Fuzzy Clustering Model Research Articles

Kernelized Mahalanobis Distance for Fuzzy Clustering

Data samples of complicated geometry and nonlinear separability are considered as common challenges to clustering algorithms. In this article, we first construct Mahalanobis distance in the kernel space and then propose a novel fuzzy clustering model with a kernelized Mahalanobis distance, namely KMD-FC. The key contributions of KMD-FC include: first, the construction of KMD matrix is innovatively transformed from the Euclidean distance kernel matrix, which is able to effectively avoid the problem of “curse of dimensionality” posed by explicitly calculating the sample covariance matrix in the kernel space; second, for the first time, the kernelized Gustafson–Kessel (GK) fuzzy C-means algorithm is achieved, which is critically important to extend the applications of the GK algorithm to the nonlinear classification tasks; finally, taking account of the overall distribution of samples in the kernel space after kernel mapping to improve the generalizability of the proposed KMD-FC clustering method. Comprehensive experiments conducted on a wide range of datasets, including synthetic datasets and machine learning repository (UCI) datasets, have validated that the proposed clustering algorithm outperformed the state-of-the-art methods in comparison.

Fuzzy local intensity clustering (FLIC) model for automatic medical image segmentation

Intensity inhomogeneity is one of the main challenges in automatic medical image segmentation. In this paper, fuzzy local intensity clustering (FLIC), which is based on the combination of level set algorithm and fuzzy clustering, is proposed to mitigate the effect of intensity variation and noise contamination. For the FLIC method, the segmentation and bias modification are carried out in a fully automatic and simultaneous manner through the local clustering of intensity and selection of the initial contour by the fuzzy method. Besides, the local entropy is integrated into the FLIC function to improve the contour evolution. Experimental results on inhomogeneous medical images indicate the superiority of the FLIC model over the other state-of-the-art segmentation methods in terms of accuracy, robustness, and computational time.

Joint non-negative and fuzzy coding with graph regularization for efficient data clustering

Non-negative matrix factorization (NMF) is an effective model in converting data into non-negative coefficient representation whose discriminative ability is usually enhanced to be used for diverse pattern recognition tasks. In NMF-based clustering, we often need to perform K-means on the learned coefficient as postprocessing step to get the final cluster assignments. This breaks the connection between the feature learning and recognition stages. In this paper, we propose to learn the non-negative coefficient matrix based on which we jointly perform fuzzy clustering, by viewing that each column of the dictionary matrix as a concept of each cluster. As a result, we formulate a new fuzzy clustering model, termed Joint Non-negative and Fuzzy Coding with Graph regularization (G-JNFC), and design an effective optimization method to solve it under the alternating direction optimization framework. Besides the convergence and computational complexity analysis on G-JNFC, we conduct extensive experiments on both synthetic and representative benchmark data sets. The results show that the proposed G-JNFC model is effective in data clustering.

Modeling groundwater quality by using hybrid intelligent and geostatistical methods.

Simulation of groundwater quality is important for managing water resources and mitigating water shortages, especially in arid and semiarid areas. Geostatistical models have been used for spatial prediction and interpolation of groundwater parameters. Recently, hybrid intelligent models have been employed for the simulation of dynamic systems. In this study, hybrid intelligent models, based on a neuro-fuzzy system integrated with fuzzy c-means data clustering (FCM) and grid partition (GP) models as well as artificial neural networks integrated with particle swarm optimization algorithm, were used to predict the spatial distribution of chlorine (Cl), electrical conductivity (EC), and sodium absorption ratio (SAR) parameters of groundwater. Results of the hybrid models were compared with geostatistical methods, including kriging, inverse distance weighting (IDW), and radial basis function (RBF). The latitude and longitude values of observation wells and qualitative parameters in three states of maximum, average, and minimum were introduced as input and output to the models, respectively. To evaluate the models, the root mean squared error (RMSE), the mean absolute error (MAE), and CC statistical criteria were used. Results showed that in the hybrid models, NF-GP with the lowest RMSE and MAE and highest CC was the most suitable model for the prediction of water quality parameters. The RMSE, MAE, and CC values were 107.175 (mg/L), 79.804 (mg/L), and 0.924 in the average state for Cl; were 518.544 (μmho/cm), 444.152 (μmho/cm), and 0.882 for electrical conductivity; and were 1.596, 1.350, and 0.582 for sodium absorption ratio, respectively. Among the geostatistical models, the kriging was found more accurate. Using the coordinates of wells will eventually allow the NF-GP to be used for more sampling and replace the visual techniques that require more time, cost, and facilities.

