Traditional Fuzzy Clustering Algorithm Research Articles

Detecting IoT Anomalies Using Fuzzy Subspace Clustering Algorithms

There are many applications of anomaly detection in the Internet of Things domain. IoT technology consists of a large number of interconnecting digital devices not only generating huge data continuously but also making real-time computations. Since IoT devices are highly exposed due to the Internet, they frequently meet with the challenges of illegitimate access in the form of intrusions, anomalies, fraud, etc. Identifying these illegitimate accesses can be an exciting research problem. In numerous applications, either fuzzy clustering or rough set theory or both have been successfully employed. As the data generated in IoT domains are high-dimensional, the clustering methods used for lower-dimensional data cannot be efficiently applied. Also, very few methods were proposed for such applications until today with limited efficacies. So, there is a need to address the problem. In this article, mixed approaches consisting of nano topology and fuzzy clustering techniques have been proposed for anomaly detection in the IoT domain. The methods first use nano topology of rough set theory to generate CORE as a subspace and then employ a couple of well-known fuzzy clustering techniques on it for the detection of anomalies. As the anomalies are detected in the lower dimensional space, and fuzzy clustering algorithms are involved in the methods, the performances of the proposed approaches improve comparatively. The effectiveness of the methods is evaluated using time-complexity analysis and experimental studies with a synthetic dataset and a real-life dataset. Experimentally, it has been found that the proposed approaches outperform the traditional fuzzy clustering algorithms in terms of detection rates, accuracy rates, false alarm rates and computation times. Furthermore, nano topological and common Mahalanobis distance-based fuzzy c-means algorithm (NT-CM-FCM) is the best among all traditional or nano topology-based algorithms, as it has accuracy rates of 84.02% and 83.21%, detection rates of 80.54% and 75.37%, and false alarm rates of 7.89% and 9.09% with the KDDCup’99 dataset and Kitsune Network Attack Dataset, respectively.

Research on Quality Evaluation of Smart Education Schools Based on Fuzzy Clustering Algorithm and Strategies for Future Development

Abstract The burgeoning field of wisdom education has led to a disparity in the quality of educational institutions, thereby necessitating enhancements to the existing school quality evaluation systems. This study refines the traditional fuzzy C-mean clustering algorithm by incorporating a Gaussian mixture distribution and information entropy regularization. It then employs this enhanced algorithm to construct a quality evaluation system for smart education schools. The improved fuzzy C-mean clustering algorithm demonstrated in this paper significantly outperforms the standard C-means used at SCU and the K-means algorithm in terms of Mean Absolute Error (MAE) and Total Hit Rate (THR). Specifically, the optimized algorithm decreased the MAE to 0.572 from 0.619, a reduction of 16.01% compared to the K-means algorithm. It increased the THR to 0.158 from 0.147, marking an improvement of 17.04% over the Kmeans algorithm. Furthermore, the refined clustering algorithm achieved an impressive accuracy of 95.71%. Analysis through this clustering approach reveals that the developed quality evaluation system accurately reflects the operational level of smart education within schools. The establishment of such a system is anticipated to significantly guide the future progression of smart education and aid in the foundational development of smart education schools.

Horizontal federated differential evolution algorithm for the optimization of fuzzy clusters

In this study, we are concerned with the optimization of fuzzy clustering (Fuzzy C-Means) on the basis of a collection of distributed datasets without violating data confidentiality and security. The optimization of fuzzy clusters is realized using the differential evolution algorithm in a federated learning environment. Fuzzy clustering plays an important role in revealing the underlying structure of a given dataset. However, traditional iterative method is easy to get stuck at local optimum. With the growing concerning on data confidentiality and security, how to reveal the underlying structure of the data that are stored locally across different sites is becoming an urgent problem. In order to overcome these two obstacles, we propose a federated differential evolution algorithm to realize fuzzy clustering. We augment the well-known differential evolution algorithm such that it can work in a federated learning environment to ensure local data privacy. The design practice of the federated differential evolution is elaborated on by highlighting its effectiveness in finding the optimal fuzzy clusters on the basis of distributed datasets. The performance of the proposed method is compared with traditional fuzzy clustering algorithm. Experimental studies completed on a series of real-world datasets coming from machine learning repository are reported to demonstrate the superiority of the proposed algorithm.

