Semi-supervised fuzzy clustering with metric learning and entropy regularization

Dental X-ray image segmentation has an important role in practical dentistry and is widely used in the discovery of odontological diseases, tooth archeology and in automated dental identification systems. Enhancing the accuracy of dental segmentation is the main focus of researchers, involving various machine learning methods to be applied in order to gain the best performance. However, most of the currently used methods are facing problems of threshold, curve functions, choosing suitable parameters and detecting common boundaries among clusters. In this paper, we will present a new semi-supervised fuzzy clustering algorithm named as SSFC-FS based on Interactive Fuzzy Satisficing for the dental X-ray image segmentation problem. Firstly, features of a dental X-Ray image are modeled into a spatial objective function, which are then to be integrated into a new semi-supervised fuzzy clustering model. Secondly, the Interactive Fuzzy Satisficing method, which is considered as a useful tool to solve linear and nonlinear multi-objective problems in mixed fuzzy-stochastic environment, is applied to get the cluster centers and the membership matrix of the model. Thirdly, theoretically validation of the solutions including the convergence rate, bounds of parameters, and the comparison with solutions of other relevant methods is performed. Lastly, a new semi-supervised fuzzy clustering algorithm that uses an iterative strategy from the formulae of solutions is designed. This new algorithm was experimentally validated and compared with the relevant ones in terms of clustering quality on a real dataset including 56 dental X-ray images in the period 2014–2015 of Hanoi Medial University, Vietnam. The results revealed that the new algorithm has better clustering quality than other methods such as Fuzzy C-Means, Otsu, eSFCM, SSCMOO, FMMBIS and another version of SSFC-FS with the local Lagrange method named SSFC-SC. We also suggest the most appropriate values of parameters for the new algorithm.

Dental X-ray image segmentation is a necessary and important process in medical diagnosis, which assists clinicians to make decisions about possible dental diseases of a patient from a dental X-ray image. It is a multi-objective optimization problem which involves basic components of fuzzy clustering, spatial structures of a dental image, and additional information of experts expressed through a pre-defined membership matrix. In our previous work, the authors presented a semi-supervised fuzzy clustering algorithm using interactive fuzzy satisficing named as SSFC-FS for this problem. An important issue of SSFC-FS is that the pre-defined membership matrix is a fixed function in the sense that it uses the same structure and parameters for all dental images. This is a shortcoming of SSFC-FS since each image has its own structure and morphology so that it needs different membership matrices. In this paper, the authors propose another new dynamic semi-supervised fuzzy clustering called SSFC-FSAI that extends SSFC-FS by employing a collection of pre-defined membership matrices for dental images. A procedure to choose a suitable pre-defined membership matrix for a given dental X-ray image is proposed and attached to SSFC-FSAI. Experimental results on a real dataset of 56 dental X-ray images from Hanoi University of Medical in 2014 - 2015 show that SSFC-FSAI has better accuracy than SSFC-FS and the relevant algorithms.

Semi-supervised clustering methods are applied in various fields. However, these methods have the limitations when the size of data is large. Thus, distributed clustering models are proposed. By separating data set into some parts, distributed models overcome the challenges of big size dataset. In this paper, a novel model, based on semi-supervised fuzzy clustering and distributed mechanism, is proposed. In our research, the method to define distributed additional information is introduced. This additional information is used to implement distributed semi-supervised fuzzy clustering model on three datasets. The main contribution in this paper is the proposal of distributed semi-supervised fuzzy clustering algorithm (denoted as DSSFCM) that performs on Master – Slave model on homogeneous datasets.

Extreme physical information and objective function in fuzzy clustering

Currently, breast cancer is one of the most common cancers among women. To aid clinicians in diagnosis, lesion regions in mammography pictures can be segmented using an artificial intelligence system. This has significant clinical implications. Clustering algorithms, as unsupervised models, are widely used in medical image segmentation. However, due to the different sizes and shapes of lesions in mammography images and the low contrast between lesion areas and the surrounding pixels, it is difficult to use traditional unsupervised clustering methods for image segmentation. In this study, we try to apply the semisupervised fuzzy clustering algorithm to lesion segmentation in mammography molybdenum target images and propose semisupervised fuzzy clustering based on the cluster centres of labelled samples (called SFCM_V, where V stands for cluster centre). The algorithm refers to the cluster centre of the labelled sample dataset during the clustering process and uses the information of the labelled samples to guide the unlabelled samples during clustering to improve the clustering performance. We compare the SFCM_V algorithm with the current popular semisupervised clustering algorithm and an unsupervised clustering algorithm and perform experiments on real patient mammogram images using DICE and IoU as evaluation metrics; SFCM_V has the highest evaluation metric coefficient. Experiments demonstrate that SFCM_V has higher segmentation accuracy not only for larger lesion regions, such as tumours, but also for smaller lesion regions, such as calcified spots, compared with existing clustering algorithms.

