Fuzzy Clustering Research Articles

Entropy Stacked Autoencoder based Diffusion Model (ESADM) and Fuzzy Clustering with Semi Supervised Fuzzy Graph Convolutional Network (FC-SSFGCN) for Rail Surface Defect Detection

Rails, fasteners, and other parts of railway track lines eventually develop flaws due to continuous strain from train operations and direct exposure to the environment; these faults directly affect the safety of train operations. Detecting defects on rail surfaces presents a formidable challenge due to the wide array of possible flaws and their unpredictable nature. However, Defect identification errors, massive variances, inadequate training sample availability, and weak contrast between faults and the surrounding background all contribute to the complexity of this procedure. In this work, rail surface and fastener flaws may be detected non-destructively using a multi-crack detection approach based on the Entropy Stacked Autoencoder Diffusion Model (ESADM). A novel approach, ESAFM, has been developed, combining a rail surface image encoder with a multi-layer, Stacked Autoencoder to extract latent materials from images showcasing different types of cracks. This integration reduces the need for significant processing resources by integrating easily into the conventional physically-based image workflow. Additionally, the Zero Shot-Semi Supervised Fuzzy Class Knowledge Graph (ZS-SSFCKG) method proposes Class Knowledge Graph Construction (CKGC), which constructs a CKG to elucidate the connection between defects and non-defects. Class features are learned by using a Fuzzy Clustering with Semi Supervised Fuzzy Graph Convolutional Network (FC-SSFGCN). The method employs a transformer encoder to capture distant relationships, allowing for the extraction of features from defect samples. This facilitates the acquisition of distinct defect image characteristics, as industrial defects vary in shape and size. The experimental results on the public Railway Track Fault Detection (RTFD)and Rail Surface Defect Datasets (RSDDs) with rail surface defects are collected from rail tracks surface defect detection.

A Comparison of K-Means and Fuzzy C-Means Clustering Algorithms for Clustering the Spread of Tuberculosis (TB) in the Lungs

A Comparison of K-Means and Fuzzy C-Means Clustering Algorithms for Clustering the Spread of Tuberculosis (TB) in the Lungs

K-Means and Fuzzy C-Means Cluster Food Nutrients for Innovative Diabetes Risk Assessment

Packaged food and beverages often pose a risk of increasing diabetes when consumed regularly. This study aims to classify these products based on their nutritional content listed on the labels, with a focus on identifying diabetes risk. The methods employed include K-Means and Fuzzy C-Means, K-Means is used to determine initial center of cluster, while Fuzzy C-Means enhances the clustering by assigning probabilistic memberships to each data point. These methods are applied to products sold in stores in Banyumas Regency, Central Java, Indonesia. This research is the first to combine these two methods in the context of product clustering based on nutritional labels. The results indicate that packaged food and beverage products can be classified into high-risk and low-risk clusters for diabetes. Consequently, this study provides important guidance for consumers in choosing healthier.

Longitudinal bi-criteria framework for assessing national healthcare responses to pandemic outbreaks

Pandemics like COVID-19 have illuminated the significant disparities in the performance of national healthcare systems (NHCSs) during rapidly evolving crises. The challenge of comparing NHCS performance has been a difficult topic in the literature. To address this gap, our study introduces a bi-criteria longitudinal algorithm that merges fuzzy clustering with Data Envelopment Analysis (DEA). This new approach provides a comprehensive and dynamic assessment of NHCS performance and efficiency during the early phase of the pandemic. By categorizing each NHCS as an efficient performer, inefficient performer, efficient underperformer, or inefficient underperformer, our analysis vividly represents performance dynamics, clearly identifying the top and bottom performers within each cluster of countries. Our methodology offers valuable insights for performance evaluation and benchmarking, with significant implications for enhancing pandemic response strategies. The study’s findings are discussed from theoretical and practical perspectives, offering guidance for future health system assessments and policy-making.