CLUSTERIZATION OF DATA ARRAYS BASED ON THE MODIFIED GRAY WOLF ALGORITHM

Context. The task of clustering arrays of multidimensional data, the main goal of which is to find classes of observations that are homogeneous in the sense of the accepted metric, is an important part of the intelligent data analysis of Data Mining. From a computational point of view, the problem of clustering turns into the problem of finding local extrema of a multiextreme function, which are repeatedly started from different points of the original data array. To speed up the process of finding these extrema using the ideas of evolutionary optimization, which includes algorithms inspired by nature, swarm algorithms, population algorithms, etc.
 Objective. The purpose of the work is to introduce a procedure for clustering data arrays based on the improved gray wolf algorithm.
 Method. A method of clustering data arrays based on the modified gray wolf algorithm is introduced. The advantage of the proposed approach is a reduction in the time of solving optimization problems in conditions where clusters are overlap. A feature of the proposed method is computational simplicity and high speed, due to the fact that the entire array is processed only once, that is, eliminates the need for multi-era self-learning, implemented in traditional fuzzy clustering algorithms.
 Results. The results of the experiments confirm the effectiveness of the proposed approach in clustering problems under the condition of classes that overlap and allow us to recommend the proposed method for use in practice to solve problems of automatic clustering big data.
 Conclusions. A method of clustering data arrays based on the modified gray wolf algorithm is introduced. The advantage of the proposed approach is the reduction of time for solving optimization problems. The results of the experiments confirm the effectiveness of the proposed approach in clustering problems under the conditions of overlapping clusters.

Interpretable fuzzy clustering using unsupervised fuzzy decision trees

In clustering process, fuzzy partition performs better than hard partition when the boundaries between clusters are vague. Whereas, traditional fuzzy clustering algorithms produce less interpretable results, limiting their application in security, privacy, and ethics fields. To that end, this paper proposes an interpretable fuzzy clustering algorithm—fuzzy decision tree-based clustering which combines the flexibility of fuzzy partition with the interpretability of the decision tree. We constructed an unsupervised multi-way fuzzy decision tree to achieve the interpretability of clustering, in which each cluster is determined by one or several paths from the root to leaf nodes. The proposed algorithm comprises three main modules: feature and cutting point-selection, node fuzzy splitting, and cluster merging. The first two modules are repeated to generate an initial unsupervised decision tree, and the final module is designed to combine similar leaf nodes to form the final compact clustering model. Our algorithm optimizes an internal clustering validation metric to automatically determine the number of clusters without their initial positions. The synthetic and benchmark datasets were used to test the performance of the proposed algorithm. Furthermore, we provided two examples demonstrating its interest in solving practical problems.

Image Processing Based on Fuzzy Mathematics Theory

In order to further improve the problems of poor rationality and weak antinoise ability of existing image processing algorithms and technical algorithms, an image processing research method based on fuzzy mathematical theory is proposed. First, aiming at the ill-posed problem of the PFCM algorithm, the neutrality and rejection degree are used to construct a regular term and embed the algorithm objective function to enhance the correlation between the attribute parameters of the fuzzy set of the sample graph, so as to solve the ill-posed problem of the PFCM algorithm. Secondly, in view of the same noise sensitivity problem of PFCM algorithm as a traditional fuzzy clustering algorithm, combined with the robust ideas of FCM_S1 and FCM_S2 algorithms, the objective function of robust segmentation algorithm for graph fuzzy clustering (RPFCM_s) is constructed. The misclassification rate of the clustering algorithm proposed in this study in image segmentation is reduced by 38%–76%, and the misclassification rate of the corresponding segmentation result of the ATPFCA algorithm is reduced by 5%–77%. Therefore, the algorithm not only improves the effective segmentation efficiency of the fuzzy mathematical theory algorithm for the processing of uneven grayscale images but also enhances the anti-noise robustness of the algorithm.