Semi-supervised clustering leverages side information such as pairwise constraints to guide clustering procedures. Despite promising progress, existing semi-supervised clustering approaches overlook the condition of side information being generated sequentially, which is a natural setting arising in numerous real-world applications such as social network and e-commerce system analysis. Given emerged new constraints, classical semi-supervised clustering algorithms need to re-optimize their objectives over all data samples and constraints in availability, which prevents them from efficiently updating the obtained data partitions. To address this challenge, we propose an efficient dynamic semi-supervised clustering framework that casts the clustering problem into a search problem over a feasible convex set, i.e., a convex hull with its extreme points being an ensemble of m data partitions. According to the principle of ensemble clustering, the optimal partition lies in the convex hull, and can thus be uniquely represented by an m-dimensional probability simplex vector. As such, the dynamic semi-supervised clustering problem is simplified to the problem of updating a probability simplex vector subject to the newly received pairwise constraints. We then develop a computationally efficient updating procedure to update the probability simplex vector in O(m2) time, irrespective of the data size n. Our empirical studies on several real-world benchmark datasets show that the proposed algorithm outperforms the state-of-the-art semi-supervised clustering algorithms with visible performance gain and significantly reduced running time.

Bias-correction fuzzy clustering algorithms

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.

During the past few years, semi-supervised clustering has emerged as a new interesting direction in machine learning research. In a semi-supervised clustering algorithm, the clustering results can be significantly improved by using side information, which is available or collected from users. There are two main kinds of side information that can be learned in semi-supervised clustering algorithms: the class labels - called seeds or the pairwise constraints. The first semi-supervised clustering was introduced in 2000, and since that, many algorithms have been presented in literature. However, it is not easy to use both types of side information in the same algorithm. To address the problem, this paper proposes a semi-supervised graph based clustering algorithm that tries to use seeds and constraints in the clustering process, called MCSSGC. Moreover, we introduces a simple but efficient active learning method to collect the constraints that can boost the performance of MCSSGC, named KMMFFQS. In order to verify effectiveness of the proposed algorithm, we conducted a series of experiments not only on real data sets from UCI, but also on a document data set applied in an Information Extraction of Vietnamese documents. These obtained results show that the proposed algorithm can significantly improve the clustering process compared to some recent algorithms.

Over the years, research on fuzzy clustering algorithms has attracted the attention of many researchers, and they have been applied to various areas, such as image segmentation and data clustering. Various fuzzy clustering algorithms have been put forward based on the initial Fuzzy C-Means clustering (FCM) with Euclidean distance. However, the existing fuzzy clustering approaches ignore two problems. Firstly, clustering algorithms based on Euclidean distance have a high error rate, and are more sensitive to noise and outliers. Secondly, the parameters of the fuzzy clustering algorithms are hard to determine. In practice, they are often determined by the user’s experience, which results in poor performance of the clustering algorithm. Therefore, considering the above deficiencies, this paper proposes a novel fuzzy clustering algorithm by combining the Gaussian kernel function and Grey Wolf Optimizer (GWO), called Kernel-based Picture Fuzzy C-Means clustering with Grey Wolf Optimizer (KPFCM-GWO). In KPFCM-GWO, the Gaussian kernel function is used as a symmetrical measure of distance between data points and cluster centers, and the GWO is utilized to determine the parameter values of PFCM. To verify the validity of KPFCM-GWO, a comparative study was conducted. The experimental results indicate that KPFCM-GWO outperforms other clustering methods, and the improvement of KPFCM-GWO is mainly attributed to the combination of the Gaussian kernel function and the parameter optimization capability of the GWO. What is more, the paper applies KPFCM-GWO to analyzes the value of an airline’s customers, and five levels of customer categories are defined.