Investigating the sustainability of renewable energy – An empirical analysis of European Union countries using a hybrid of projection pursuit fuzzy clustering model and accelerated genetic algorithm based on real coding

Renewable energy sustainability plays a significant role in ensuring energy security, improving environment and promoting sustainable development of economic and social. This paper focuses on assessing and analyzing the sustainability and influencing factors of 27 EU countries’ renewable energy. By DPSIR-Four-Dimensional indicators system, four sustainability dimensions of energy, economy, society and environment are considered and integrated. To deal with the randomness and fuzziness of multi-dimensional metadata, and to conduct assessment without standard, we develop a nonlinear multi-factor assessment model (projection pursuit fuzzy clustering model with accelerated genetic algorithm based on real coding). The results show that the CO2 emissions, energy productivity, non-renewable energy emission intensity, energy dependence, electricity price and policy support are closer related to the renewable energy sustainability. The strongest sustainability countries are Denmark and Sweden. From the overall analysis, time-series analysis shows that general sustainable level is a wave of growth. The geographical analysis shows that the countries with better sustainable development are mainly located in the central region, showing a belt distribution from north to south. The Sustainability decreases from the middle to the sides.

Low-Rank Tensor Regularized Fuzzy Clustering for Multiview Data

Since data are collected from a range of sources via different techniques, multiview clustering has become an emerging technique for unsupervised data classification. However, most existing soft multiview clustering methods only consider the pairwise correlations and ignore high-order correlations among multiple views. To integrate more comprehensive information from different views, this article innovates a fuzzy clustering model using the low-rank tensor to address the multiview data clustering problem. Our method first conducts a standard fuzzy clustering on different views of the data separately. Then, the obtained soft partition results are aggregated as the new data to be handled by a Kullback-Leibler (KL) divergence-based fuzzy model with low-rank tensor constraints. The KL divergence function, which replaces the traditional minimized Euclidean distance, can enhance the robustness of the model. More importantly, we formulate fuzzy partition matrices of different views as a third-order tensor. So, a low-rank tensor is introduced as a norm constraint in the KL divergence-based fuzzy clustering to obtain dexterously high-order correlations of different views. The minimization of the final model is convex and we present an efficient augmented Lagrangian alternating direction method to handle this problem. Specially, the global membership is derived by using tensor factorization. The efficiency and superiority of the proposed approach are demonstrated by the comparison with state-of-the-art multiview clustering algorithms on many multiple-view data sets.

Fuzzy clustering and AR models for damage detection in CFRP coupons considering loading effect

Fuzzy clustering and AR models for damage detection in CFRP coupons considering loading effect

Fuzzy‐based nuclear analysis segregation model for distinguishing the properties of repository liquids and gas in gas storage

The geophysical well logging analysis is a major task of petroleum research and development, where petroleum oil (gas), transition petroleum layers, water layers, and dry-layer segments are precisely distinguished from each other. The resistivity of the particular oil and gas layers in developing countries is below or close to the water layers. As electrical properties show, the particular oil and gas layer of water layers is not legitimately recognizable. The features of oil and gas strata and their strong components are different in the investigative field from those of different petroleum fields. In this way, various techniques and thoughts ought to be utilized to comprehend the particular issues in the examination zone. A nuclear analysis–based segregation model for distinguishing the properties of repository liquids is worked by utilizing the crude pipeline and distilled unit of oil (gas) layers, transitional oil water layers, water layers, and dry layers using dynamic nonlinear fuzzy clustering model. With directly complex transformation models, reservoir fluids can be separated. The outcomes are analyzed with various model, and the proposed method shows promising outcomes.

