Fuzzy Cluster Validation Based on Fuzzy PCA-Guided Procedure

2013 ◽  
pp. 17-28
Author(s):  
K. Honda ◽  
A. Notsu ◽  
T. Matsui ◽  
H. Ichihashi
Keyword(s):  
Fuzzy Clustering ◽  
Fuzzy Cluster ◽  
Cluster Validation ◽  
View Point ◽  
Objective Functions ◽  
Geometrical Features ◽  
Validity Measures ◽  
Robust Cluster

Cluster validation is an important issue in fuzzy clustering research and many validity measures, most of which are motivated by intuitive justification considering geometrical features, have been developed. This paper proposes a new validation approach, which evaluates the validity degree of cluster partitions from the view point of the optimality of objective functions in FCM-type clustering. This approach makes it possible to evaluate the validity degree of robust cluster partitions, in which geometrical features are not available because of their possibilistic natures.

Fuzzy Cluster Validation Based on Fuzzy PCA-Guided Procedure

2011 ◽  
Vol 1 (1) ◽  
pp. 49-60 ◽  
Author(s):  
K. Honda ◽  
A. Notsu ◽  
T. Matsui ◽  
H. Ichihashi
Keyword(s):  
Fuzzy Clustering ◽  
Fuzzy Cluster ◽  
Cluster Validation ◽  
View Point ◽  
Objective Functions ◽  
Geometrical Features ◽  
Validity Measures ◽  
Robust Cluster

Cluster validation is an important issue in fuzzy clustering research and many validity measures, most of which are motivated by intuitive justification considering geometrical features, have been developed. This paper proposes a new validation approach, which evaluates the validity degree of cluster partitions from the view point of the optimality of objective functions in FCM-type clustering. This approach makes it possible to evaluate the validity degree of robust cluster partitions, in which geometrical features are not available because of their possibilistic natures.

GIVING FUZZINESS TO SPATIAL CLUSTERS: A NEW INDEX FOR CHOOSING THE OPTIMAL NUMBER OF CLUSTERS

2013 ◽  
Vol 22 (03) ◽  
pp. 1350009 ◽  
Author(s):  
GEORGE GREKOUSIS
Keyword(s):  
Fuzzy Clustering ◽  
Spatial Clustering ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Fuzzy Cluster ◽  
Cluster Validation ◽  
Number Of Clusters ◽  
A Value ◽  
Membership Value ◽  
Optimal Number Of Clusters

Choosing the optimal number of clusters is a key issue in cluster analysis. Especially when dealing with more spatial clustering, things tend to be more complicated. Cluster validation helps to determine the appropriate number of clusters present in a dataset. Furthermore, cluster validation evaluates and assesses the results of clustering algorithms. There are numerous methods and techniques for choosing the optimal number of clusters via crisp and fuzzy clustering. In this paper, we introduce a new index for fuzzy clustering to determine the optimal number of clusters. This index is not another metric for calculating compactness or separation among partitions. Instead, the index uses several existing indices to give a degree, or fuzziness, to the optimal number of clusters. In this way, not only do the objects in a fuzzy cluster get a membership value, but the number of clusters to be partitioned is given a value as well. The new index is used in the fuzzy c-means algorithm for the geodemographic segmentation of 285 postal codes.

A Fuzzy Cluster Algorithm of Heavy Metal City Topsoil Pollution

2013 ◽  
Vol 830 ◽  
pp. 341-344
Author(s):  
Jun Jun Du ◽  
Sheng Ping Jin ◽  
Qiong Li ◽  
She Sheng Zhang
Keyword(s):  
Heavy Metals ◽  
Heavy Metal ◽  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Fuzzy Ahp ◽  
Science Research ◽  
Fuzzy Cluster ◽  
Metal Pollutants ◽  
Fuzzy Cluster Algorithm ◽  
Heavy Metal Pollutants

Consider heavy metal pollution of topsoil in the city of world today is a hot science research project. A fuzzy clustering algorithm l is constructed ed by analyzing the propagation characteristics of heavy metal pollutants. Considering topography, areas, factories, roads, , irredentist, etc. we calculate a evaluation on comprehensive pollution, and the degree of heavy metals pollution, by using fuzzy clustering and fuzzy AHP. The results show that the index of the comprehensive pollution of heavy metals on the region, and the weight of pollution of each category.

