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Gliomas are the brain tumors in glial cells, which are categorized into four numerical grades, I-II-III-IV, to quantize the aggressiveness and severity of the tumors; while divided into two major groups, high-grade (HG) and low-grade (LG), in general. Among many differences between these groups, one of the most distinct and characteristic features could be seen in the shape of the tumor boundaries by magnetic resonance imaging (MRI). Due to aggressive nature of the HG tumors in proliferation phase, the boundaries of HG tumors become more shape-wise complex compared to the LG tumors, which could be differentiated by analyzing the fractal complexity of the cell membranes. However, the complexity cannot be either manually calculated or estimated by eye inspection without a reference point with one single image or sometimes even with an image set. Therefore, we present an automated glioma grading framework to provide an insight on the grades with a novel contouring and fractal dimension analysis system. The primary component of the proposed system is an automated Nakagami imaging module with a specialized fuzzy c-means algorithm to contour the boundaries of the whole tumors. The contoured images, afterwards, are analyzed by the Minkowski–Bouligand and Hausdorff methods for two panning options to generate the fractal dimensions and to estimate the fractal complexities for classifying the gliomas The results are greatly encouraging that the overall classification accuracy is computed as 88.31 % using the basic support vector machines (SVM) classifier; while as 91.96 % with the arbitrary thresholding appended. The outcomes of this paper with implementable mathematical infrastructure would be very useful and beneficial as an expert system in intelligent and automatic glioma grading, for researchers and medical experts. • We proposed a novel automated glioma-grading framework. • 2D FLAIR MRI images consisting of HG and LG gliomas are analyzed. • Raw images are highlighted by Nakagami module and contoured by fuzzy 2-means. • Fractal dimensions of the contoured images are analyzed by two methods. • Overall accuracy is computed as ACC=91.96 % with a SVM classifier. [ABSTRACT FROM AUTHOR]

Semi-supervised clustering aims to guide the clustering by utilizing auxiliary information about the class labels. Among the semi-supervised clustering categories, the constraint-based approach uses the available pairwise constraints in some steps of the clustering procedure, usually by adding new terms to the objective function. Considering this category, Semi-supervised FCM (SSFCM) is a semi-supervised version of the fuzzy c -means algorithm, which takes advantage of fuzzy logic and auxiliary class distribution knowledge. Despite the performance enhancement caused by incorporating this extra knowledge in the clustering process, semi-supervised fuzzy approaches still suffer from some problems. All the data attributes in the feature space are assumed to have equal importance in the cluster formation, while some features may be more informative than others. Thus the feature importance issue is not addressed in the semi-supervised category. This paper proposes a novel Semi-Supervised Fuzzy c -means approach, which is designed based on Feature-Weight, and Cluster-Weight learning, named SSFCM-FWCW. Inspired by the SSFCM, a fuzzy objective function is presented, which is composed of (1) a semi-supervised term representing the external class knowledge; (2) a feature weighting; and (3) a cluster weighting. Both feature weights and cluster weights are determined adaptively during the clustering. Considering these two techniques leads to insensitivity to the initial center selection, insensitivity to noise, and consequently helps to form an optimal clustering structure. Experimental comparisons are carried out on several benchmark datasets to evaluate the proposed approach's performance, and promising results are achieved. The Matlab implementation source code of the proposed method is publicly accessible at https://github.com/Amin-Golzari-Oskouei/SSFCM-FWCW. • This paper proposes a novel Semi-Supervised Fuzzy C-means approach based on Feature-Weight and Cluster-Weight learning. • An adaptive weight for each feature in each cluster applies based on its importance in forming the clusters. • The weight of the clusters is calculated dynamically to decrease cluster center initialization sensitivity. • Considering the conjunction of feature and cluster weighting helps form an optimal clustering structure. [ABSTRACT FROM AUTHOR]

Abstract Among fuzzy clustering methods, fuzzy c-means (FCM) is the most recognized algorithm. In this algorithm, it is assumed that all the features are of equal importance. In real applications, however, the importance of the features are different and there exist some features that are more important than the others. These important features should basically have more effects than the other features in the forming of optimal clusters. The basic FCM algorithm does not support this idea. Also, the FCM algorithm suffers from another problem; the algorithm is very sensitive to initialization, whereas a bad initialization leads to a poor local optima. Some improved versions of FCM have been proposed in the literature, each of which has somehow mitigated the first problem or the second one. In this paper, motivated by these weaknesses of the FCM, the goal is to solve the two problems at the same time. In doing so, an automatic local feature weighting scheme is proposed to properly weight the features of each clusters. And, a cluster weighting process is performed to mitigate the initialization sensitivity of the FCM. Feature weighting and cluster weighting are performed simultaneously and automatically during the clustering process resulting in high quality clusters, regardless of the initial centers. Extensive experiments conducted on a synthetic dataset and 16 real world datasets indicate that the proposed algorithm outperforms the state-of-the-arts algorithms. The convergence proof of the proposed algorithm is also provided. Highlights • Feature weighting and cluster weighting are used to improve the FCM clustering method. • Feature weighting is carried out based on importance of each feature in the clusters. • Weights of the clusters are calculated considering the importance of their features. • Feature weighting and cluster weighting are performed simultaneously. [ABSTRACT FROM AUTHOR]