Multiple-perspective consumer segmentation using improved weighted Fuzzy k-prototypes clustering and swarm intelligence algorithm for fresh apricot market

Leveraging clustering technology for consumer segmentation is crucial for discerning the nuanced differences among fresh apricot consumer groups and subsequently executing precise marketing strategies. To achieve a more comprehensive and lucid consumer segmentation and identify typical characteristics of apricot consumers in different clusters, this research constructs a novel multiple-perspective segmentation indicator system for fresh apricot consumers. Given the diverse degrees of importance and types of consumer segmentation variables, and the inherent sensitivity of the original Fuzzy k-prototypes (FKP) algorithm to clustering centers, we proposed the weighted Fuzzy k-prototypes (WFKP) algorithms for mixed data (MD) optimized by the particle swarm optimization (PSO) algorithm (MDPSO-WFKP) and mixed data sparrow search algorithm (SSA) (MDSSA-WFKP), both incorporating information entropy weighting for mixed attributes. We test the proposed algorithms on four University of California Irvine machine learning repository (UCI) datasets and the consumer segmentation dataset, and the performance of all selected evaluation indexes shows significant improvement. These findings unequivocally validate the efficacy of the proposed methodologies. Since the MDSSA-WFKP algorithm has the best comprehensive effect on the evaluation indexes, we use it to conduct in-depth apricot consumer segmentation research and find that the apricot consumers can be subdivided into three groups with differentiation: ‘Buddhist-like youths’, ‘Upscale attribute enthusiasts’, and ‘Quality-oriented consumers’. Finally, this paper gives the corresponding marketing suggestions based on the characteristics of the segmented groups.

An Efficient Tour Construction Heuristic for Generating the Candidate Set of the Traveling Salesman Problem with Large Sizes

In this paper, we address the challenge of creating candidate sets for large-scale Traveling Salesman Problem (TSP) instances, where choosing a subset of edges is crucial for efficiency. Traditional methods for improving tours, such as local searches and heuristics, depend greatly on the quality of these candidate sets but often struggle in large-scale situations due to insufficient edge coverage or high time complexity. We present a new heuristic based on fuzzy clustering, designed to produce high-quality candidate sets with nearly linear time complexity. Thoroughly tested on benchmark instances, including VLSI and Euclidean types with up to 316,000 nodes, our method consistently outperforms traditional and current leading techniques for large TSPs. Our heuristic’s tours encompass nearly all edges of optimal or best-known solutions, and its candidate sets are significantly smaller than those produced with the POPMUSIC heuristic. This results in faster execution of subsequent improvement methods, such as Helsgaun’s Lin–Kernighan heuristic and evolutionary algorithms. This substantial enhancement in computation time and solution quality establishes our method as a promising approach for effectively solving large-scale TSP instances.

Discriminative fuzzy [formula omitted]-means clustering with local structure preservation for high-dimensional data

K-means clustering, which aims to distribute data points into K different clusters, is an effective technique for data mining and machine learning. However, several factors degrade clustering performance in real-world applications. High-dimensional data containing redundant features is one of the key issues in the clustering process. Many traditional hard or fuzzy versions of K-means clustering fail to handle high-dimensional data effectively. In this paper, we present a novel model referred to as discriminative fuzzy K-means clustering, which incorporates discriminative projection and p-Laplacian graph regularization into a joint framework. Specifically, the proposed model can reduce the negative impact of redundant features and enhance the discriminative power when projecting the original data into a lower-dimensional space. It simultaneously preserves the structural locality properties of the data by performing p-Laplacian graph regularization on the membership matrix. Consequently, clustering performance is significantly enhanced for high-dimensional data. Finally, an effective algorithm is presented to solve the formulated optimization problem. Experimental results obtained on benchmark datasets are promising and demonstrate the superiority of the proposed method.

Ultra-Short-Term Photovoltaic Power Prediction by NRGA-BiLSTM Considering Seasonality and Periodicity of Data

Photovoltaic (PV) power generation is highly stochastic and intermittent, which poses a challenge to the planning and operation of existing power systems. To enhance the accuracy of PV power prediction and ensure the safe operation of the power system, a novel approach based on seasonal division and a periodic attention mechanism (PAM) for PV power prediction is proposed. First, the dataset is divided into three components of trend, period, and residual under fuzzy c-means clustering (FCM) and the seasonal decomposition (SD) method according to four seasons. Three independent bidirectional long short-term memory (BiLTSM) networks are constructed for these subsequences. Then, the network is optimized using the improved Newton–Raphson genetic algorithm (NRGA), and the innovative PAM is added to focus on the periodic characteristics of the data. Finally, the results of each component are summarized to obtain the final prediction results. A case study of the Australian DKASC Alice Spring PV power plant dataset demonstrates the performance of the proposed approach. Compared with other paper models, the MAE, RMSE, and MAPE performance evaluation indexes show that the proposed approach has excellent performance in predicting output power accuracy and stability.