Fuzzy Smooth Equilibrium Method for Clustering

Clustering model plays an indispensable role in exploring data structures. To extend supervised learning to unsupervised, the maximum margin clustering model has been proposed. Maximum margin-based frameworks develop a powerful tool for supervised learning. It could yield good results by combining with some fuzzy clustering models. However, such methods characterized by high computational cost and are sensitive to the nearest neighbor relationships between data objects. Sometimes, they could lead to degenerate solutions. By reconstructing the Laplacian matrix with different similarity measurements, a new fuzzy smooth equilibrium clustering (FSEC) model is proposed. This model combines MMC with spectral clustering, but there is no need to solve the eigenvalue decomposition problem. Using the equilibrium regularization term can avoid degenerate solutions. Numerous experiments have established the effectiveness of the newly FSEC model.

Teaching Teacher Recommendation Method Based on Fuzzy Clustering and Latent Factor Model

Colleges and universities attach great importance to the quality of undergraduate teaching. To virtually guarantee the course's teaching quality, the key lies in recommending suitable teachers for the course scientifically. It is a seemingly simple but very complicated problem. Moreover, with the development of colleges and universities, new courses are continually set up, and new teachers are introduced, which further complicates the problem. The problem has not been solved well for many years. Therefore, we propose a course teacher recommendation model (FCTR-LFM) based on fuzzy clustering and the latent factor model (LFM) to solve this problem. Firstly, under the guidance of pedagogy theories and methods, we conduct quantitative modeling for teachers and courses' relevant characteristics and combine the quantitative results with historical teaching scores to establish a large-scale sparse course teaching evaluation matrix as the recommendation dataset. Next, we adopt the improved fuzzy clustering model to realize teachers' automatic clustering according to their characteristics and use the teacher cluster to reconstruct the teaching evaluation matrix, significantly reducing the dataset's size and reducing the sparsity. Then, we used the improved LFM to predict the score items in the evaluation matrix, including the missing score items. Finally, the prediction evaluation scores are sorted according to the course, and the TOP-N recommendation of the course teachers is realized. The experimental results show that FCTR-LFM can realize the prediction and recommendation well using the optimized parameters. It effectively solves the problem that there is no scientific basis for recommending suitable teachers for the course for a long time.

Big data precision marketing and consumer behavior analysis based on fuzzy clustering and PCA model

Precision marketing is faced with multiple levels of problems, such as pollution of the data environment and unscientific algorithms, which need to be sorted out urgently. Based on neural network technology, this paper constructs a neural network-based precision marketing model and focuses on data mining to study user churn prediction and user value enhancement, which are the two most important factors affecting marketing revenue. Moreover, this paper conducts an empirical test of the product strategy and market strategy adopted by big data precision marketing. According to the characteristics of the user population and the application scenarios of the product, this paper puts the corresponding precision marketing methods in a targeted manner and analyzes the performance of the model through experimental research. The research results show that precision marketing methods based on big data information platforms need to be more detailed and more comprehensive. At the same time, precision marketing methods need to correspond to the sensitive information characteristics of target users and consider the background and current situation of actual market execution to effectively play it role.

MVFCC: A Multi-View Fuzzy Consensus Clustering Model for Malware Threat Attribution

The rise of emerging cyberthreats has led to a shift of focus on identifying the source of threat instead of the type of attack to provide a more effective defense to compromised environments against malicious acts. The most complex type of cyberthreat is the Advanced Persistent Threat (APT) attack that is usually backed by one or more states and lunched using a range of clandestine techniques aiming at high-value targets. Finding the source of the attackers and the associated campaign behind the threats can lead to taking an optimum defense decision in a more timely fashion. Threat attribution is an act of attributing an attack to the source of the attack. Threat attribution can not be fully achieved by a single piece of evidence (i.e. single view) from malicious actors as the evidence could get obfuscated by the actor to evade the detection mechanism. In this article, we propose a multi-view fuzzy consensus clustering model for attributing cyber threat payloads (malware) to its actor. We conduct over 4000 experiments to find out the best combinations of all 12 extracted views for the attribution task. Our experiments use five well-know APT families payloads. To avoid bias in the results, we apply a fuzzy pattern tree and multi-modal fuzzy classifier for our inference engines of all views. To define an optimum distinction among the malicious actor’s behavior we implemented the consensus clustering technique. The comparison analysis of a single-view versus multi-view result justifies a significant improvement in the accuracy rate of attribution for all actors. The obtained results from the multi-view aspect of our proposed model give 95.2% accuracy.

