of e-commerce enterprises can be achieved by reducing supply chain inventory and order quantity. E-commerce enterprises that excel in their enterprise production quality (0.741), credibility (0.748), and product sales competitiveness (0.726) are more competitive. E-commerce enterprises can utilize the ability of big data analysis to achieve diversification.

Improving fuzzy clustering model for probability density functions using the two-objective genetic algorithm

Improving fuzzy clustering model for probability density functions using the two-objective genetic algorithm

Fuzzy clustering method with approximate orthogonal regularization

As a widely used unsupervised learning method, clustering model plays an indispensable role in exploring data structures. Spectral analysis is a useful technique for clustering problems. The spectral analysis could yield good results when used in conjunction with fuzzy clustering models. However, the existing methods are limited by factors such as the definition of the similarity graph and predetermined number of clusters. In this paper, we propose a new fuzzy clustering model with the approximate orthogonal regularization. To obtain the relatively stable results, we reconstruct the Laplacian matrix with geometrically-nearest-neighbor similarity measurement. This new Laplacian matrix can represent the properties of datasets. For this constrained optimization problem, by applying the indicator function to simplify it as an unconstrained optimization problem. Then we propose an algorithm based on Alternating Direction Method of Multipliers (ADMM) and theoretically prove its convergence. We make some empirical experiments on both synthetic and real datasets. The experimental results demonstrate the model’s effectiveness and showcase the desirable properties of the resulting solutions.

GIS-based mineral prospectivity mapping using machine learning methods: A case study from Zhuonuo ore district, Tibet

The Zhunuo ore concentration area (ZOCA) is the most potential prospective area of Cu-Au (Mo) in the west of the southern subterrane, Tibet. Single traditional prospective methods (e.g., stream sedimentary geochemistry) often produced larger area and false abnormal information in the Gangdese orogenic belt because of the high altitude and the intense weather and erosion, which can not meet the urgent demand of the current situation for Cu resources. In this study, we combinedamineral system approachwith GIS-basedmachine learningapproachsto obtain geologically meaningful mineral prospective maps. The detail steps include: (i) establishing the mineral system conception model of porphyry copper deposits (PCDs); (ii) transforming the targeted porphyry metallogenic system components into spatial proxies associated with the crucial ore-forming processes; (iii) extracting the spatial proxies: proximity to intrusive rocks (source), NE orientation faults (transport and/or physical trap), Fe-oxide and propylitization hydrothermal alterations zone (hydrothermal fluids) and the metallogenic strength diagram of Cu-Mo-W-Bi-Au-Ag-Pb-Zn (deposition); (iv) Radial Basis Functions Link Networks (RBFLN), Random forests (RF) Supervised and Fuzzy Clustering (FC) unsupervised machine learning methods were applied to capture the complex and crucial mineralization information between known deposit types and evidence layers; (vi) model estimation and delineating prospective potential targets: Receiver operating characteristic curve (ROC), predictive-area (P-A) plotting and normalised density (Nd) were used to evaluate the predictive models results. The results indicate that the RBFLN model, RF model, and FC model show high predictive accuracy. The AUC values under the ROC area of the RBFLN model, RF model, and FC model are 0.99, 0.96, and 0.94, respectively. The RBFLN model outperforms the RF model and FC model, the predictive-area plotting of RBFLN occupies 12% of the study area containing 88% of the known deposits. The predictive-area plotting of the RF model and FC model showed that 14% and 21% of the study area contained 86% and 79% of the known deposits, respectively. The normalized density (Nd) of a layer is defined as the ratio of the prediction success rate (Pr) of the P-A plotting to the corresponding area (Oa). The normalized density of the RBFLN model, the RF model, and the FC model are 7.33, 6.14, and 3.76, respectively, which revealed that the results of the three predictive models all have positive indications. These studies show that RBFLN supervised machine learning method is a more robustness and generalization capability. The predictive results also provide prospective potential targets (e.g., northern Cimabanshuo, northwest Wubaduolai, and southwestern and western Zhunuo PCD) for further exploration, and this method can be also applicable to other mineral systems and districts.

Fuzzy clustering of financial time series based on volatility spillovers

AbstractIn this paper we propose a framework for fuzzy clustering of time series based on directional volatility spillovers. In the case of financial time series, detecting clusters of volatility spillovers provides insights into the market structure, which can be useful to both portfolio managers and policy makers. We measure directional—i.e. “From” and “To” the others—volatility spillovers with a methodology based on the generalized forecast-error variance decomposition. Then, we propose a weighted fuzzy clustering model for grouping stocks with a similar degree of directional spillovers. By using a weighted approach, we allow the algorithm to decide which dimension of spillover is more relevant for clustering. Moreover, a robust clustering model is also proposed to alleviate the effect of possible outlier stocks. We apply the proposed clustering model for the analysis of spillover effects in the Italian stock market.

Graph-Based Soft-Balanced Fuzzy Clustering

Spectral clustering have attracted more and more attention due to their well-defined mathematical frameworks and superior performance. However, there still exist two limitations to be solved: 1) most spectral clustering methods consist of two independent stages, which may cause unpredictable deviation of obtained clustering results from the genuine ones and lead to severe information loss and performance degradation; 2) spectral clustering methods employ the hard clustering mode, which lacks interpretability for data points in the boundary area belonging to multiple clusters. To simultaneously address these challenging issues for spectral clustering, we propose a Graph based soft-Balanced Fuzzy Clustering (GBFC) model. Specifically, we explicitly preserve the nonnegative property of the clustering indicator matrix to enhance the interpretability of clustering results. Moreover, row normalization is imposed on the cluster indicator matrix to show the membership of each data point to different clusters. Additionally, a novel balanced constraint is designed to regularize the clustering results and constrain the size of clusters. We can directly obtain the clustering assignments without any post-processing, and the limitations of the previous two-stage clustering framework can be effectively addressed. Extensive experiments performed on both synthetic datasets and real world datasets demonstrate the superiority and effectiveness of the proposed algorithm compared with several state-of-the-art methods.

Pairwise constraints-based semi-supervised fuzzy clustering with multi-manifold regularization

Introducing a handful of pairwise constraints into fuzzy clustering models to revise memberships has been proven beneficial to boosting clustering performance. However, current pairwise constraints-based semi-supervised fuzzy clustering methods suffer from common deficiencies, i.e., the insufficient and imprecise revisions of memberships, by which the further improvement of clustering performance may be encumbered. To yield more pleasurable results, this paper proposes a new pairwise constraints-based semi-supervised fuzzy clustering method with multi-manifold regularization (MMRFCM), which can overcome the above deficiencies simultaneously. Firstly, data are regarded as located in various manifolds, and the multi-manifold regularization is delicately designed to sufficiently revise memberships for all data objects to guarantee good overall clustering performance. Secondly, local structural information is incorporated into designed multi-manifold regularization to ensure the precision and stability of the revisions on memberships. Thirdly, the approximated non-linear similarities evolving from ensemble p-Laplacian are applied to discover implicit local structures more thoroughly to further strengthen the effect of the multi-manifold regularization. Based on these strategies, MMRFCM efficiently exploits pairwise constraints to sufficiently and precisely modify memberships during the clustering process and thus achieves excellent results. Like most fuzzy clustering methods, MMRFCM is solved by alternative updates and the solutions are locally optimal. In the comprehensive experiments conducted on different types of datasets, MMRFCM successfully outperforms several classical and state-of-the-art fuzzy clustering methods in terms of clustering accuracy (CA), normalized mutual information (NMI), and adjusted rand index (ARI). The excellent results demonstrate the superiority, stability, and reliability of the proposed method.