Asymmetric deviation entropy regularization for semi-supervised fuzzy C-means clustering and its fast Algorithm

Compared with traditional unsupervised clustering, semi-supervised clustering is a more powerful computing method and plays a vital role in pattern analysis and machine learning. The reason for these is that semi-supervised approaches can take advantage of semi-supervised information, which can significantly boost the performance of clustering. Existing methods for semi-supervised fuzzy c-means clustering (FCM) suffer from the following issues: it is generally uneasy to assign the appropriate membership degree value based on traditional entropy regularization using semi-supervised information involved in their objective function. To address this problem, we systematically propose a novel Fuzzy Symmetric Relative Entropy Clustering with Pairwise-Constraints (FSREC-PC) by introducing entropy regularization into the objective function. Moreover, FSREC-PC introduces symmetric relative entropy as a regularized term in its objective function such that its resulting formulas have the clear membership meaning compared with the other semi-supervised FCM algorithms. Further experiments conducted in UCI data show that the proposed clustering algorithm can derive a better performance.

Recently, semi-supervised clustering has been remarked and discussed in many research fields. In semi-supervised clustering, prior knowledge or information are often formulated as pairwise constraints, that is, must-link and cannot-link. Such pairwise constraints are frequently used in order to improve clustering properties. In this paper, we will propose a new semi-supervised fuzzy c-means clustering by using clusterwise tolerance and pairwise constraints. First, the concept of clusterwise tolerance and pairwise constraints are introduced. Second, the optimization problem of fuzzy cmeans clustering using clusterwise tolerance based pairwise constraint is formulated. Especially, must-link constraint is considered and introduced as pairwise constraints. Third, a new clustering algorithm is constructed based on the above discussions. Finally, the effectiveness of proposed algorithm is verified through numerical examples.

In this paper, a novel semi-supervised fuzzy clustering algorithm, MFM-SFCM, based on a membership fusion mechanism is proposed for Diffusion-weighted imaging (DWI) brain infarction lesion segmentation. The proposed MFM-SFCM algorithm addresses the issue of weakened constraints and insufficient influence of labeled samples on the clustering process that arises in the semi-supervised fuzzy C-means clustering (SFCM) when emphasizing supervised information. By using a new membership fusion mechanism, MFM-SFCM eliminates this issue, greatly improving the accuracy of clustering results and accelerating convergence speed. This allows fuzzy clustering to achieve good results in the segmentation of DWI brain infarction lesions using a small amount of labeled information. The effectiveness of the MFM-SFCM algorithm is demonstrated through experiments conducted on a real-world dataset of DWI brain images.

Rolling bearing is of great importance in modern industrial products, the failure of which may result in accidents and economic losses. Therefore, fault diagnosis of rolling bearing is significant and necessary and can enhance the reliability and efficiency of mechanical systems. Therefore, a novel fault diagnosis method for rolling bearing based on semi-supervised clustering and support vector data description (SVDD) with adaptive parameter optimization and improved decision strategy is proposed in this study. First, variational mode decomposition (VMD) was applied to decompose the vibration signals into sets of intrinsic mode functions (IMFs), where the decomposing mode number K was determined by the central frequency observation method. Next, fuzzy entropy (FuzzyEn) values of all IMFs were calculated to construct the feature vectors of different types of faults. Later, training samples were clustered with semi-supervised fuzzy C-means clustering (SSFCM) for fully exploiting the information inside samples, whereupon a small number of labeled samples were able to provide sufficient data distribution information for subsequent SVDD algorithms and improve its recognition ability. Afterwards, SVDD with improved decision strategy (ID-SVDD) that combined with k-nearest neighbor was proposed to establish diagnostic model. Simultaneously, the optimal parameters C and σ for ID-SVDD were searched by the newly proposed sine cosine algorithm improved with adaptive updating strategy (ASCA). Finally, the proposed diagnosis method was applied for engineering application as well as contrastive analysis. The obtained results reveal that the proposed method exhibits the best performance in all evaluation metrics and has advantages over other comparison methods in both precision and stability.