Abstract Classical fuzzy time series forecasts are comprised of three steps: fuzzification, identification of fuzzy relation, and defuzzification. In this paper, we propose a new approach and add an error learning step to improve forecasts. In the fuzzification step, a hybrid method, based on the fuzzy c-means clustering and the fuzzy Silhouette criterion, is employed to determine the optimal number of intervals, which avoids time-consuming iterations of the whole algorithm. In the defuzzification step, an optimization model is set up to explain the rule of defuzzification. In the model structure, an error term is assembled into the traditional model to express model error, which is predicted by linear fitting and abnormal errors processing. Learning of model errors and considering of data characteristics guarantee good interpretability and accuracy. The numerical results show that the proposed approach has superior forecast performance to existing methods. Highlights • Fuzzy c-means clustering and fuzzy Silhouette criterion are employed to determinate the optimal number of intervals. • The model error is learned by linear fitting and abnormal errors processing. • An optimization model is set up to explain the rule of defuzzification. [ABSTRACT FROM AUTHOR]

Abstract Segmentation of brain magnetic resonance (MR) images has a significant impact on the computer-aided diagnosis and analysis. However, due to the presence of noise in medical images, many segmentation methods suffer from limited segmentation accuracy. To reduce the effect of noise and achieve high segmentation accuracy many approaches based on the local and nonlocal information in the spatial domain have been proposed in the past. Recently, the authors have proposed a discrete cosine transform (DCT)-based local and nonlocal fuzzy C-means method (DCT-LNLFCM) which performs much better than the existing methods. However, the method is slow in speed. This paper presents a fast DCT-based nonlocal fuzzy C-means (DCT-NLFCM) segmentation method which is not only very fast than the DCT-LNLFCM, but also provides better segmentation results. The proposed method uses DCT-based MR pre-filtered image to achieve high segmentation accuracy and its histogram enables to achieve very high computation speed. Detailed experiments are conducted to establish the superiority of the proposed method over the state-of-the-art unsupervised methods. Highlights • A fast DCT-based MR image segmentation approach proposed. • The approach provides very high segmentation accuracy. • The algorithm is very fast as compared to the existing DCT-based algorithm. • The DCT-domain pre-filtered image is used to achieve high speed. • The proposed method is robust to noise. [ABSTRACT FROM AUTHOR]

Accurate segmentation of brain tissues from magnetic resonance images (MRI) is a crucial requirement for the quantitative analysis of brain images. Due to the presence of noise in brain MRI, many segmentation methods suffer from low segmentation accuracy. The existing methods deal the noise sensitivity of the MRI segmentation in the spatial domain by combining the local and nonlocal information in the fuzzy C-means (FCM) method. These methods are prone to loosing image details while reducing the effect of noise. In this paper, we propose a transform domain approach using the discrete cosine transform (DCT). Working in the transform domain has an advantage over the spatial domain in which the intensity of the image is decorrelated and the image information is represented by the independent frequency bands. The low and middle level frequency bands represent the holistic and fine structures of the image and the high frequency band mostly carries the noise information. In the proposed method, called the DCT-based local and nonlocal FCM (DCT-LNLFCM), the distance function of the FCM is represented as the sum of the local and nonlocal distances which themselves are the weighted values of the Euclidean distance used in the FCM. Since the weights are computed in the transform domain, a good tradeoff is achieved between noise insensitivity and preservation of the image details. This results in the high accuracy of the MRI segmentation. Detailed experimental results are presented and comparison with the state-of-the-art techniques is performed to demonstrate the high performance of the proposed approach. The proposed method provides an improvement in the average segmentation accuracy from 1.10% to 2.03% on simulated images and 1.52% to 1.91% on real images. [ABSTRACT FROM AUTHOR]

Cluster analysis is a very useful data mining approach. Although many clustering algorithms have been proposed, it is very difficult to find a clustering method which is suitable for all types of datasets. This study proposes an evolutionary-based clustering algorithm which combines a metaheuristic with a kernel intuitionistic fuzzy c -means (KIFCM) algorithm. The KIFCM algorithm improves the fuzzy c -means (FCM) algorithm by employing an intuitionistic fuzzy set and a kernel function. According to previous studies, the KIFCM algorithm is a promising algorithm. However, it still has a weakness due to its high sensitivity to initial centroids. Thus, this study overcomes this problem by using a metaheuristic algorithm to improve the KIFCM result. The metaheuristic can provide better initial centroids for the KIFCM algorithm. This study applies three metaheuristics, particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC) algorithms. Though the hybrid method is not new, this is the first paper to combine metaheuristics and KIFCM. The proposed algorithms, PSO-KIFCM, GA-KIFCM and ABC-KIFCM algorithms are evaluated using six benchmark datasets. The results are compared with some other clustering algorithms, namely K -means, FCM, Kernel fuzzy c-means (KFCM) and KIFCM algorithms. The results prove that the proposed algorithms achieve better accuracy. Furthermore, the proposed algorithms are applied to solve a case study on customer segmentation. This case study is taken from franchise stores selling women's clothing in Taiwan. For this case study, the proposed algorithms also exhibit better cluster construction than other tested algorithms. [ABSTRACT FROM AUTHOR]

