Fuzzy Clustering Methods to Identify the Epidemiological Situation and Its Changes in European Countries during COVID-19

The main research question concerned the identification of changes in the COVID-19 epidemiological situation using fuzzy clustering methods. This research used cross-sectional time series data obtained from the European Centre for Disease Prevention and Control. The identification of country types in terms of epidemiological risk was carried out using the fuzzy c-means clustering method. We also used the entropy index to measure the degree of fuzziness in the classification and evaluate the uncertainty of epidemiological states. The proposed approach allowed us to identify countries’ epidemic states. Moreover, it also made it possible to determine the time of transition from one state to another, as well as to observe fluctuations during changes of state. Three COVID-19 epidemic states were identified in Europe, i.e., stabilisation, destabilisation, and expansion. The methodology is universal and can also be useful for other countries, as well as the research results being important for governments, politicians and other policy-makers working to mitigate the effects of the COVID-19 pandemic.

Fuzzy Clustering Methods with Rényi Relative Entropy and Cluster Size

In the last two decades, information entropy measures have been relevantly applied in fuzzy clustering problems in order to regularize solutions by avoiding the formation of partitions with excessively overlapping clusters. Following this idea, relative entropy or divergence measures have been similarly applied, particularly to enable that kind of entropy-based regularization to also take into account, as well as interact with, cluster size variables. Particularly, since Rényi divergence generalizes several other divergence measures, its application in fuzzy clustering seems promising for devising more general and potentially more effective methods. However, previous works making use of either Rényi entropy or divergence in fuzzy clustering, respectively, have not considered cluster sizes (thus applying regularization in terms of entropy, not divergence) or employed divergence without a regularization purpose. Then, the main contribution of this work is the introduction of a new regularization term based on Rényi relative entropy between membership degrees and observation ratios per cluster to penalize overlapping solutions in fuzzy clustering analysis. Specifically, such Rényi divergence-based term is added to the variance-based Fuzzy C-means objective function when allowing cluster sizes. This then leads to the development of two new fuzzy clustering methods exhibiting Rényi divergence-based regularization, the second one extending the first by considering a Gaussian kernel metric instead of the Euclidean distance. Iterative expressions for these methods are derived through the explicit application of Lagrange multipliers. An interesting feature of these expressions is that the proposed methods seem to take advantage of a greater amount of information in the updating steps for membership degrees and observations ratios per cluster. Finally, an extensive computational study is presented showing the feasibility and comparatively good performance of the proposed methods.

An Unsupervised Hybrid Symbolic Fuzzy Clustering Approach for Efficient Sclera Segmentation

This article performs the sclera segmentation task by proposing a new hybrid symbolic fuzzy c-means (HSFCM) clustering method. Practically, though the data point exhibits some sort of similarity, unfortunately they are not undistinguishable and exhibit some sort of dissimilarity. Thus, to capture these disparities, the proposed work uses symbolic interval valued representation method. Further, to handle uncertainty and imprecision, the paper has proposed to use symbolic fuzzy clustering methods. To assess the performance of the proposed method, extensive experimentation is conducted on SSRBC2016 dataset. The proposed clustering method is compared with existing FCM, KFCM, RSKFCM method in terms of cluster validity indices and accuracy. The obtained outcomes demonstrated that the proposed method performed better compared to the contemporary methods.

A study of longitudinal mobile health data through fuzzy clustering methods for functional data: The case of allergic rhinoconjunctivitis in childhood

The use of mobile communication devices in health care is spreading worldwide. A huge amount of health data collected by these devices (mobile health data) is nowadays available. Mobile health data may allow for real-time monitoring of patients and delivering ad-hoc treatment recommendations. This paper aims at showing how this may be done by exploiting the potentialities of fuzzy clustering techniques. In fact, such techniques can be fruitfully applied to mobile health data in order to identify clusters of patients for diagnostic classification and cluster-specific therapies. However, since mobile health data are full of noise, fuzzy clustering methods cannot be directly applied to mobile health data. Such data must be denoised prior to analyzing them. When longitudinal mobile health data are available, functional data analysis represents a powerful tool for filtering out the noise in the data. Fuzzy clustering methods for functional data can then be used to determine groups of patients. In this work we develop a fuzzy clustering method, based on the concept of medoid, for functional data and we apply it to longitudinal mHealth data on daily symptoms and consumptions of anti-symptomatic drugs collected by two sets of patients in Berlin (Germany) and Ascoli Piceno (Italy) suffering from allergic rhinoconjunctivitis. The studies showed that clusters of patients with similar changes in symptoms were identified opening the possibility of precision medicine.