Fast Fuzzy Clustering Based on Anchor Graph

Fuzzy clustering is one of the most popular clustering approaches and has attracted considerable attention in many fields. However, high computational cost has become a bottleneck which limits its applications in large-scale problems. Moreover, most fuzzy clustering algorithms are sensitive to noise. To address these issues, a novel fuzzy clustering algorithm, called fast fuzzy clustering based on anchor graph (FFCAG), is proposed. The FFCAG algorithm integrates anchor-based similarity graph construction and membership matrix learning into a unified framework, such that the prior knowledge of anchors can be further utilized to improve clustering performance. Specifically, FFCAG first constructs an anchor-based similarity graph with a parameter-free neighbor assignment strategy. Then, it designs a quadratic programming model to learn the membership matrix of anchors, which is very different from traditional fuzzy clustering algorithms. More importantly, a novel balanced regularization term is introduced into the objective function to produce more accurate clustering results. Finally, we adopt an alternating optimization algorithm with guaranteed convergence to solve the proposed method. Experimental results performed on synthetic and real-world datasets demonstrate the proposed FFCAG can significantly reduce the computational time with comparable, even superior, clustering performance, compared with state-of-the-art algorithms.

FAST FUZZY CREDIBILISTIC CLUSTERING BASED ON DENSITY PEAKS DISTRIBUTION OF DATA BROAKYSIS

Context. The problem of clustering (classification without a teacher) is often occures when processing data arrays of various natures, which is quite an interesting and integral part of artificial intelligence. To solve this problem, there are many known methods and algorithms based on the principles of the distribution density of observations in the analyzed data. However, these methods are rather complicated in software implementation and are not without drawbacks, namely: the problem of determining significant clusters in datasets of different densities, multiepoch self-learning, getting stuck in local extrema of goal functions, etc. It should be noted that the methods based on the analysis of the peaks of the data distribution density are clear in nature, therefore, to expand the capabilities of these methods, it is advisable to introduce their fuzzy modification. Objective. The aim of the work is to introduce fast fuzzy data clustering using density peaks distribution of the datasets, that can find the prototypes (centroids) of clusters that overlapping regardless of the amount of incoming data. Method. The problem of fuzzy clustering data arrays based on a hybrid method that based on the simultaneous use of a credibilistic approach to fuzzy clustering and an algorithm for finding the types of distribution density of the initial data is proposed. A feature of the proposed method is computational simplicity and high speed, due to the fact that the entire array is processed only once, that is, eliminates the need for multi-era self-learning, implemented in traditional fuzzy clustering algorithms. Results. A feature of the proposed method of fast fuzzy credibilistic clustering using of density peaks distribution is characterized by computational simplicity and high speed due to the fact that the entire array is processed only once, that is, the need for multiepoch self-learning is eliminated, which is implemented in traditional fuzzy clustering algorithms. The results of the computational experiment confirm the effectiveness of the proposed approach in clustering problems under conditions in the case when the clusters are ovelap. Conclusions. The experimental results allow us to recommend the developed method for solving the problems of automatic clustering and data classification, as quickly as possible to find the centroids of clusters. The proposed method of fast fuzzy credibilistic clustering using of density peaks distribution of dataset is intended for use in computational intelligence systems, neuro-fuzzy systems, in training artificial neural networks and in clustering problems.

A Study on the Quality Evaluation of English Teaching Based on the Fuzzy Comprehensive Evaluation of Bat Algorithm and Big Data Analysis