Grinding plays a prominent role in modern manufacturing due to its capacity for producing parts of high accuracy and precision. Among the various grinding variables, the specific grinding energy (e c ) is key because it measures the energy required to remove the unit volume of part material and therefore it gives information about the performance of the grinding process. In addition, a measure of the specific grinding energy is also useful for estimating the power requirements of the grinding machine. Thus, a Recurrent Neural Network (RNN) is used for predicting e c in a more realistic manner that involves the development of the e c over time. Moreover, since performing grinding experiments is a highly time and resource consuming task, it would be very useful to downsize the required dataset to train the RNN since it could substantially reduce the time and costs involved in carrying out the experiments to generate the dataset, as well as in training the RNNs. Therefore, in this work a methodology combining Fuzzy C-Means (FCM) and RNNs for downsizing the dataset and predicting specific grinding energy is proposed. Unlike other approaches for reducing the dataset using FCM, in the current work the inputs are weighted. To achieve this, the knowledge is extracted from the weights of satisfactorily trained RNN obtained from previous work. The results show that under reduced training datasets (weighted and non-weighted FCM inputs) and non-reduced datasets (all available experiments), superior results were yielded with the RNNs obtained with the weighted approach. In fact, in some cases, for the reduced training dataset (weighted) the error is halved. Furthermore, the results show that it is more advantageous to use a reduced training dataset obtained after FCM, since this reduces the costs associated with experimental time, as well as the training time required for RNNs. [ABSTRACT FROM AUTHOR]

In this study, we develop an approach to multivariate time series anomaly detection focused on the transformation of multivariate time series to univariate time series. Several transformation techniques involving Fuzzy C-Means (FCM) clustering and fuzzy integral are studied. In the sequel, a Hidden Markov Model (HMM), one of the commonly encountered statistical methods, is engaged here to detect anomalies in multivariate time series. We construct HMM-based anomaly detectors and in this context compare several transformation methods. A suite of experimental studies along with some comparative analysis is reported. [ABSTRACT FROM AUTHOR]

In this paper, a fuzzy clustering technique for image segmentation is developed by incorporating a hybrid of local spatial membership and data information into the conventional hard C-means (HCM) algorithm. This incorporation is a threefold procedure. (1) The membership function of a pixel is spatially smoothed in the pixel vicinity. (2) The Kullback-Leibler (KL) divergence between the pixel membership function and the smoothed one is added to the HCM objective function for fuzzification. (3) The resulting fuzzified HCM is regularized by adding a weighted HCM-like function where the original pixel data are replaced by locally smoothed ones. Thereby the weight is proportional to the residual of the locally smoothed membership. This residual decreases when many pixels existing in the pixel vicinity belong to the same cluster. Thus, the weighted distance decreases, allowing the pixel membership to follow the dominant membership in the pixel vicinity. The simulation results of segmenting synthetic, medical and media images have shown that the proposed algorithm provides better performance compared to several previously developed algorithms. For example, in a synthetic image, with added white Gaussian noise having a variance of 0.3, the proposed algorithm provides accuracy, sensitivity and specificity of 92%, 84% and 94.7% respectively, while the algorithm with the closest results provides 81.9% of accuracy, 62.2% of sensitivity and 86.8% of specificity. In addition, the proposed algorithm shows the capability to identify the number of clusters. [ABSTRACT FROM AUTHOR]

Information granules form an abstract and efficient characterization of large volumes of numeric data. Fuzzy clustering is a commonly encountered information granulation approach. A reconstruction (degranulation) is about decoding information granules into numeric data. In this study, to enhance quality of reconstruction, we augment the generic data reconstruction approach by introducing a transformation mapping of the originally produced partition matrix and setting up an adjustment mechanism modifying a localization of the prototypes. We engage several population-based search algorithms to optimize interaction matrices and prototypes. A series of experimental results dealing with both synthetic and publicly available data sets are reported to show the enhancement of the data reconstruction performance provided by the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the sensor-energy optimization in 3D Wireless Sensor Networks (WSNs), which determines an optimal topology of sensors to prolong the network lifetime and reduce the energy expenditure. A new mathematical model for clustering in 3D WSN, considering energy consumption, constraints of communication and a 3D energy function, is presented. Using the Lagrange multiplier method, solutions of the model consisting of cluster centres and the membership matrix are computed and used in the new algorithm, called FCM-3 WSN. Experimental validation on real 3D datasets demonstrates that FCM-3 WSN outperforms the relevant methods, namely, Low-Energy Adaptive Clustering Hierarchy (LEACH), Centralized LEACH (LEACH-C), Single-hop Clustering and Energy-Efficient Protocol (SCEEP), Hybrid-Low Energy Adaptive Clustering Hierarchy (H-LEACH), K-Means and Fuzzy C-Means (FCM). [ABSTRACT FROM AUTHOR]

Fuzzy sets, rough sets are efficient tools to handle uncertainty and vagueness in the medical images and are widely used for medical image segmentation. Soft sets are a new mathematical approach to uncertainty and vagueness. In this paper, a hybrid segmentation algorithm based on soft sets namely soft fuzzy rough c-means is proposed to extract the white matter, gray matter and the cerebro spinal fluid from MR brain image with bias field correction. In this algorithm, soft fuzzy rough approximations are applied to obtain the rough regions of image. These approximations are free from defining thresholds, weight parameters and are less complex compared to the existing rough set based algorithms. Soft sets use similarity coefficients to find the similarity of the clusters formed in present and previous step. The proposed algorithm does not involve any negative region, hence all the pixels participate in clustering avoiding clustering mistakes. Also, the histogram based centroids choose the centroids close to the ground truth that in turn effect the definition of approximations, standardizing the clusters. The proposed algorithm evaluated through simulation, compared it with existing k-means, rough k-means, fuzzy c-means and other hybrid algorithms. The soft fuzzy rough c-means algorithm outperforms the considered algorithms in all analyzed scenarios even in extracting the tumor from the brain tissue. [ABSTRACT FROM AUTHOR]