Grey clustering model based on kernel and information field

PurposeThe purpose of this paper is to propose a grey clustering model based on kernel and information field to deal with the situation in which both the observation values and the turning points of the whitenization weight function are interval grey numbers.Design/methodology/approachFirst, the “unreduced axiom of degree of greyness” was expanded to obtain the inference of “information field not-reducing”. Then, based on the theoretical basis of inference, the expression of whitenization weight function with interval grey number was provided. The grey clustering model and fuzzy clustering model were compared to analyse the relationship and difference between the two models. Finally, the paper model and the fuzzy clustering model were applied to the example analysis, and the interval grey number clustering model was established to analyse the influencing factors of regional drought disaster risk in Henan Province.FindingsThe example analysis results illustrate that although the two clustering methods have different theoretical basis, they are suitable for dealing with complex systems with uncertainty or grey characteristic, solving the problem of incomplete system information, which has certain feasibility and rationality. The clustering results of case study show that five influencing factors of regional drought disaster risk in Henan Province are divided into three classes, consistent with the actual situation, and they show the validity and practicability of the clustering model.Originality/valueThe paper proposes a new whitenization weight function with interval grey number that can transform interval grey number operations into real number operations. It not only simplifies the calculation steps, but it has a great significance for the “small data sets and poor information” grey system and has a universal applicability.

Use of Variable Fuzzy Clustering to Quantify the Vulnerability of a Power Grid to Earthquake Damage

The power grid is a critical component of city infrastructure. If it is damaged by an earthquake, there can be a huge impact on the safety and well-being of society and individuals. Identifying nodes in the grid that are highly vulnerable to earthquake damage is significant for effective pre-earthquake damage prevention, emergency response, and post-earthquake relief. Three indicators, the probability of node disconnection, the node hierarchical level, and the node critical threshold, were chosen, and their combined ability to represent node vulnerability to damage from an earthquake event was analyzed. A variable fuzzy clustering model was used to classify and order the nodes in the grid. The 20-node power grid of a city was used as an example to show how highly vulnerable nodes were identified, and how the reasons for the high vulnerability of these nodes were drawn out of the analysis. Countermeasures were given to reduce network vulnerability. The variable fuzzy clustering method used in this paper offers a new perspective on network vulnerability, and it quantifies the vulnerability of grid nodes more comprehensively than existing methods of assessing grid vulnerability. This research is significant as a baseline reference for future studies of grid vulnerability.

Segmentation and Diagnosis of Liver Carcinoma Based on Adaptive Scale-Kernel Fuzzy Clustering Model for CT Images.

Medical image analysis plays an important role in computer-aided liver-carcinoma diagnosis. Aiming at the existing image fuzzy clustering segmentation being not suitable to segment CT image with non-uniform background, a fast robust kernel space fuzzy clustering segmentation algorithm is proposed. Firstly, the sample in euclidean space is mapped into the high dimensional feature space through the kernel function. Then the linear weighted filtering image is obtained by combining the current pixel with its neighborhood pixels through the space information in CT image. Finally, the two-dimensional histogram between the clustered pixel and its neighborhood mean is introduced into the robust kernel space image fuzzy clustering, and the iterative expression of the fast robust fuzzy clustering in kernel space is obtained by using Lagrange multiplier method. The experimental results on four databases show that our proposed method can segment liver tumors from abdominal CT volumes effectively and automatically, and the comprehensive segmentation performance of the proposed method is superior to that of several existing methods.