In this paper, the fuzzy comprehensive evaluation model based on the bat algorithm quantifies the qualitative evaluation effectively and provides a feasible and convenient English teaching quality evaluation system by combining quantitative evaluation with objective index data. Firstly, the English teaching quality evaluation model is constructed based on the fuzzy comprehensive evaluation analysis method and the weight values of each factor are calculated; secondly, the three types of data in the model are processed separately. This includes standardizing the data of objective indicators such as students’ course grades and weakening the influence of course difficulty on this indicator. The fuzzy comprehensive evaluation model based on the bat algorithm quantifies the qualitative evaluation to make the calculated comprehensive evaluation of English teaching quality more comprehensive and objective; then the comprehensive calculation of English teaching quality evaluation is completed, and the English teaching quality evaluation model is constructed by extracting keywords based on the qualitative evaluation; finally, a runnable English teaching quality evaluation system is designed and implemented. A fuzzy comprehensive evaluation algorithm based on improved bat algorithm optimization is proposed. The algorithm uses the improved fuzzy comprehensive evaluation algorithm to optimize the initial clustering centers and adopts a new objective function to guide the clustering process, thus improving the clustering quality of the fuzzy comprehensive evaluation algorithm. Comparative analysis through models shows that the improved algorithm improves the clustering accuracy to a certain extent when compared with the traditional fuzzy comprehensive evaluation clustering algorithm for analysis. The bat algorithm is one of the stochastic global optimization models. It can take advantage of the group, integrate global search and local search, and achieve rapid convergence. Therefore, it plays an important role in optimizing the evaluation of English teaching quality. This study enriches the theoretical study of English teaching quality evaluation to a certain extent and can play a role in strengthening and improving English teaching quality evaluation at the present stage.

Extraction of plateau lake water bodies based on an improved FCM algorithm

Changes in plateau body lake water are an important indicator of global ecosystem changes, and a timely and accurate grasp of this change information can provide a scientific reference for the formulation of relevant policies. The traditional fuzzy C-means clustering (FCM) algorithm takes into account the ambiguity of the classification of the ground object pixels but does not consider the rich spectral information of the neighboring pixels and is very sensitive to the background noise” of the remote sensing image, resulting in low water extraction accuracy. Aiming to compensate for the shortcomings of the traditional FCM algorithm, this paper proposes an improved FCM algorithm. This algorithm replaces the Euclidean distance of the traditional FCM algorithm with a combination of the Mahalanobis distance and spectral angle matching (SAM) to fully take into account the spectral information of neighboring pixels and improve the clustering accuracy. The study selected Sentinel-2 images of the Fuxian Lake and Xingyun Lake basins during normal, wet, and dry periods as the data source. Under the same conditions, the clustering accuracy was compared with the traditional FCM algorithm, improved FCM algorithm, K-means clustering method and iterative self-organizing data analysis (ISODATA) clustering method. The experimental results show that the improved FCM algorithm has a higher water extraction accuracy than the traditional FCM algorithm, K-means clustering method and ISODATA clustering method. The kappa coefficient and overall accuracy (OA) of the improved FCM algorithm can be increased by 5.56%–9.45% and 2.66%–5.32%, respectively, and the omission error and commission error can be reduced by 1.72%–4.55% and 12.14%–22.10%, respectively. When the improved FCM algorithm is used, the extraction accuracy is higher for plateau deep lakes than for plateau shallow lakes, and the extraction effect for lakes with poor water environments is more significant than that of other methods. The improved FCM algorithm better maintains the integrity of the water boundary and overcomes the influence of a certain number of mountain shadows and urban building pixels on the clustering results.

Application of FCMAlgorithm Combined with Artcial Neural Network in TBM Operation Data

Fuzzy clustering theory is widely used in data mining of full-face tunnel boring machine. However, the traditional fuzzy clustering algorithm based on objective function is difficult to effectively cluster functional data. We propose a new Fuzzy clustering algorithm, namely FCM–ANN algorithm. The algorithm replaces the clustering prototype of the FCM algorithm with the predicted value of the articial neural network. This makes the algorithm not only satisfy the clustering based on the traditional similarity criterion, but also can effectively cluster the functional data. In this paper, we rst use the t-test as an evaluation index and apply the FCM–ANN algorithm to the synthetic datasets for validity testing. Then the algorithm is applied to TBM operation data and combined with the crossvalidation method to predict the tunneling speed. The predicted results are evaluated by RMSE and R2 . According to the experimental results on the synthetic datasets, we obtain the relationship among the membership threshold, the number of samples, the number of attributes and the noise. Accordingly, the datasets can be effectively adjusted. Applying the FCM–ANN algorithm to the TBM operation data can accurately predict the tunneling speed. The FCM–ANN algorithm has improved the traditional fuzzy clustering algorithm, which can be used not only for the prediction of tunneling speed of TBM but also for clustering or prediction of other functional data.