The brain magnetic resonance (MR) image has an embedded bias field. This field needs to be corrected to obtain the actual MR image for classification. Bias field, being a slowly varying nonlinear field, needs to be estimated. In this paper, we have proposed three schemes and in turn three algorithms to segment the given MR image while estimating the bias field. The problem is compounded when the MR image is corrupted with noise in addition to the inherent bias field. The notions of possibilistic and fuzzy membership have been combined to take care of the modeling of the bias field and noise. The weighted typicality measure together with the weighted fuzzy membership has been used to model the image. The above resulted in the proposed Bias Corrected Possibilistic Fuzzy C-Means (BCPFCM) strategy and the algorithm. Further reinforcing the neighbourhood data to the modeling aspect has resulted in the two other strategies namely Bias Corrected Possibilistic Neighborhood Fuzzy C-Means (BCPNFCM) and Bias Corrected Separately weighted Possibilistic Neighborhood Fuzzy C-Means (BCSPNFCM). The proposed algorithms have successfully been tested with synthetic data with bias field of low and high spatial frequency. Noisy brain MR images with Gaussian Noise of varying strength have been considered from the BrainWeb database. The algorithms have also been tested on real brain MR data set with axial and sagittal view and it has been found that the proposed algorithms produced segmentation results with less percentage of misclassification errors as compared to the Bias Corrected Fuzzy C-Means (BCFCM) algorithm proposed by Ahmed et al. [4] . The performance of the proposed algorithms has been compared with algorithms from other paradigm in the context of Tanimoto's index. [ABSTRACT FROM AUTHOR]

Microscopic images have the potential to talk about much precious information about the internal structure of living organisms. But the naked eye is not always efficient enough to explore various hidden information from the microscopic images and here the need for automated image analysis tools comes into the picture. The interval type 2 fuzzy C-Means clustering and cuckoo search-based microscopic image segmentation approach is proposed in this work. The proposed algorithm will be known as the EFECS (Enhanced Fuzzy Elitist Cuckoo Search algorithm) approach that overcomes the dependency on the initial selection of the cluster centers by using the randomness of the EFECS method. EFECS method uses interval type 2 fuzzy membership to update the cluster centers. The proposed EFECS method is compared with some well-known methods to prove its superiority. The results are verified using both qualitative and quantitative manner. Experimental results established the superiority and the real-life applicability of the proposed EFECS algorithm. On average (for 150 images), the proposed approach archives 0.901537 DB index value (5 clusters), 0.629407 XB index value (5 clusters), 2.84774 Dunn index value (5 clusters), and 4.368482 β index value (7 clusters) that outperforms its nearest competitors CS with 0.904246 DB index value (7 clusters), ACO with 0.763519 XB index value (9 clusters), CS with 2.59191 Dunn index value (5 clusters), and ACO with 4.24919 β index value (7 clusters) respectively. Moreover, on average, the proposed approach achieves MSE values 297.8501535 (3 clusters), 303.4967502 (5 clusters), 296.6295076 (7 clusters), 311.9109645 (9 clusters) that also outperforms other approaches. [ABSTRACT FROM AUTHOR]

Due to uncertainty value of objects in microarray gene expression high dimensional cancer database, finding available subtypes of cancers is considered as challenging task. Researchers have invented mathematical assisted clustering techniques in clustering relevant gene expression of cancer subtypes, but the techniques have failed to provide proper outcome results with less error. Hence, it is an essential one in finding efficient computational clustering techniques to cluster the high dimensional gene expression cancer database for perfect diagnosis of cancer subtypes. This paper presents robust clustering techniques to identify perfect similarity between the uncertain objects of high dimensional cancer database. In order to obtain the robust clustering techniques, this paper incorporates both membership functions of fuzzy c-means and possibilistic c-means. In addition, this paper presents prototype initialization algorithm to avoid random initialization of initial prototypes. Benchmarks datasets were used to show the effectiveness of the proposed methods. The proposed methods were successfully implemented with microarray high dimensional gene expression cancer databases to separate available subtypes of cancer regions. The clustering accuracies of proposed and existed clustering methods indicate that the proposed methods are superior to the existed methods. [ABSTRACT FROM AUTHOR]

Fuzzy C-means (FCM) partitions the observations partially into several clusters based on the principles of fuzzy theory. However, minimization on the Euclidean distance in FCM tends to detect hyper-spherical shaped clusters, which is unfeasible for the real world problems. In this paper, an effective FCM algorithm that adopts the symmetry similarity measure is proposed in order to search for the appropriate clusters, regardless of the geometric structures and overlapping characteristic. Experimental results on several artificial and real life datasets with different nature and the performance assessment with other existing clustering algorithms demonstrate its superiority. [ABSTRACT FROM AUTHOR]