To improve the effectiveness and robustness of the existing semisupervised fuzzy clustering for segmenting image corrupted by noise, a kernel space semisupervised fuzzy C-means clustering segmentation algorithm combining utilizing neighborhood spatial gray information with fuzzy membership information is proposed in this paper. The mean intensity information of neighborhood window is embedded into the objective function of the existing semisupervised fuzzy C-means clustering, and the Lagrange multiplier method is used to obtain its iterative expression corresponding to the iterative solution of the optimization problem. Meanwhile, the local Gaussian kernel function is used to map the pixel samples from the Euclidean space to the high-dimensional feature space so that the cluster adaptability to different types of image segmentation is enhanced. Experiment results performed on different types of noisy images indicate that the proposed segmentation algorithm can achieve better segmentation performance than the existing typical robust fuzzy clustering algorithms and significantly enhance the antinoise performance.

Structural damage detection is a key part of structural health monitoring. In recent years, intelligent detecting methods are used in this field and show good performance. This paper proposed a structural damage detection method based on data fusion and semi-supervised fuzzy C-means clustering. Compared with other intelligent method, our method can detect the damage location and extent, meanwhile, provide a confidence. Experiment results on a benchmark model show effectiveness of the proposed methods.

The dynamic expansion of cyber threats poses an urgent need for the development of new methods, methods, and systems for their detection. The subject of the study is the process of ensuring the resilience of computer systems in the presence of cyber threats. The goal is to develop a self-adaptive method for computer systems resilience in the presence of cyberattacks. Results. The article presents a self-adaptive system to ensure the resilience of corporate networks in the presence of botnets’ cyberattacks. Resilience is provided by adaptive network reconfiguration. It is carried out using security scenarios selected based on a cluster analysis of the collected network features inherent cyberattacks. To select the necessary security scenarios, the proposed method uses fuzzy semi-supervised c-means clustering. To detect host-type cyberattacks, information about the hosts’ network activity and reports of host antiviruses are collected. To detect the network type attacks, the monitoring of network activity is carried out, which may indicate the appearance of a cyberattack. According to gathered in the network information concerning possible attacks performed by botnet the measures for the resilient functioning of the network are assumed. To choose the needed scenario for network reconfiguration, the clustering is performed. The result of the clustering is the scenario with the list of the requirement for the reconfiguration of the network parameters, which will assure the network’s resilience in the situation of the botnet’s attacks. As the mean of the security scenario choice, the semi-supervised fuzzy c-means clustering was used. The clustering is performed based on labeled training data. The objects of the clustering are the feature vectors, obtained from a payload of the inbound and outbound traffic and reports of the antiviral tool about possible hosts’ infection. The result of clustering is a degree of membership of the feature vectors to one of the clusters. The membership of feature vector to cluster gives an answer to question what scenario of the network reconfiguration is to be applied in the situation of the botnet’s attack. The system contains the clusters that indicate the normal behavior of the network. The purpose of the method is to select security scenarios following cyberattacks carried out by botnets to mitigate the consequences of attacks and ensure a network functioning resilience. Conclusions. The self-adaptive method for computer systems resilience in the presence of cyberattacks has been developed. Based on the proposed method, a self-adaptive attack detection, and mitigation system has been developed. It demonstrates the ability to ensure the resilient functioning of the network in the presence of botnet cyberattacks at 70 %.

This paper presents a new semi-supervised fuzzy c-means clustering for data with clusterwise tolerance by opposite criteria. In semi-supervised clustering, pairwise constraints, that is, must-link and cannot-link, are frequently used in order to improve clustering performances. From the viewpoint of handling pairwise constraints, a new semi-supervised fuzzy c-means clustering is proposed by introducing clusterwise tolerance-based pairwise constraints. First, a concept of clusterwise tolerance-based pairwise constraints is introduced. Second, the optimization problems of the proposed method are formulated. Especially, must-link and cannot-link are handled by opposite criteria in our proposed method. Third, a new clustering algorithm is constructed based on the above discussions. Finally, the effectiveness of the proposed algorithm is verified through numerical examples.