UNMANNED VEHICLE CONTROL SYSTEM BASED ON FUZZY CLUSTERING. PART 2. FUZZY CLUSTERING AND SOFTWARE IMPLEMENTATION

This article continues the description of the control system for ground unmanned vehicles as part of the integration of a phenomenological approach to modeling the behavior of agents and methods of fuzzy clustering in order to improve the quality of decisions. As a result, adaptive fuzzy clustering methods provide support for adaptive ground unmanned vehicles control, which minimizes the risks of accidents (emergencies involving ground unmanned vehicles) and maximizes traffic (total output stream) in conditions of heavy traffic. The second part is devoted to the description of the developed fuzzy clustering algorithm, software implementation and experiments. As a result, within the framework of the developed model of ground unmanned vehicles movement, fuzzy clustering methods are used to ensure the procedure for choosing the most preferable (least dense) lane in conditions of heavy traffic and to support continuous information exchange between ground unmanned vehicles. The software implementation of the developed simulation model in the AnyLogic environment was performed and numerical experiments aimed at analyzing scenarios of the development of the road situation with the participation of the ground unmanned vehicles ensemble were carried out. Various behavioral scenarios of the developed ground unmanned vehicles control system were investigated, and agent clustering was performed for each scenario under consideration. As a result of numerical experiments, the effectiveness of using the proposed fuzzy clustering procedure to assess the density of the road flow and adaptive control and maneuvering of the ground unmanned vehicles is confirmed.

An Efficient Segmentation and Classification System in Medical Images Using Intuitionist Possibilistic Fuzzy C-Mean Clustering and Fuzzy SVM Algorithm

The herpesvirus, polyomavirus, papillomavirus, and retrovirus families are associated with breast cancer. More effort is needed to assess the role of these viruses in the detection and diagnosis of breast cancer cases in women. The aim of this paper is to propose an efficient segmentation and classification system in the Mammography Image Analysis Society (MIAS) images of medical images. Segmentation became challenging for medical images because they are not illuminated in the correct way. The role of segmentation is essential in concern with detecting syndromes in human. This research work is on the segmentation of medical images based on intuitionistic possibilistic fuzzy c-mean (IPFCM) clustering. Intuitionist fuzzy c-mean (IFCM) and possibilistic fuzzy c-mean (PFCM) algorithms are hybridised to deal with problems of fuzzy c-mean. The introduced clustering methodology, in this article, retains the positive points of PFCM which helps to overcome the problem of the coincident clusters, thus the noise and less sensitivity to the outlier. The IPFCM improves the fundamentals of fuzzy c-mean by using intuitionist fuzzy sets. For the clustering of mammogram images for breast cancer detector of abnormal images, IPFCM technique has been applied. The proposed method has been compared with other available fuzzy clustering methods to prove the efficacy of the proposed approach. We compared support vector machine (SVM), decision tree (DT), rough set data analysis (RSDA) and Fuzzy-SVM classification algorithms for achieving an optimal classification result. The outcomes of the studies show that the proposed approach is highly effective with clustering and also with classification of breast cancer. The performance average segmentation accuracy for MIAS images with different noise level 5%, 7% and 9% of IPFCM is 91.25%, 87.50% and 85.30% accordingly. The average classification accuracy rates of the methods (Otsu, Fuzzy c-mean, IFCM, PFCM and IPFCM) for Fuzzy-SVM are 79.69%, 92.19%, 93.13%, 95.00%, and 98.85%, respectively.