The fuzzy C-means (FCM) algorithm has got significant importance due to its unsupervised form of learning and more tolerant to variations and noise as compared to other methods in medical image segmentation. In this paper, we propose a conditional spatial fuzzy C-means (csFCM) clustering algorithm to improve the robustness of the conventional FCM algorithm. This is achieved through the incorporation of conditioning effects imposed by an auxiliary (conditional) variable corresponding to each pixel, which describes a level of involvement of the pixel in the constructed clusters, and spatial information into the membership functions. The problem of sensitivity to noise and intensity inhomogeneity in magnetic resonance imaging (MRI) data is effectively reduced by incorporating local and global spatial information into a weighted membership function. The experimental results on four volumes of simulated and one volume of real-patient MRI brain images, each one having 51 images, show that the csFCM algorithm has superior performance in terms of qualitative and quantitative studies such as, cluster validity functions, segmentation accuracy, tissue segmentation accuracy and receiver operating characteristic (ROC) curve on the image segmentation results than the k-means, FCM and some other recently proposed FCM-based algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a new color image segmentation method based on a multiobjective optimization algorithm, named improved bee colony algorithm for multi-objective optimization (IBMO). Segmentation is posed as a clustering problem through grouping image features in this approach, which combines IBMO with seeded region growing (SRG). Since feature extraction has a crucial role for image segmentation, the presented method is firstly focused on this manner. The main features of an image: color, texture and gradient magnitudes are measured by using the local homogeneity, Gabor filter and color spaces. Then SRG utilizes the extracted feature vector to classify the pixels spatially. It starts running from centroid points called as seeds. IBMO determines the coordinates of the seed points and similarity difference of each region by optimizing a set of cluster validity indices simultaneously in order to improve the quality of segmentation. Finally, segmentation is completed by merging small and similar regions. The proposed method was applied on several natural images obtained from Berkeley segmentation database. The robustness of the proposed ideas was showed by comparison of hand-labeled and experimentally obtained segmentation results. Besides, it has been seen that the obtained segmentation results have better values than the ones obtained from fuzzy c-means which is one of the most popular methods used in image segmentation, non-dominated sorting genetic algorithm II which is a state-of-the-art algorithm, and non-dominated sorted PSO which is an adapted algorithm of PSO for multi-objective optimization. [ABSTRACT FROM AUTHOR]

For most of rock engineering and engineering geology projects, strength and deformability parameters of intact rocks have crucial importance. However, it is highly challenging to obtain these parameters from weak and very weak rocks due to their nature and testing requirements. For this reason, prediction models are commonly used to obtain desired parameters indirectly. When developing a prediction model, data sets having sufficient size are required. If sufficient data size is not provided for a prediction model, insufficient data problem arises. The main purpose of this study was to investigate the use of synthetic data in indirect determination of rock strength by employing fuzzy C-means (FCM) and adaptive neuro-fuzzy inference system (ANFIS). For the purpose, the experiments were carried out in two stages; (i) uniaxial compressive strength (UCS) prediction by using real data with ANFIS, and (ii) production of synthetic data sets having different sizes, and synthetic data set evaluation in modeling. According to the results obtained, FCM is a practical and suitable method for synthetic data production. Development of prediction models for rock strength by using synthetic data is found to be successful based on statistical performance indices. Additionally, the use of proposed size for synthetic data reduces modeling effort significantly because it eliminates the iterative approach in modeling, hence development of models for limited number of data becomes more practical. [ABSTRACT FROM AUTHOR]

In view of the shortcomings of Worst opposition learning and Random-scaled differential mutation Biogeography-Based Optimization (WRBBO) in solving complex optimization problems, such as insufficient search ability and low search efficiency, an improved WRBBO, Multi-population BBO (MPBBO) is proposed. Firstly, a multi-population strategy is adopted: the whole sorted population is divided into 3 different subgroups (high-level, median-level and low-level) through golden section to get some population diversity. Secondly, an aptitude-based teaching approach is proposed to be beneficial to each subgroup's development: a sinusoidal-scaled differential mutation operator is performed on the high-level subgroup to mostly get stronger exploration and reduce the computing cost, a heuristic crossover with dynamic fine adjustment is hybridized with a horizontal crossover and a vertical one to form a multi-crossover on the median-level subgroup to mainly get stronger exploitation, and a best agent guiding strategy is used on the low-level subgroup to improve the search ability. Finally, an information sharing way is adopted: all the individuals in 3 subgroups share information by merging and sorting them. The experimental results on the complex functions from CEC-2013 and CEC-2017 test sets show that MPBBO obtains stronger search ability and higher efficiency than WRBBO and quite a few other state-of-the-art algorithms. MPBBO is applied to image segmentation with fast and robust fuzzy c-means (FRFCM), and the results show that FRFCM-MPBBO has more significant advantages than its comparison methods. [Display omitted] • An effective multi-population strategy is presented to get population diversity. • A sinusoidal-scaled differential mutation is adopted on the high-level subgroup. • A best agent guiding strategy is adopted on the low-level subgroup for exploration. • A multi-crossover is adopted on the median-level subgroup for exploitation. • Proposed algorithm has better performance on 86 functions and image segmentation. [ABSTRACT FROM AUTHOR]

Highlights: [•] We introduce and examine a new methodology for training radial basis function (RBF) neural networks. [•] We use fuzzy clustering in order to improve the functionality of the Optimum Steepest Descent (OSD) learning algorithm. [•] We employed this new method in an online radar pulse classification system, which needs quick retraining of the network once new unseen emitters detected. [Copyright &y& Elsevier]

Abstract: This paper presents the Region Splitting and Merging-Fuzzy C-means Hybrid Algorithm (RFHA), an adaptive unsupervised clustering approach for color image segmentation, which is important in image analysis and in understanding pattern recognition and computer vision field. Histogram thresholding technique is applied in the formation of all possible cells, used to split the image into multiple homogeneous regions. The merging technique is applied to merge perceptually close homogeneous regions and obtain better initialization for the Fuzzy C-means clustering approach. Experimental results have demonstrated that the proposed scheme could obtain promising segmentation results, with 12% average improvement in clustering quality and 63% reduction in classification error compared with other existing segmentation approaches. [Copyright &y& Elsevier]

