A Kernel Fuzzy Clustering Algorithm with Spatial Constraint Based on Improved Expectation Maximization for Image Segmentation

Kernelized Fuzzy C-means Clustering with Adaptive Thresholding for Segmenting Liver Tumors

Fuzzy c-means clustering algorithm (FCM) is one of the most widely used methods for image segmentation. In order to overcome the sensitivity of FCM to noise in images, we introduce a novel non local adaptive spatial constraint term, which is defined by using the non local spatial information of pixels, into the objective function of FCM and propose an adaptive non local spatial fuzzy image segmentation algorithm (ANLS_FIS). In this method, the non-local spatial information of each pixel plays a different role in image segmentation. ANLS_FIS can effectively deal with noise while preserving the geometrical edges in the image. Experiments on synthetic and real images, especially magnetic resonance (MR) images, show that ANLS_FIS is more robust than the modified FCM algorithms with local spatial constraint.

There is always much difficult in the MR image segmentation. Although fuzzy c-means(FCM) clustering algorithm has been widely used in the field of image segmentation study, some inherent deficiencies of this algorithm especially the high cost of computation made the algorithm to be difficult widely used in practice. A novel algorithm, based on kernel fuzzy c-means (KFCM) clustering algorithm and the k-nearest neighbor (KNN) algorithm, is proposed to improve the performance of MR image segmentation. In this algorithm, the statistical gray level histogram of image is used in KFCM algorithm to speed up the algorithm. Furthermore, the spatial information of image is also considered by k-nearest neighbor algorithm based on kernel methods. With kernel methods each pixel of image is mapped into a high-dimensional feature space where FCM algorithm and KNN algorithm are carried out. Experiments show that the proposed algorithm is effective and efficient in image segmentation.

Image segmentation plays an important role in machine vision, image recognition, and imaging applications. Based on the fuzzy c-means clustering algorithm, a kernel-distance-based intuitionistic fuzzy c-means clustering (KIFCM) algorithm is proposed. First, a fuzzy complement operator is used to generate the membership degree whereby the hesitation degree of intuitionistic fuzzy set is generated; second, a kernel-induced function is used to calculate the distance from each point to the cluster center instead of the Euclidean distance; third, a new objective function that includes the hesitation degree is established, and the optimization of the objective function results in new iterative expressions for the membership degree and the cluster center. The proposed KIFCM algorithm is compared with the fuzzy c-means clustering (FCM) algorithm, the kernel fuzzy c-means clustering (KFCM) algorithm, and the intuitionistic fuzzy c-means clustering (IFCM) algorithm in segmenting five images. The experimental results verify the effectiveness and superiority of our proposed KIFCM algorithm.

An intelligent interval forecasting system based on fuzzy time series and error distribution characteristics for air quality index

Fuzzy c‐means (FCMs) with spatial constraints have been considered as an effective algorithm for image segmentation. The well‐known Gaussian mixture model (GMM) has also been regarded as a useful tool in several image segmentation applications. In this study, the authors propose a new algorithm to incorporate the merits of these two approaches and reveal some intrinsic relationships between them. In the authors model, the new objective function pays more attention on spatial constraints and adopts Gaussian distribution as the distance function. Thus, their model can degrade to the standard GMM as a special case. Our algorithm is fully free of the empirically pre‐defined parameters that are used in traditional FCM methods to balance between robustness to noise and effectiveness of preserving the image sharpness and details. Furthermore, in their algorithm, the prior probability of an image pixel is influenced by the fuzzy memberships of pixels in its immediate neighbourhood to incorporate the local spatial information and intensity information. Finally, they utilise the mean template instead of the traditional hidden Markov random field (HMRF) model for estimation of prior probability. The mean template is considered as a spatial constraint for collecting more image spatial information. Compared with HMRF, their method is simple, easy and fast to implement. The performance of their proposed algorithm, compared with state‐of‐the‐art technologies including extensions of possibilistic fuzzy c‐means (PFCM), GMM, FCM, HMRF and their hybrid models, demonstrates its improved robustness and effectiveness.

In this paper, an unsupervised change detection method for multitemporal remote sensing images is proposed. Firstly, the difference image is obtained from two multitemporal images acquired on the same geographical area but at different time instances. Then the difference image is decomposed by nonsubsampled contour let transform (NSCT). For each pixel in the difference image, a feature vector is extracted using the NSCT coefficients and the difference image itself which are in the same position. The final change map is achieved by clustering the feature vectors using kernel fuzzy c-means (KFCM) clustering algorithm into two classes: changed and unchanged. The change detection results are compared with those of several state-of-the-art methods. And the experimental results demonstrate that the proposed method yields superior performance.

As the coupling and integration of multi-energy flow in the integrated energy system (IES) deepen increasingly, the cascading failure will develop across different energy systems more easily and widely through the energy hub (EH). And it brings great challenges to the security and reliability of IES. The defects of the present cascading failure model of IES have been summarized, and a novel search strategy of fault chains in IES combined heating and power network was proposed in this paper. First, the initial risk assessment index of each energy branch is proposed to form the initial fault sets. Then, combined heat and power control (CHPC) strategies are introduced to deal with the branch overload conditions during the cascading failure. What is more, in order to reduce the workload and overcome the limitation of present methods, we analyzed the relevance of the branches to be predicted by using the kernel fuzzy C-means (KFCM) clustering algorithm and select the branches with the highest value of relevance as the subsequent failure. Based on the predicted fault chain, vulnerability analysis is presented to locate critical component and find out the correlation between cascading outages. The comprehensive evaluation index is also established to effectively evaluate the impact severity of cascading failure. Finally, the case studies are carried out on the combined heating and power systems to demonstrate the effectiveness of the proposed method.

