Power-Regularized Fuzzy Clustering for Spherical Data

2018 ◽  
Vol 22 (2) ◽  
pp. 163-171
Author(s):  
Yuchi Kanzawa ◽  
Keyword(s):  
Fuzzy Clustering ◽  
Numerical Experiments ◽  
Clustering Methods ◽  
Clustering Method ◽  
Spherical Data ◽  
Fuzzy Clustering Method ◽  
Fuzzy Clustering Methods ◽  
Artificial Datasets

In this paper, a power-regularization-based fuzzy clustering method is proposed for spherical data. Power regularization has not been previously applied to fuzzy clustering for spherical data. The proposed method is transformed to the conventional fuzzy clustering method, entropy-regularized fuzzy clustering for spherical data (eFCS), for a specified fuzzification parameter value. Numerical experiments on two artificial datasets reveal the properties of the proposed method. Furthermore, numerical experiments on four real datasets indicate that this method is more accurate than the conventional fuzzy clustering methods: standard fuzzy clustering for spherical data (sFCS) and eFCS.

Extension-Based Clustering Method: An Approach to Support Adaptable Design of the Product

2007 ◽  
Author(s):  
Yanwei Zhao ◽  
Huijun Tang ◽  
Nan Su ◽  
Wanliang Wang
Keyword(s):  
Fuzzy Clustering ◽  
Design Method ◽  
Direct Method ◽  
Threshold Value ◽  
Minimal Distance ◽  
Clustering Methods ◽  
Clustering Method ◽  
Adaptable Design ◽  
Fuzzy Clustering Method ◽  
Distance Formula

Design for product adaptability is one of the techniques used to provide customers with products that exactly meet their requirements. Clustering methods have been used extensively in the study of product adaptability design. Of the clustering methods, the fuzzy clustering method is the most widely in the design field. The three main kinds of fuzzy clustering methods are the transitive closure method, the dynamic direct method and the maximum tree method. The dynamic direct clustering method has been found to produce design solutions with the lowest cost. In this paper, a new approach for obtaining adaptable product designs using the clustering method is proposed. The method consists of three steps. Firstly, the extension distance formula is used to determine the distance between two products in a product database. The product design space and the distances between individuals are used as grouping criteria in this step. Secondly, the minimal distance between products is used to obtain the clustering index. Thirdly, the threshold value is used to divide the products in the database into groups. Customer demands and the results obtained from the adaptable function (based on the extension distance formula) are used to evaluate the fitness of the groups and their corresponding products. The product with the largest adaptable function value to demand ratio is selected product. In order to the show the advantage of using the extension-clustering method, both the extension-clustering method and the dynamic direct method are presented and compared. The comparison indicates that the extension-clustering method leads to quicker evaluations of design alternatives and results that more closely match customers’ demands. An example of the adaptable design of circular saws tools is used to demonstrate that with the extension-clustering design method a high variety of intelligent configurations can be obtained with significant rapidity.

scholarly journals Fuzzy C-Means Clustering Algorithm with Multiple Fuzzification Coefficients

Algorithms ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 158
Author(s):  
Tran Dinh Khang ◽  
Nguyen Duc Vuong ◽  
Manh-Kien Tran ◽  
Michael Fowler
Keyword(s):  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Clustering Methods ◽  
Clustering Method ◽  
Machine Learning Technique ◽  
Practical Applications ◽  
Fuzzy C Means ◽  
Fuzzy Clustering Method ◽  
Learning Technique ◽  
Fuzzy C Means Clustering

Clustering is an unsupervised machine learning technique with many practical applications that has gathered extensive research interest. Aside from deterministic or probabilistic techniques, fuzzy C-means clustering (FCM) is also a common clustering technique. Since the advent of the FCM method, many improvements have been made to increase clustering efficiency. These improvements focus on adjusting the membership representation of elements in the clusters, or on fuzzifying and defuzzifying techniques, as well as the distance function between elements. This study proposes a novel fuzzy clustering algorithm using multiple different fuzzification coefficients depending on the characteristics of each data sample. The proposed fuzzy clustering method has similar calculation steps to FCM with some modifications. The formulas are derived to ensure convergence. The main contribution of this approach is the utilization of multiple fuzzification coefficients as opposed to only one coefficient in the original FCM algorithm. The new algorithm is then evaluated with experiments on several common datasets and the results show that the proposed algorithm is more efficient compared to the original FCM as well as other clustering methods.