Abstract: Fuzzy clustering is a widely applied method for extracting the underlying models within data. It has been applied successfully in many real-world applications. Fuzzy c-means is one of the most popular fuzzy clustering methods because it produces reasonable results and its implementation is straightforward. One problem with all fuzzy clustering algorithms such as fuzzy c-means is that some data points which are assigned to some clusters have low membership values. It is possible that many samples may be assigned to a cluster with low-confidence. In this paper, an efficient and noise-aware implementation of support vector machines, namely relaxed constraints support vector machines, is used to solve the mentioned problem and improve the performance of fuzzy c-means algorithm. First, fuzzy c-means partitions data into appropriate clusters. Then, the samples with high membership values in each cluster are selected for training a multi-class relaxed constraints support vector machine classifier. Finally, the class labels of the remaining data points are predicted by the latter classifier. The performance of the proposed clustering method is evaluated by quantitative measures such as cluster entropy and Minkowski scores. Experimental results on real-life data sets show the superiority of the proposed method. [Copyright &y& Elsevier]

Abstract: Swarm intelligence based automatic fuzzy clustering is recently an important and interesting unsupervised learning problem. In this article, an automatic fuzzy clustering technique is proposed based on a novel version of Artificial Bee Colony (ABC) algorithm. The idea of variable length genotypes is introduced to the ABC, and a novel version of ABC, called Variable string length Artificial Bee Colony (VABC) algorithm, is proposed. The VABC algorithm is derived from the ABC by redefining or modifying some operations in the ABC: the fixed length strings are represented by using variable length strings, the scheme for producing candidate solutions is modified, and some mutation operations are introduced. Use of VABC allows the encoding of variable number of clusters. This makes the VABC based Fuzzy C-Means clustering technique (VABC-FCM) not require a priori specification of the number of clusters. Moreover, the VABC-FCM has powerful global search ability under rational parameter setting. Some artificial data sets and real-life data sets are applied to validate the performance of VABC-FCM. The experimental results show that VABC-FCM can automatically evolve the optimal number of clusters and find proper fuzzy partitioning for these data sets when a rational validity index is adopted. Finally, the performance of VABC-FCM is compared with those of the Variable string length Genetic Algorithm based Fuzzy C-Means clustering (VGA-FCM), Particle Swarm Optimization algorithm based Fuzzy C-Means clustering (PSO-FCM), and Differential Evolutional algorithm based Fuzzy C-Means clustering (DE-FCM). The results show that the VABC-FCM outperforms VGA-FCM, PSO-FCM and DE-FCM in most of the cases. [Copyright &y& Elsevier]

Abstract: The kernelized fuzzy c-means algorithm uses kernel methods to improve the clustering performance of the well known fuzzy c-means algorithm by mapping a given dataset into a higher dimensional space non-linearly. Thus, the newly obtained dataset is more likely to be linearly seprable. However, to further improve the clustering performance, an optimization method is required to overcome the drawbacks of the traditional algorithms such as, sensitivity to initialization, trapping into local minima and lack of prior knowledge for optimum paramaters of the kernel functions. In this paper, to overcome these drawbacks, a new clustering method based on kernelized fuzzy c-means algorithm and a recently proposed ant based optimization algorithm, hybrid ant colony optimization for continuous domains, is proposed. The proposed method is applied to a dataset which is obtained from MIT–BIH arrhythmia database. The dataset consists of six types of ECG beats including, Normal Beat (N), Premature Ventricular Contraction (PVC), Fusion of Ventricular and Normal Beat (F), Artrial Premature Beat (A), Right Bundle Branch Block Beat (R) and Fusion of Paced and Normal Beat (f). Four time domain features are extracted for each beat type and training and test sets are formed. After several experiments it is observed that the proposed method outperforms the traditional fuzzy c-means and kernelized fuzzy c-means algorithms. [Copyright &y& Elsevier]

Abstract: Unbalanced data that are minority classes with few samples presented in many fields. The mean of unbalanced data is difficult to formalize so that traditional algorithms are limited in solving unbalanced data. In this paper, a novel algorithm based on analysis of variance (ANOVA), fuzzy C-means (FCM) and bacterial foraging optimization (BFO) is proposed to classify unbalanced data. ANOVA can measure the difference between the means of two or more groups in which the observed variance is partitioned into components due to various explanatory variables. FCM is a method of fuzzy clustering algorithm that allows one piece of data to belong to two or more clusters. Natural selection tends to eliminate animals with poor foraging strategies and favors the propagation of genes of those animals that have successful foraging strategies. BFO can model the mechanism of natural selection and solve many application problems. The proposed algorithm combines the advantages of ANOVA, FCM and BFO. ANOVA has the ability to select beneficial feature subsets. FCM has the ability to identify data into clusters with certain membership degrees, and BFO has the fast ability to converge to global optima. In this paper, microarray data of ovarian cancer and zoo dataset are used to test the performance for the proposed algorithm. The performance of the proposed algorithm is supported by simulation results. From simulation results, the classification accuracy of the proposed algorithm outperforms other existing approaches. [Copyright &y& Elsevier]