Intuitionistic Fuzzy Clustering Image Segmentation Based on Flower Pollination Optimization with Nearest Neighbor Searching

In order to overcome shortcomings of the traditional fuzzy clustering algorithm for image segmentation, such as that are easily affected by noise, sensitive to the initial value of clustering center, easily falling into local optimum, and inadequate ability of fuzzy information processing, an intuitionistic fuzzy clustering image segmentation algorithm is proposed based on flower pollination optimization with nearest neighbor searching. Firstly, a novel extraction strategy of image spatial information is proposed, and then an intuitionistic fuzzy clustering objective function with image spatial information is constructed to improve the algorithm’s robustness against noise and enhance the ability of the algorithm to process the image fuzzy information. In order to overcome the defects of sensitivity to clustering centers and easily falling into local optimum, a flower pollination algorithm based on nearest neighbor learning search mechanism is proposed. Experimental results show that the proposed method can get satisfactory segmentation results on a variety of noisy images.

Fuzzy clustering based on feature weights for multivariate time series

As an important set of techniques for data mining, time series clustering methods had been studied by many researchers. Although most existing solutions largely focus on univariate time series clustering, there has been a surge in interest in the clustering of multivariate time series data. In this paper, a feature-weighted clustering method is proposed based on two distance measurement methods called dynamic time warping (DTW) and shape-based distance (SDB). There are four stages in the proposed clustering algorithm. First, we pick cluster centers by the pop clustering method called clustering by fast search and find of density peaks (DPC). Next, by considering the overall matching of multivariate time series, a fuzzy membership matrix is generated by performing DTW on all variables. We then reconsider the contribution of each independent dimension by utilizing SBD to measure distances within each dimension and construct multiple fuzzy membership matrices. Finally, we utilize a traditional fuzzy clustering algorithm called fuzzy c-means to cluster the fuzzy membership matrices and generate clustering results. Simultaneously, a feature weight calculation method and novel equation for constructing fuzzy membership matrices are applied during the clustering process. We compare the proposed method to other clustering methods and the results indicate that the proposed method can improve clustering accuracy for multivariate time series datasets.

Robust Self-Sparse Fuzzy Clustering for Image Segmentation

Traditional fuzzy clustering algorithms suffer from two problems in image segmentations. One is that these algorithms are sensitive to outliers due to the non-sparsity of fuzzy memberships. The other is that these algorithms often cause image over-segmentation due to the loss of image local spatial information. To address these issues, we propose a robust self-sparse fuzzy clustering algorithm (RSSFCA) for image segmentation. The proposed RSSFCA makes two contributions. The first concerns a regularization under Gaussian metric that is integrated into the objective function of fuzzy clustering algorithms to obtain fuzzy membership with sparsity, which reduces a proportion of noisy features and improves clustering results. The second concerns a connected-component filtering based on area density balance strategy (CCF-ADB) that is proposed to address the problem of image over-segmentation. Compared to the integration of local spatial information into the objective functions, the presented CCF-ADB is simpler and faster for the removal of small areas. Experimental results show that the proposed RSSFCA addresses two problems in current fuzzy clustering algorithms, i.e., the outlier sensitivity and the over-segmentation, and it provides better image segmentation results than state-of-the-art algorithms.

Multispectral Image Segmentation Based on a Fuzzy Clustering Algorithm Combined with Tsallis Entropy and a Gaussian Mixture Model

Accurate multispectral image segmentation is essential in remote sensing research. Traditional fuzzy clustering algorithms used to segment multispectral images have several disadvantages, including: (1) they usually only consider the pixels’ grayscale information and ignore the interaction between pixels; and, (2) they are sensitive to noise and outliers. To overcome these constraints, this study proposes a multispectral image segmentation algorithm based on fuzzy clustering combined with the Tsallis entropy and Gaussian mixture model. The algorithm uses the fuzzy Tsallis entropy as regularization item for fuzzy C-means (FCM) and improves dissimilarity measure using the negative logarithm of the Gaussian Mixture Model (GMM). The Hidden Markov Random Field (HMRF) is introduced to define prior probability of neighborhood relationship, which is used as weights of the Gaussian components. The Lagrange multiplier method is used to solve the segmentation model. To evaluate the proposed segmentation algorithm, simulated and real multispectral images were segmented using the proposed algorithm and two other algorithms for comparison (i.e., Tsallis Fuzzy C-means (TFCM), Kullback–Leibler Gaussian Fuzzy C-means (KLG-FCM)). The study found that the modified algorithm can accelerate the convergence speed, reduce the effect of noise and outliers, and accurately segment simulated images with small gray level differences with an overall accuracy of more than 98.2%. Therefore, the algorithm can be used as a feasible and effective alternative in multispectral image segmentation, particularly for those with small color differences.