Fuzzy clustering of mixed data

A fuzzy clustering model for data with mixed features is proposed. The clustering model allows different types of variables, or attributes, to be taken into account. This result is achieved by combining the dissimilarity measures for each attribute by means of a weighting scheme, so as to obtain a distance measure for multiple attributes. The weights are objectively computed during the optimization process. The weights reflect the relevance of each attribute type in the clustering results. Two simulation studies and two empirical applications were carried out that show the effectiveness of the proposed clustering algorithm in finding clusters that would be otherwise hidden if a multi–attributes approach were not pursued.

Research on human resource performance and decision-making evaluation based on fuzzy mathematics and clustering model

Research on human resource performance and decision-making evaluation based on fuzzy mathematics and clustering model

Cross Sectional and Longitudinal Fuzzy Clustering of the NUTS and Positioning of the Italian Regions with Respect to the Regional Competitiveness Index (RCI) Indicators with Contiguity Constraints

In socio-economical clustering often the empirical information is represented by time-varying data generated by indicators observed over time on a set of subnational (regional) units. Usually among these units may exist contiguity relations, spatial but not only. In this paper we propose a fuzzy clustering model of multivariate time-varying data, the longitudinal fuzzy C-Medoids clustering with contiguity constraints. The temporal aspect is dealt with by using appropriate measures of dissimilarity between time trajectories. The contiguity among units is dealt with adding a contiguity matrix as a penalization term in the clustering model. The cross sectional fuzzy C-Medoids clustering with contiguity constraints is obtained considering one instant of time. The model is applied to the classification of the European NUTS on the basis of the observed dynamics of the Basic, Efficiency and Innovation subindexes of the Regional Competitiveness Index (RCI) 2013 and 2016. The positioning of the Italian regions is analyzed through the values of the medoids of the clusters and shows the peculiarities of the regions with respect to the subindexes either in single times or in the dynamic. Two contiguity constraints, one based on the European Western, Southern, Central and Northern geographic areas and one on the level of GDP—taken into account in the computation of the RCI—are also introduced in the models.

Membership Affinity Lasso for Fuzzy Clustering

Fuzzy clustering generates a membership vector for each data point in the dataset to indicate its belongingness to different clusters. This procedure can be regarded as an encoding process and the obtained vectors of memberships are the new representations of original data. Naturally, the affinities between new representations or the vectors of memberships should be consistent with the ones between original data points. For example, the data points close to each other should also take similar membership vectors. Such constraints on the affinities of memberships are valuable prior knowledge that should be imposed to the objective function of fuzzy clustering for better performance. To this end, we introduce the membership affinity lasso for fuzzy clustering in this paper. Utilizing alternating direction method of multipliers, an efficient approach is derived to optimize the general membership affinity lasso regularized fuzzy clustering model in offline manner. As illustrative examples, three new fuzzy clustering algorithms with the membership affinity lasso are proposed. Experiments on the synthetic and real data demonstrate the superiority and flexibility of the proposed algorithms.

Enhancing recommendation stability of collaborative filtering recommender system through bio-inspired clustering ensemble method

In recent years, internet technologies and its rapid growth have created a paradigm of digital services. In this new digital world, users suffer due to the information overload problem and the recommender systems are widely used as a decision support tool to address this issue. Though recommender systems are proven personalization tool available, the need for the improvement of its recommendation ability and efficiency is high. Among various recommendation generation mechanisms available, collaborative filtering-based approaches are widely utilized to produce similarity-based recommendations. To improve the recommendation generation process of collaborative filtering approaches, clustering techniques are incorporated for grouping users. Though many traditional clustering mechanisms are employed for the users clustering in the existing works, utilization of bio-inspired clustering techniques needs to be explored for the generation of optimal recommendations. This article presents a new bio-inspired clustering ensemble through aggregating swarm intelligence and fuzzy clustering models for user-based collaborative filtering. The presented recommendation approaches have been evaluated on the real-world large-scale datasets of Yelp and TripAdvisor for recommendation accuracy and stability through standard evaluation metrics. The obtained results illustrate the advantageous performance of the proposed approach over its peer works of recent times.