Abstract: This work aims to define a new strategy for extracting and stereo matching of buildings using very high resolution multi spectral IKONOS images having a ratio base/height about 0.53, we do not have the intrinsic and extrinsic parameters of the images acquisition system. These images contain dense urban scenes including various kinds of roads, cars, vegetation and buildings. We are interested by buildings, some of them have different shapes or colours and others have close colours or shapes, so, they generate a lot of “false matches”. To solve this issue, we propose in this paper an approach based on soft computing field in order to extract regions of interest (buildings) and to match them, it contains two main steps: region segmentation and thresholding step using a specific fuzzy thresholding algorithm and a neural Hopfield matching stage based on new constraints including geometric and photometric regions properties. The presented strategy is nearly all automatic, it is fast and simple and the results of its applied tests on several kinds of stereo dense urban images are satisfactory. [Copyright &y& Elsevier]

Abstract: This study proposes a method, designated as the GRP-index method, for the classification of continuous value datasets in which the instances do not provide any class information and may be imprecise and uncertain. The proposed method discretizes the values of the individual attributes within the dataset and achieves both the optimal number of clusters and the optimal classification accuracy. The proposed method consists of a genetic algorithm (GA) and an FRP-index method. In the FRP-index method, the conditional and decision attribute values of the instances in the dataset are fuzzified and discretized using the Fuzzy C-means (FCM) method in accordance with the cluster vectors given by the GA specifying the number of clusters per attribute. Rough set (RS) theory is then applied to determine the lower and upper approximate sets associated with each cluster of the decision attribute. The accuracy of approximation of each cluster of the decision attribute is then computed as the cardinality ratio of the lower approximate sets to the upper approximate sets. Finally, the centroids of the lower approximate sets associated with each cluster of the decision attribute are determined by computing the mean conditional and decision attribute values of all the instances within the corresponding sets. The cluster centroids and accuracy of approximation are then processed by a modified form of the PBMF-index function, designated as the RP-index function, in order to determine the optimality of the discretization/classification results. In the event that the termination criteria are not satisfied, the GA modifies the initial population of cluster vectors and the FCM, RS and RP-index function procedures are repeated. The entire process is repeated iteratively until the termination criteria are satisfied. The maximum value of the RP cluster validity index is then identified, and the corresponding cluster vector is taken as the optimal classification result. The validity of the proposed approach is confirmed by cross validation, and by comparing the classification results obtained for a typical stock market dataset with those obtained by non-supervised and pseudo-supervised classification methods. The results show that the proposed GRP-index method not only has a better discretization performance than the considered methods, but also achieves a better accuracy of approximation, and therefore provides a more reliable basis for the extraction of decision-making rules. [Copyright &y& Elsevier]

Abstract: Soft computing techniques proved to be successful in many application areas. In this paper we investigate the application in psychopathological field of two well known soft computing techniques, fuzzy logic and genetic algorithms (GAs). The investigation started from a practical need: the creation of a tool for a quick and correct classification of mental retardation level, which is needed to choose the right treatment for rehabilitation and to assure a quality of life that is suitable for the specific patient condition. In order to meet this need we researched an adaptive data mining technique that allows us to build interpretable models for automatic and reliable diagnosis. Our work concerned a genetic fuzzy system (GFS), which integrates a classical GA and the fuzzy C-means (FCM) algorithm. This GFS, called genetic fuzzy C-means (GFCM), is able to select the best subset of features to generate an efficient classifier for diagnostic purposes from a database of examples. Additionally, thanks to an extension of the FCM algorithm, the proposed technique could also handle databases with missing values. The results obtained in a practical application on a real database of patients and comparisons with established techniques showed the efficiency of the integrated algorithm, both in data mining and completion. [Copyright &y& Elsevier]

The fuzzy c-means (FCM) algorithm is a popular method for data clustering and image segmentation. However, the main problem of this algorithm is that it is very sensitive to the initialization of primary clusters, so it may not perform well in segmenting complex images. Another problem with the FCM is the equal importance of the image features used during the segmentation process, which causes unstable performance on different images. In this paper, we propose an FCM-based color image segmentation approach, termed CGFFCM, applying an automatic cluster weighting scheme to reduce the sensitivity to the initialization, and a group-local feature weighting strategy to better image segmentation. Also, we combine the proposed clustering algorithm with the Imperialist Competitive Algorithm (ICA) to optimize the feature weighting process. In addition, we apply an efficient combination of image features to increase the segmentation quality. The performance of CGFFCM is evaluated and compared with state-of-the-art methods (such as SMKIFC (semi-supervised surrogate-assisted multi-objective kernel intuitionistic fuzzy clustering), and A-PSO-IT2IFCM (alternate particle swarm optimization based adaptive interval type-2 intuitionistic FCM clustering algorithm)) using the Berkeley benchmark dataset. The results obtained by CGFFCM are 95%, 79%, and 91%, in terms of average Accuracy , NMI , and F-score metrics, respectively, which all are better than the competitors. The implementation source code of CGFFCM is made publicly available at https://github.com/Amin-Golzari-Oskouei/CGFFCM. • A cluster weighting scheme to reduce the sensitivity of the image segmentation to the selection of initial centers. • A group-local feature weighting strategy to measure the importance and weights of image features precisely. • An automatic way to calculate the cluster and feature weights simultaneously during the learning process. • A combination of ICA meta-heuristic algorithm with proposed clustering algorithm to find the optimal group feature weights. [ABSTRACT FROM AUTHOR]