Suppressed possibilistic fuzzy c-means clustering based on shadow sets for noisy data with imbalanced sizes

Possibilistic fuzzy c-means clustering (PFCM) algorithm generates fewer overlapping clustering centers than the possibilistic c-means clustering (PCM) algorithm and possesses better noise immunity than fuzzy c-means clustering (FCM) algorithm. However, with the increasing noise intensity and number of clusters, PFCM still faces the problem of getting partially overlapping clustering centers or mislocated centers in noise regions. Moreover, the sample-size imbalance increasingly intensifies the difficulty of positioning centers of small clusters. To solve the above problems, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets (S-SPFCM) is proposed by introducing the shadow set theory and the "suppressed competitive learning" strategy. Firstly, KL divergence is introduced in the objective function of PFCM to increase the anti-noise robustness of fuzzy memberships against long-range noise and outliers. Secondly, to reduce the number of overlapping centers caused by possibilistic memberships, the shadow set theory is introduced to divide each class adaptively into three regions (core, shadow, and exclusion regions) by an uncertainty balance method. The suppressed competitive learning method is extended by modifying the memberships of points within the three regions, thus artificially guiding the iterative track of clustering centers. Meanwhile, to further reduce the influence of imbalanced sizes, a scheme to reset mislocated centers in the core and shadow regions is also designed. In addition, to improve the segmentation performance of S-SPFCM for noisy images, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets and local information (SL-SPFCM) is also proposed. The SL-SPFCM first improves the Euclidean distance by a distance filtering scheme. Then SL-SPFCM introduces the local median membership of each pixel into the KL divergence of the objective function. Finally, experiments on synthetic datasets and color images which are characteristic of imbalanced sizes and noise injection demonstrate the proposed S-SPFCM and SL-SPFCM algorithms achieve smaller center deviations and higher clustering accuracy compared with several state-of-the-art clustering algorithms.

Fuzzy C-Means Clustering via Slime Mold and the Fisher Score

Fuzzy C-Means Clustering via Slime Mold and the Fisher Score

Modular stochastic configuration network with attention mechanism for soft measurement of water quality parameters in wastewater treatment processes

Due to the complex and multi-distributed nature of wastewater treatment process data, stochastic configuration networks (SCNs) face difficulties such as large network structure and complex construction process when dealing with data modeling tasks. To address these challenges, this paper proposes a modular stochastic configuration network with attention mechanism, which integrates the advantages of modular partitioning, attention mechanism, and SCN. The model employs a fuzzy mean clustering strategy to simplify and decompose the complex multi-case and multi-distribution nonlinear modeling task, thereby reducing the modeling complexity of a single model. Furthermore, the model utilizes a stochastic configuration algorithm to learn the subtasks and construct corresponding sub-networks. The output weights are then assigned to each sub-network based on the attention mechanism to obtain the model’s final output. The validity of the proposed method is validated through two benchmark experiments. Then the model is applied to measure effluent ammonia nitrogen. The results indicate that compared with the classical randomized and modularized network models, the proposed model exhibits certain advantages in terms of learning accuracy and generalization performance.

Exploring meta-heuristics for partitional clustering: methods, metrics, datasets, and challenges

Partitional clustering is a type of clustering that can organize the data into non-overlapping groups or clusters. This technique has diverse applications across the different various domains like image processing, pattern recognition, data mining, rule-based systems, customer segmentation, image segmentation, and anomaly detection, etc. Hence, this survey aims to identify the key concepts and approaches in partitional clustering. Further, it also highlights its widespread applicability including major advantages and challenges. Partitional clustering faces challenges like selecting the optimal number of clusters, local optima, sensitivity to initial centroids, etc. Therefore, this survey describes the clustering problems as partitional clustering, dynamic clustering, automatic clustering, and fuzzy clustering. The objective of this survey is to identify the meta-heuristic algorithms for the aforementioned clustering. Further, the meta-heuristic algorithms are also categorised into simple meta-heuristic algorithms, improved meta-heuristic algorithms, and hybrid meta-heuristic algorithms. Hence, this work also focuses on the adoption of new meta-heuristic algorithms, improving existing methods and novel techniques that enhance clustering performance and robustness, making partitional clustering a critical tool for data analysis and machine learning. This survey also highlights the different objective functions and benchmark datasets adopted for measuring the effectiveness of clustering algorithms. Before the literature survey, several research questions are formulated to ensure the effectiveness and efficiency of the survey such as what are the various meta-heuristic techniques available for clustering problems? How to handle automatic data clustering? What are the main reasons for hybridizing clustering algorithms? The survey identifies shortcomings associated with existing algorithms and clustering problems and highlights the active area of research in the clustering field to overcome these limitations and improve performance.

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.