Clustering with pairwise constraints has been a popular method in semi-supervised clustering not only due to effectiveness but also the wide application domain. This paper works on semi-supervised fuzzy clustering with pairwise constraints. Specifically, we formulate two variants of Pairwise Constrained Fuzzy C-Means (PCFCM), referred to as PCFCM-vio and PCFCM-dist, by incorporating different penalty terms into the objective function of FCM. For PCFCM-vio, the penalt term (i.e., - vio) is defined as the total violation of assignments in terms of fuzzy memberships regarding to the constrained pairs. We show that PCFCM-vio is a more generalized form of existing pairwise constrained fuzzy clustering approaches. For the second approach PCFCM-dist, the penalty term (i.e., - dist) is the total Euclidean distance of memberships for those constrained pairs. Through theoretical analysis, we find the connection between the two forms of regularization, based on which we present a unified frame work of algorithm for the two approaches. Experimental results with both simulated data and real world data are provided, which demonstrate and compare the performance of the two proposed PCFCM variants.

Semi-supervised fuzzy clustering with metric learning and entropy regularization

This paper applies fuzzy clustering algorithm to recognize the transformer winding's pressed state based on transformer's vibration signal. We propose a new semi-supervised fuzzy kernel clustering algorithm (SFKC) based on some modifications for the fuzzy clustering methods. The first modification is that the new algorithm uses prior knowledge to guide the clustering process. Second, it uses kernel function to map the samples to high dimensional feature space for clustering. Third, dynamic weight of the feature is carried out considering the different effects of sample features. The accuracy and reliability of the proposed algorithm are verified by the standard test data set. Then the algorithm is applied to recognize transformer winding's pressed state. According to the vibration characteristics of the transformer, we construct a sample set incorporating multi-sensors and multi-features for clustering. After clustering, we use the clustering centers and feature weights to recognize new unlabeled sample. The results show that the method is feasible.

In machine learning and pattern recognition fields, collecting labeled examples costs human efforts, while vast amounts of unlabelled data are often readily available and offer some additional information. In practice, many applications require a dimensionality reduction method to deal with the partially labeled problem. In this paper, we propose a semi-supervised clustering framework, which is based on feature projection and semi-supervised fuzzy clustering. High dimensional data is mapped into a low dimensional space with feature projection. A mapping of learning data is generalized to a new datum which is classified in the low dimensional space with constrained fuzzy clustering. With the experiment on different datasets, the results show the method has good clustering performance for handling data of high dimensionality.

Dental segmentation from X-ray images using semi-supervised fuzzy clustering with spatial constraints

The idea behind distance metric learning (DML) is to accentuate the distance relations found in the training data, maintaining whether the data patterns are similar or dissimilar. In this paper, we investigate in using DML (GDML, LMNN, MCML and NCA) in semi-supervised Fuzzy c-means clustering and apply them on a real, biomedical dataset and on UCI datasets. We used a cross validation setting with varying amount of labelled data to test our methodology. Out of eight datasets, statistical significant improvement was found on five datasets using ssFCM with DML. This shows that DML can improve ssFCM clustering for some datasets. Further analysis using 2D PCA projection and sum of squared distances before and after DML transformation of the original data are carried out. Interestingly, DML was found to worsen ssFCM clustering in the NTBC dataset with hierarchical clusters.

In a previous work, suitable initialisation techniques were incorporated with semi-supervised Fuzzy c-Means clustering (ssFCM) to improve clustering results on a trial and error basis. In this work, we present a single fully-automatic version of an existing semi-supervised Fuzzy c-means clustering framework which uses genetically-modified prototypes (ssFCMGA). Initial prototypes are generated by GA to initialise the ssFCM algorithm without experimentation of different initialisation techniques. The framework is tested on a real, biomedical dataset NTBC and on the Arrhythmia UCI dataset, using varying amounts of labelled data from 10 % to 60 % of the total data patterns. Different ssFCM threshold values and fitness functions for ssFCMGA are also investigated (sGAs). We used accuracy and NMI to measure class-label agreement and internal measures WSS, BSS, CH, CWB, DB and DU to evaluate cluster quality of the clustering algorithms. Results are compared with those produced by the existing ssFCM. While ssFCMGA and sGAs produced slightly lower agreement level than ssFCM with known class labels based on accuracy and NMI, the other six measurements showed improvement in the results in terms of compactness and well-separatedness (cluster quality), particularly when labelled data are low at 10 %. Furthermore, the cluster quality are shown to further improve using ssFCMGA with a more complex fitness function (sGA2). This demonstrates the application of GA in ssFCM improves cluster quality without exploration of different initialisation techniques.