Fuzzy clustering partitions data points of a dataset into clusters in which one data point can belong to more than one cluster. In the literature, a number of fuzzy clustering algorithms have been proposed. This paper reviews various fuzzy clustering algorithms such as Fuzzy C-Means (FCM), Possibilistic C-Means (PCM), Possibilistic Fuzzy C-Means (PFCM), Intuitionistic Fuzzy C-Means (IFCM), Kernel Fuzzy C-Means (KFCM), and Density-Oriented Fuzzy C-Means (DOFCM). We have demonstrated the experimental performance of these algorithms on some standard and synthetic datasets which include—Bensaid, Square (DUNN), D15, and D45 dataset. Then, the results are analyzed and compared to see the effectiveness of these algorithms in presence of noise and outliers.

Semi-supervised clustering is a special form of classification that uses a large amount of unlabeled data together with labeled data to achieve better classification results. This paper introduces a semi-supervised fuzzy clustering algorithm of relational data with multiple prototype representation (SS-CLAMP) that aims to furnish a partition and a set of prototypes for each fuzzy cluster as well as to learn a relevance weight for each dissimilarity matrix by optimizing an adequacy criterion that measures the fit between the fuzzy clusters and their representatives in a competitive way and that takes into account pairwise constraints must-link and cannot-link. Experiments with real-valued data sets show the usefulness of the proposed algorithm.

Possibilistic fuzzy c-means clustering (PFCM) algorithm improves the noise sensitivity of the fuzzy c-means clustering (FCM) algorithm and the serious coincident clustering phenomenon of the possibilistic c-means clustering (PCM) algorithm. However, the Euclidean distance of the PFCM treats all features equally in the clustering process and doesn't consider the imbalance between sample features, resulting in low clustering accuracy. Furthermore, as the number of clusters increases, the PFCM still has a partially coincident clustering problem due to the lack of between-class relationships of possibilistic memberships. Therefore, a feature weighted cutset-type possibilistic fuzzy c-means clustering (FW-C-PFCM) algorithm is proposed by introducing the cutset theory and feature weights into the PFCM in this paper. Firstly, the proposed FW-C-PFCM introduces a feature weighted parameter in the objective function, and different features should take different weight values according to the distribution of samples. Secondly, the cutset theory is utilized to divide the data into inner core and outer core regions, and some possibilistic memberships inside each cluster core are modified in the iterative process. Finally, the experiments on synthetic multi-class datasets and the Iris dataset show that the FW-C-PFCM improves the partially coincident clustering phenomenon and overcomes the imbalance between sample features. The comparative experiments on a color image also indicate that the FW-C-PFCM enhances the segmentation accuracy and generates better clustering results than PFCM.

Coarse resolution captured in remote sensing causes the combination of different materials in one pixel, called the mixed pixel. Spectral unmixing estimates the combination of endmembers in mixed pixels and their corresponding abundance maps in the Hyper/Multi spectral image. In this paper, a nonlinear spectral unmixing based on semi-supervised fuzzy clustering is proposed. First, pure pixels (endmembers) using Vertex Component Analysis (VCA) are extracted and those pixels are the labelled pixels where the membership value of each is 1 for the corresponding endmember and 0 for the others. Second, the semi-supervised fuzzy clustering is applied to find the membership matrix defining the fraction of the endmember in each mixed pixel and hence extract the abundance maps. The experiments were conducted on both synthetic data such as the Legendre data and real data such as Jasper Ridge data. The non-linearity of the Legendre data was performed by the Fan model on different signal-tonoise ratio values. The results of the new unmixing model show its significant performance when compared with four state-of the art unmixing algorithms

This paper presents semi-supervised agglomerative hierarchical clustering algorithm using clusterwise tolerance based pairwise constraints. In semi-supervised clustering, pairwise constraints, that is, must-link and cannot-link, are frequently used in order to improve clustering properties. From that sense, we will propose another way named clusterwise tolerance based pairwise constraints to handle must-link and cannot-link constraints inL2-space. In addition, we will propose semi-supervised agglomerative hierarchical clustering algorithm based on it. We will, moreover, show the effectiveness of the proposed method through numerical examples.