Assessing water quality of kazerun county in southwest Iran: Multi-analytical techniques, deterministic vs. probabilistic water quality index, geospatial analysis, fuzzy C-means clustering, and machine learning

Water quality is critical to human health and the environment, especially in arid and semi-arid regions. Hence, the objectives of this study were to assess drinking water quality, identify critical parameters, investigate spatial patterns, and investigate accurate predictive models for the water quality index (WQI) in the Kazerun county in southwest Iran. To address this issue using deterministic and probabilistic WQI, correlation matrix, fuzzy C-Means (FCM) clustering, geostatistics, and adaptive network-based fuzzy inference system (ANFIS) with FIS generation by fuzzy C-Means (FCM-ANFIS) and sub-clustering (SC-ANFIS).Various software tools, including Excel, MATLAB, Python, and GIS were used to analyze groundwater data collected from 25 sampling sites. Water parameters, including pH, Cl−, SO4−2, EC, NO3−, NO2−, Ca2+, Mg2+, and F−, were examined. The results showed that F− levels were within acceptable limits set by the US EPA, but about one-third of sites posed potential health risks based on WHO guidelines. In one-third of regions, the levels of Mg2+ exceeded the recommended guidelines. In deterministic and probabilistic approaches, water quality was excellent in 68% and 81.3% of sites, respectively. Sobol sensitivity analysis identified SO4−2> Mg2+>Cl− > EC > F− > NO3− as significant WQI variables. Spearman correlation matrix shows substantial positive correlations between WQI and EC, F−, SO4−2, Mg2+, and Cl− were shown by the Spearman correlation matrix. Based on the FCM results, the southeast and central sites (56% of sites) have similar water quality. In comparison, the northern and four central sites (28% of sites) have distinct regional features, and the southern sites (16% of sites) had unique water quality characteristics. Geostatistical analyses showed that pH had the most substantial local clustering, while SO4−2 had significant high-value clustering. Furthermore, hot spot research revealed specific sites with high pH, F−, NO3−, and Cl− levels. The FCM-ANFIS model outperformed the SC-ANFIS model, emphasizing FCM clustering's importance in water quality forecasting accuracy.

Development of Statistical Downscaling Model Based on Volterra Series Realization, Principal Components, Climate Classification, and Ridge Regression

This paper applied the fuzzy function approach, combined with the ridge regression model, to produce daily rainfall projections from large-scale climate variables. This study developed a statistical downscaling model based on principal components, c-means fuzzy clustering, Volterra series, and ridge regression. The model is known, hereafter as SDC2R2. In the developed downscaling model, the use of ridge regression, instead of multiple linear regression, is proposed to downscale daily rainfall with wide range (WR) predictors. The WR predictors were applied to sufficiently incorporate climate change signals. The developed model also captured the non-linear interactions of the climate variables by applying the transformation of Volterra series realization over WR predictors. This transformation was performed by applying principal components as orthogonal filters. Further, these principal components were clustered by using c-means clustering and non-linear transformations were applied on these membership functions, to improve the prediction ability of the model. The reanalysis of climate data from the National Centres for Environmental Prediction (NCEP) was used to develop the model and was validated by using the Global Climate Model (GCM) for four locations in the Manawatu River basin. The developed model was used to obtain future daily rainfall projections from three Representative Concentrative Pathways (RCP 2.6, RCP 4.5, and RCP 8.5) scenarios from the Canadian Earth System Model (CanESM2) GCM. The performance of the model was compared with a widely used statistical downscaling model (SDSM). It was observed that the model performed better than SDSM in downscaling rainfall on a daily basis. Every scenario indicated that there is a probability of obtaining high future rainfall frequency. The results of this study provide valuable information for decision-makers since climate change may potentially impact the Manawatu basin.

Neuro‐fuzzy‐based cluster formation scheme for energy‐efficient data routing in IOT‐enabled WSN