Epileptic EEG Detection Using a Multi-View Fuzzy Clustering Algorithm with Multi-Medoid

Using clustering algorithms to automatically analyze EEGs of patients and to identify the characteristic waves of epilepsy is of high clinical value. Traditional clustering algorithms mostly use a calculated virtual single representative medoid point to describe the cluster structure, but this single representative medoid point has insufficient information. To accurately capture more accurate intracluster structural information, a representative multi-medoid points strategy is adopted, which describes the cluster structure by assigning representative weights to each sample in the cluster. Considering that the multi-view learning mechanism combines information from each view to improve the algorithm's clustering performance, a multi-view fuzzy clustering algorithm with multi-medoid (MvFMMdd) is proposed. This algorithm discards the approach of the traditional fuzzy clustering algorithm, which uses a single virtual representative point to characterize the cluster structure, and uses several real representative points to describe the cluster structure. Experiments verify the medical significance of the proposed algorithm.

DGFCM: A New Dynamic Clustering Algorithm

This paper applies the dynamic self-organizing maps algorithm to determining the number of clustering. The text eigenvector is acquired based on the vector space model (VSM) and TF.IDF method. The number of clustering acquired by the dynamic self-organizing maps. The threshold GT control the network’s growth.Compared to the traditional fuzzy clustering algorithm, the present algorithm possesses higher precision. The example demonstrates the effectiveness of the present algorithm.

An Integrated Algorithm of Spatial Fuzzy C-Means Clustering and Level Set for Indoor Scene Image Segmentation

Traditional fuzzy clustering algorithm is applicable for noiseless image segmentation. However, it is powerless for the images with noise, special point values and defects. An algorithm which combines spatial fuzzy clustering and level set for indoor scene segmentation is proposed in this paper. Firstly, the image is classified using fuzzy clustering with space information to get a larger difference in image gray level; secondly, the image is segmented using level set; finally, the contour in the boundary of target area is gotten accurately. The improved method can not only preserve details of images but also reduce the number of iterations. The results show that the proposed method has good segmentation quality and efficiency in segmentation for indoor scene image.

Classification of Ship’ Magnetic Field and Feature Selection Based on the Improved Weighted Fuzzy Clustering Algorithm

Magnetic field data of ship has three-component,and traditional weighted fuzzy clustering algorithm(FCA) can’t deal with the three-component data. We improve the traditional FCA by changing the objective function and added weights calculation of three-component of magnetic field in the function.Give the equation to compute the weights of three-component.Put forward new steps for improved algorithm.Use ships’ data to test the improved algorithm and giving the conclusion.

Ensemble Fuzzy Clustering for Mixed Numeric and Categorical Data

In data mining, clustering is one of the major tasks and aims at grouping the data objects into meaningful classes (clusters) such that the similarity of objects within clusters is maximized, and the similarity of objects between clusters is minimized. The dataset sometimes may be in mixed nature that is it may consist of both numeric and categorical type of data. Naturally these two types of data may differ in their characteristics. Due to the differences in their characteristics, in order to group these types of mixed data, it is better to use the ensemble clustering method which uses split and merge approach to solve this problem. In this paper, the original mixed dataset is splitted into numeric dataset and categorical dataset and clustered using both traditional clustering algorithms (K-Means and K-Modes) and fuzzy clustering algorithms (Fuzzy C-Means and Fuzzy C-Modes). The resultant clusters are combined using ensemble clustering methods and evaluated by both f-measure and entropy measure. It is found that splitting is more beneficial and applying fuzzy clustering algorithms yields better results than traditional clustering algorithms.