DIABETIC RETINOPATHY DIAGNOSIS USING KERNEL FUZZY C MEANS WITH CONVOLUTIONAL NEURAL NETWORK BASED RESIDUAL MODEL

In this paper, the method that measuring dataset of knitted yarns is clustered using improving fuzzy kernel c-Means (FKCM) clustering algorithm is proposed. In FKCM clustering algorithm, the data of low dimension input space is mapped to high dimension feature space, FCM clustering algorithm is performed in feature space, then the constraint optimization distance matrix and membership matrix of testing samples are computed by utilizing iterative algorithm, and the clustering result can be acquired according maximum membership principle. Subsequently, the Kernel F cluster validity index is designed for seeking the fitness cluster number and the corresponding relationship model of clusters sequence number and quality grades is constructed. Improving FKCM clustering algorithm is more efficient than other clustering algorithms, and clustering result can provide the training samples for constructing quality grades and clusters recognition function of new samples. The combination of improving FKCM and KF index provides an efficient data analysis method for multi-index dataset.

Intrusion Detection System (IDS) has been a challenging area to be developed in recent years since there are so many kinds of network attacks that are difficult to be classified by system. Moreover, there is always the possibility of the upcoming new attack. Therefore, Intrusion detection system must be improved by new classifiers to obtain the best results not only for classifying attack but also recognizing a new type of attack in an advanced way. These developments will be beneficial for managing security systems in an upcoming era. There are several classifier algorithms for Intrusion Detection System such as Support Vector Machine (SVM) and Fuzzy Kernel C-Means (FKCM). SVM classifier is known as one of the techniques to improve efficiency in attack detection while FKCM is famous because it provides better results to reduce the number of selected data features. Each of classifiers is using kernel trick to improve the classifying matter. In this study, we will compare proposed model which are FKCM with rbf, FKCM with polynomial kernel, SVM with rbf, and SVM with polynomial kernel to find a better result that could increase the accuracy of classifying network attacks. KDD Cup 1999 will be used to evaluate each model. In this study, the use of SVM with polynomial kernel brings the best result with 100 % accuracy can be obtained in 1.9 second.

According to the problem of small samples and nonlinear feature in fault diagnosis of marine diesel engine, comprehensively using the methods of grey relational analysis and kernel fuzzy c-means clustering, a method solving fault diagnosis of marine diesel engine is proposed. Firstly, kernel fuzzy c-means clustering was made on historical fault dataset. Secondly, the preliminary fault diagnosis was made on testing samples by using grey relational analysis and kernel fuzzy cmeans clustering separately. Finally, the final fault diagnosis results were got by the linear weighting matrix of fuzzy membership matrix and grey relational matrix. The fault diagnosis results of MAN B&W 10L90MC marine diesel engine show that this method can improve the accuracy of marine diesel engine.

Data clustering is an important step in data mining and machine learning. It is especially crucial to analyze the data structures for further procedures. Recently a new clustering algorithm known as ‘neutrosophic c-means’ (NCM) was proposed in order to alleviate the limitations of the popular fuzzy c-means (FCM) clustering algorithm by introducing a new objective function which contains two types of rejection. The ambiguity rejection which concerned patterns lying near the cluster boundaries, and the distance rejection was dealing with patterns that are far away from the clusters. In this paper, we extend the idea of NCM for nonlinear-shaped data clustering by incorporating the kernel function into NCM. The new clustering algorithm is called Kernel Neutrosophic c-Means (KNCM), and has been evaluated through extensive experiments. Nonlinear-shaped toy datasets, real datasets and images were used in the experiments for demonstrating the efficiency of the proposed method. A comparison between Kernel FCM (KFCM) and KNCM was also accomplished in order to visualize the performance of both methods. According to the obtained results, the proposed KNCM produced better results than KFCM.

<span id="docs-internal-guid-94842888-7fff-2ae1-cd5c-026943b95b7f"><span>Cancer is one of the diseases with the highest mortality rate in the world. Cancer is a disease when abnormal cells grow out of control that can attack the body's organs side by side or spread to other organs. Lung cancer is a condition when malignant cells form in the lungs. To diagnose lung cancer can be done by taking x-ray images, CT scans, and lung tissue biopsy. In this modern era, technology is expected to help research in the field of health. Therefore, in this study feature extraction from CT images was used as data to classify lung cancer. We used CT scan image data from SPIE-AAPM Lung CT challenge 2015. Fuzzy C-Means and fuzzy kernel C-Means were used to classify the lung nodule from the patient into benign or malignant. Fuzzy C-Means is a soft clustering method that uses Euclidean distance to calculate the cluster center and membership matrix. Whereas fuzzy kernel C-Means uses kernel distance to calculate it. In addition, the support vector machine was used in another study to obtain 72% average AUC. Simulations were performed using different k-folds. The score showed fuzzy kernel C-Means had the highest accuracy of 74%, while fuzzy C-Means obtained 73% accuracy. </span></span>

This paper considers the investigation of the optimal number of clusters for datasets that are modeled as the Gaussian mixture. For that purpose, the adaptive method that is based on the modified Expectation Maximization (EM) algorithm is developed. The modification is conducted within the hidden variable of the standard EM algorithm. Assuming that data are multivariate normally distributed, where each component of the Gaussian mixture corresponds to one cluster, the modification is provided by utilizing the fact that the Mahalanobis distance of samples follows a Chi-square distribution. Besides, the quantity measure is constructed in order to determine number of clusters. The proposed method is presented in several numerical examples.