Distribution-based imaging is a promising methodology mainly to differentiate suspicious regions from surrounding tissues by applying a distribution to the images vertically or horizontally, ideally in both directions. The methodology is very useful for contouring and highlighting desired regions even under near-zero contrast conditions; it also leads to flexible segmentation of the lesions by parametric kernels and provides robust results when supported by solid post-segmentation protocols. Given these benefits, what we propose in this research is a specialized fuzzy 2-means algorithm enhanced by parametric distribution-based imaging framework to offer novel solutions for multiple-sclerosis (MS) identification and segmentation from flair MRI images. The interchangeable distributions employed in this research are Rayleigh, Weibull, Gamma, Exponential and Chi-square, which all are mathematically transmuted from Nakagami distribution. The Nakagami m-parameter is defining the shape of the distributions unless a special parameter exists; while the highlighted areas are segmented by fuzzy 2-means. All parameters are optimized using a set of MICCAI 2016 MS lesion segmentation challenge taken by Siemens Verio 3T scanner and 0.8245 dice score is achieved by Nakagami-Gamma. However, when the optimized framework is tested by other 4 sets with same resolution and size properties, the highest average dice score 0.7113 is obtained by Nakagami–Rayleigh; while Nakagami-Gamma transmutation is resulted in 0.7112 dice score with significantly better sensitivity. • We proposed a novel distribution-based imaging methodology for MS lesion segmentation. • This paper is the first instance of Nakagami transmutations for MS lesion detection. • The lesions are highlighted by mathematical transmutations of Nakagami distribution. • Suspicious regions are segmented by specialized fuzzy 2 means as the final classifier. • Dice score of 0.7113 is obtained for MICCAI 2016 experiment by Nakagami–Rayleigh. [ABSTRACT FROM AUTHOR]

The problem of finding anomalies (outliers) in databases is one of the most important issues in modern data analysis. One of the reasons is the occurrence of this issue in almost every type of database, including numerical, categorical, time, mixed, or graphic data. There are currently many methods often dedicated to specific data analysis. Finally, this topic is extremely interesting per se, as a research problem that intrigues researchers. One of the classic methods of data analysis dedicated to finding the anomalies in the data is Isolation Forest. However, this method, with a few exceptions, has not been modified from the time of its first publication, and, in particular, it has not yet appeared in combination with the typical fuzzy methods used for grouping such as Fuzzy C-Means (FCM) clustering. In this study, we thoroughly analyze this approach, as well as several related ones. We examine the possibilities of this technique and analyze it in detail for characteristics of data (database size, number of attributes, records, their type, etc.). It is worth noting that FCM allows to obtain membership grades of elements forming Isolation Forest nodes to clusters on the basis of which these nodes are built. Hence, at the stage of calculating the anomaly scores, this information is effectively used, in particular to express how much a given element may belong to a group of similar elements, which can be inferred from the characteristics of the cluster in which it lies. In this study, we propose a set of methods enhancing the Isolation Forest on a basis of Fuzzy C-Means. The results of numerical experiments carried using 27 various datasets and reported in this paper lead us to the conclusion that FCM can play a pivotal role in an enhancement of Isolation Forest approach and raises up the values of particular measures of effectiveness of the anomaly detection methods. • Fuzzy enhancements of Isolation Forest are proposed. • Fuzzy C-Means method is applied to split the tree nodes. • Different variants of search tree building are considered. • Numerical experiments' results demonstrating the efficiency are presented. • The experiments on real world logistic dataset are conducted. [ABSTRACT FROM AUTHOR]

In clustering, similarity measure has been one of the major factors for discovering the natural grouping of a given dataset by identifying hidden patterns. To determine a suitable similarity measure is an open problem in clustering analysis for several years. The purpose of this study is to make known a divergence based similarity measure. The notion of the proposed similarity measure is derived from Jeffrey-divergence. Various features of the proposed similarity measure are explained. Afterwards we develop fuzzy c-means (FCM) by making use of the proposed similarity measure, which guarantees to converge to local minima. The various characteristics of the modified FCM algorithm are also addressed. Some well known real-world and synthetic datasets are considered for the experiments. In addition to that two remote sensing image datasets are also adopted in this work to illustrate the effectiveness of the proposed FCM over some existing methods. All the obtained results demonstrate that FCM with divergence based proposed similarity measure outperforms three latest FCM algorithms. • A notion of similarity measure is proposed, which is derived from Jeffrey-divergence. • Various properties of the proposed similarity measure are explained. • The proposed similarity measure is merged with the traditional FCM clustering algorithm. • The proof of convergence theorem of the modified FCM algorithm is also discussed. [ABSTRACT FROM AUTHOR]

This paper presents an efficient Meta-cognitive Fuzzy C-Means (McFCM) clustering approach inspired by human meta-cognitive learning principles. Unlike other clustering approaches that use all the samples for learning, McFCM adopts a human like cognitive learning strategy to select the samples for learning, resulting in the use of lesser samples and faster convergence. McFCM consists of two units namely, a cognitive and a meta-cognitive unit. The cognitive unit is the basic fuzzy clustering unit which clusters the input data. The meta-cognitive unit consists of a replica of the cognitive unit along with performance measures for monitoring and learning strategies used for control actions. The meta-cognitive unit controls the learning process in the cognitive unit by deciding on what-to-learn, when-to-learn and how-to-learn. Detailed performance evaluation of McFCM is presented using seven benchmark classification problems from the UCI repository and the results have been statistically compared with other well known existing clustering methods. The results show a superior performance of McFCM. Performance of McFCM is also presented using a real world Autism Spectrum Disorder Detection problem with better classification accuracy compared to other existing methods. • An efficient clustering approach based on human meta-cognitive learning principles. • Proposed approach selects lesser samples for learning. • Automatic selection of optimal number of clusters and cluster center updating. • Results indicate better generalization with minimal computational effort. [ABSTRACT FROM AUTHOR]