SummaryInternet of things–enabled wireless sensor networks face challenges like inflexibility, poor scalability, suboptimal cluster head selection, and energy inefficiencies. This is due to the faster data transmission rates between cluster nodes during data packet routing. This creates unnecessary energy consumption burdens for those actively transmitting nodes. Conceptually, an effective cluster formation phase supports better data routing mechanisms, while sustaining the energy efficiency of individual nodes. This paper proposes a Neuro‐Fuzzy based Cluster Formation (NFCF) scheme to facilitate adaptive and energy‐efficient cluster topologies. NFCF utilizes fuzzy logic and neural networks to identify optimal super nodes for flexible cluster formations. This approach enables configurable cluster sizes along with inclusion/exclusion criteria for member nodes based on energy thresholds. Parameters evaluated for node selection include the degree of super node, expected energy per cluster, energy variance, and residual energy. Nodes not meeting the thresholds are excluded. The neural network updates fuzzy rules to guide optimal clustering decisions based on anticipated energy dynamics under different conditions. The performance of the proposed NFCF scheme is evaluated based on objective function changes related to data transmission, individual node energy variation, energy variance before and after transmissions, and averaged end‐to‐end delay across transmission cycles. Results are compared against genetic fuzzy clustering, fuzzy energy‐aware clustering, fuzzy‐based distributed clustering, fuzzy logic‐based multi‐hop clustering, and fuzzy weighted k‐means clustering.

Framework for Regional to Global Extension of Optical Water Types for Remote Sensing of Optically Complex Transitional Water Bodies

Water quality indicator algorithms often separate marine and freshwater systems, introducing artificial boundaries and artifacts in the freshwater to ocean continuum. Building upon the Ocean Colour- (OC) and Lakes Climate Change Initiative (CCI) projects, we propose an improved tool to assess the interactions across river–sea transition zones. Fuzzy clustering methods are used to generate optical water types (OWT) representing spectrally distinct water reflectance classes, occurring within a given region and period (here 2016–2021), which are then utilized to assign membership values to every OWT class for each pixel and seamlessly blend optimal in-water algorithms across the region. This allows a more flexible representation of water provinces across transition zones than classic hard clustering techniques. Improvements deal with expanded sensor spectral band-sets, such as Sentinel-3 OLCI, and increased spatial resolution with Sentinel-2 MSI high-resolution data. Regional clustering was found to be necessary to capture site-specific characteristics, and a method was developed to compare and merge regional cluster sets into a pan-regional representative OWT set. Fuzzy clustering OWT timeseries data allow unique insights into optical regime changes within a lagoon, estuary, or delta system, and can be used as a basis to improve WQ algorithm performance.

Tools for analysing fuzzy clusters of sequences data

Tools for analysing fuzzy clusters of sequences data

Multi Autonomous Underwater Vehicle (AUV) Distributed Collaborative Search Method Based on a Fuzzy Clustering Map and Policy Iteration

Collaborative search with multiple Autonomous Underwater Vehicles (AUVs) significantly enhances search efficiency compared to the use of a single AUV, facilitating the rapid completion of extensive search tasks. However, challenges arise in underwater environments characterized by weak communication and dynamic complexities. In large marine areas, the limited endurance of a single AUV makes it impossible to cover the entire area, necessitating a collaborative approach using multiple AUVs. Addressing the limited prior information available in uncertain marine environments, this paper proposes a map-construction method using fuzzy clustering based on regional importance. Furthermore, a collaborative search method for large marine areas has been designed using a policy-iteration-based reinforcement learning algorithm. Through continuous sensing and interaction during the marine search process, multiple AUVs constantly update the map of regional importance and iteratively optimize the collaborative search strategy to achieve higher search gains. Simulation results confirm the effective utilization of limited information in uncertain environments and demonstrate enhanced search gains in collaborative scenarios.

Point and interval forecasting approach for short-term urban subway passenger flow based on residual term decomposition and fuzzy information granulation

Accurate forecasting information of short-term subway passenger flow is an important scientific reference for daily operations and urban management. The rapid time-varying nature of subway passenger flow caused by various factors that affect travel behavior poses a huge challenge to accurate forecasting. The complexity and uncertainty of data mainly focus on residual terms that deeply reflect the fluctuations. Reasonably mining the residual terms has become the key to achieving accurate forecasting. Therefore, this paper proposes a sophisticated decomposition strategy to extract and analyze the useful information hidden in the residual terms. Firstly, the potential trend, seasonal and residual terms from the original data are extracted by seasonal-trend decomposition procedure based on loess. Secondly, the residual term is decomposed into a series of subcomponents with different frequency features by symplectic geometric mode decomposition. Thirdly, these subcomponents are classified into three clusters based on fuzzy C-means clustering (FCM), and then the corresponding forecasting models are matched to the three obtained clusters and trend and seasonal terms. Finally, based on a decomposition-ensemble framework and information granulation for high-frequency components, we have established point and interval forecasting approach, respectively. Three experiments on real data sets in Beijing, Guangzhou and Shenzhen are conducted to verify the performance of the proposed approach, and the experimental results show that our approach is superior to all benchmark models and contributes to improving operational management and service quality.