Fuzzy Clustering Method for Spherical Data Based on q-Divergence

2019 ◽  
Vol 23 (3) ◽  
pp. 561-570 ◽  
Author(s):  
Masayuki Higashi ◽  
◽  
Tadafumi Kondo ◽  
Yuchi Kanzawa
Keyword(s):  
Conventional Method ◽  
Fuzzy Clustering ◽  
Optimization Problem ◽  
Clustering Algorithm ◽  
Clustering Method ◽  
Kl Divergence ◽  
Spherical Data ◽  
Fuzzy Clustering Algorithm ◽  
Fuzzy Clustering Method ◽  
Vectorial Data

This study presents a fuzzy clustering algorithm for classifying spherical data based on q-divergence. First, it is shown that a conventional method for vectorial data is equivalent to the regularization of another conventional method using q-divergence. Next, based on the knowledge that q-divergence is a generalization of Kullback-Leibler (KL)-divergence and that there is a conventional fuzzy clustering method for classifying spherical data based on KL-divergence, a fuzzy clustering algorithm for spherical data is derived based on q-divergence. This algorithm uses an optimization problem built by extending KL-divergence in the conventional method to q-divergence. Finally, some numerical experiments are conducted to verify the proposed methods.

scholarly journals Classification of Countries According to their Tourism Statistics via Different Cluster Analysis Methods and the Place of Turkey in this Structure

2013 ◽  
Author(s):  
Selay Giray
Keyword(s):  
Cluster Analysis ◽  
Hong Kong ◽  
Russian Federation ◽  
Fuzzy Clustering ◽  
Clustering Methods ◽  
Clustering Method ◽  
Analysis Methods ◽  
Fuzzy Clustering Method ◽  
The World

The aim of this study is to classify the countries according to their tourism indicators via different cluster analysis methods and compare the findings. Using classical cluster analysis and fuzzy clustering together will be more appropriate to determine the World tourism structure. In this way the findings can be interpreted more detailed and comparatively. Data obtained from website of Worldbank (3 basic international tourism statistics of 159 countries for the year 2010) and findings are gained using NCSS (statistical software) 2007. According to the findings of fuzzy clustering method, Turkey belogs to a cluster which contains ABD, United Kingdom, China, Austria, France, Germany, Italy, Malaysia, Spain, Hong Kong, Russian Federation, and Ukraine. According to the findings of classical clustering method (k means), Turkey is in the same cluster with same countries except Hong Kong. Also the findings of two techniques are similar about Turkey. Such a result can be expected correspondingly grading the countries about international their tourism data in 2011. Different clustering methods findings are steady about Euroasian countries too. Except Russian Federation and Ukraine all of the other Euroasian countries are located together in same cluster depending upon two different clustering methods. In conclusion two different clustering methods provide consistent (similar) results about the classification of countries according their internatianol tourism statistics.

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

PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0242197
Author(s):  
Paolo Giordani ◽  
Serena Perna ◽  
Annamaria Bianchi ◽  
Antonio Pizzulli ◽  
Salvatore Tripodi ◽  
...  
Keyword(s):  
Fuzzy Clustering ◽  
Mobile Health ◽  
Functional Data ◽  
Ad Hoc ◽  
Health Data ◽  
Allergic Rhinoconjunctivitis ◽  
Clustering Methods ◽  
Fuzzy Clustering Method ◽  
Communication Devices ◽  
Fuzzy Clustering Methods

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

2020 ◽  
pp. 21-29
Author(s):  
A. S. Akopov ◽  
N. K. Khachatryan ◽  
L. A. Beklaryan ◽  
A. L. Beklaryan
Keyword(s):  
Control System ◽  
Fuzzy Clustering ◽  
Numerical Experiments ◽  
Heavy Traffic ◽  
Unmanned Vehicles ◽  
Software Implementation ◽  
Total Output ◽  
Clustering Methods ◽  
The Road ◽  
Fuzzy Clustering Methods

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 Unsupervised Hybrid Symbolic Fuzzy Clustering Approach for Efficient Sclera Segmentation

2021 ◽  
Vol 10 (1) ◽  
pp. 1-14
Author(s):  
B. S. Harish ◽  
M. S. Maheshan ◽  
C. K. Roopa ◽  
S. V. Aruna Kumar
Keyword(s):  
Fuzzy Clustering ◽  
Clustering Methods ◽  
Cluster Validity ◽  
Clustering Method ◽  
Cluster Validity Indices ◽  
Validity Indices ◽  
Fuzzy Clustering Methods ◽  
Clustering Approach ◽  
Representation Method ◽  
Segmentation Task

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.

scholarly journals Fuzzy Clustering Methods with Rényi Relative Entropy and Cluster Size

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1423
Author(s):  
Javier Bonilla ◽  
Daniel Vélez ◽  
Javier Montero ◽  
J. Tinguaro Rodríguez
Keyword(s):  
Relative Entropy ◽  
Fuzzy Clustering ◽  
Cluster Size ◽  
Computational Study ◽  
Gaussian Kernel ◽  
Clustering Methods ◽  
Rényi Divergence ◽  
Divergence Measures ◽  
Fuzzy Clustering Methods ◽  
Rényi Relative Entropy

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.

GT2-CFC: General Type-2 Collaborative Fuzzy Clustering method

2021 ◽  
Author(s):  
Fariba Salehi ◽  
Mohammad Reza Keyvanpour ◽  
Arash Sharifi
Keyword(s):  
Fuzzy Clustering ◽  
General Type ◽  
Clustering Method ◽  
Fuzzy Clustering Method
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