Special Issue on Recent Methodological Developments in Fuzzy Clustering and Related Topics

2018 ◽  
Vol 22 (4) ◽  
pp. 523-523
Author(s):  
Sadaaki Miyamoto
Keyword(s):  
Fuzzy Clustering ◽  
Standard Technique ◽  
Unsupervised Classification ◽  
Support Vector ◽  
Network Data ◽  
Data Types ◽  
Difference Of Convex Functions ◽  
Leibler Divergence ◽  
Validity Measures ◽  
Application Fields

Various applications of data analysis and their effects have been reported recently. With the remarkable progress in classification methods, one example being support vector machines, clustering as the main method of unsupervised classification has also been studied extensively. Consequently, fuzzy methods of clustering is becoming a standard technique. However, unsolved theoretical and methodological problems in fuzzy clustering remain and have to be studied more deeply. This issue collects five papers concerned with fuzzy clustering and related fields, and in all of them the main interest is methodology. Kondo and Kanzawa consider fuzzy clustering with a new objective function using q-divergence, which is a generalization of the well-known Kullback-Leibler divergence. Among different data types, they focus on categorical data. They also show the relations of different methods of fuzzy c-means. Thus, this study tends to further generalize methods of fuzzy clustering, trying to find the methodological boundaries of the capabilities of fuzzy clustering models. Kitajima, Endo, and Hamasuna propose a method of controlling cluster sizes so that the resulting clusters have an even size, which is different from the optimizing of cluster sizes dealt with in other studies. This technique enhances application fields of clustering in which cluster sizes are more important than cluster shapes. Hamasuna et al. study the validity measures of clusters for network data. Cluster validity measures are generally proposed for points in Euclidean spaces, but the authors consider the application of validity measures to network data. Several validity measures are modified and adapted to network data, and their effectiveness is examined using simple network examples. Ubukata et al. propose a new method of c-means related to rough sets, a method based on a different idea from well-known rough c-means by Lingras. Finally, Kusunoki, Wakou, and Tatsumi study the maximum margin model for the nearest prototype classifier that leads to the optimization of the difference of convex functions. All papers include methodologically important ideas that have to be further investigated and applied to real-world problems.

Track Routing Optimization Model Based on Fuzzy Clustering Method

2014 ◽  
Vol 670-671 ◽  
pp. 1540-1544
Author(s):  
Pin Chao Meng ◽  
Wei Shi Yin ◽  
Zhi Xia Jiang ◽  
Yan Zhong Li
Keyword(s):  
Fuzzy Clustering ◽  
Programming Model ◽  
Objective Functions ◽  
Clustering Method ◽  
Routing Scheme ◽  
Passenger Demand ◽  
Routing Optimization ◽  
Fuzzy Clustering Method ◽  
Objective Function Values ◽  
Operation Cost

In order to determine the routing scheme of a line in city track traffic, a nonlinear constrained multi-objective 0-1 programming model is established, with the intervals as variables, and the optimal matching between the spatial characteristics of passenger demand and routing, as well as the minimization of operation cost as the objective functions. The equality constraint is built based on fuzzy clustering method, the number of variables is reduced, and the weighted coefficients are computed with objective function values. Taking Chongqing Rail Transit Line 1 as an example, a selectable routing scheme is calculated.

Soft Sensor Modeling Based on Radial Basis Function Neural Network and Fuzzy C-Means

2011 ◽  
Vol 219-220 ◽  
pp. 1263-1266
Author(s):  
Xi Huai Wang ◽  
Jian Mei Xiao
Keyword(s):  
Neural Network ◽  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Soft Sensor ◽  
Fuzzy Cluster ◽  
Training Data ◽  
Temperature Estimation ◽  
Data Set ◽  
Slab Temperature ◽  
Walking Beam Reheating Furnace

A neural network soft sensor based on fuzzy clustering is presented. The training data set is separated into several clusters with different centers, the number of fuzzy cluster is decided automatically, and the clustering centers are modified using an adaptive fuzzy clustering algorithm in the online stage. The proposed approach has been applied to the slab temperature estimation in a practical walking beam reheating furnace. Simulation results show that the approach is effective.

scholarly journals Fuzzy clustering and fuzzy c-means partition cluster analysis and validation studies on a subset of citescore dataset

2019 ◽  
Vol 9 (4) ◽  
pp. 2760
Author(s):  
K. Varada Rajkumar ◽  
Adimulam Yesubabu ◽  
K. Subrahmanyam
Keyword(s):  
Cluster Analysis ◽  
Fuzzy Clustering ◽  
Time Complexity ◽  
Clustering Algorithm ◽  
Fuzzy Cluster ◽  
Fuzzy Cluster Analysis ◽  
Fuzzy C Means ◽  
A Value ◽  
Data Points ◽  
Partition Clustering

A hard partition clustering algorithm assigns equally distant points to one of the clusters, where each datum has the probability to appear in simultaneous assignment to further clusters. The fuzzy cluster analysis assigns membership coefficients of data points which are equidistant between two clusters so the information directs have a place toward in excess of one cluster in the meantime. For a subset of CiteScore dataset, fuzzy clustering (fanny) and fuzzy c-means (fcm) algorithms were implemented to study the data points that lie equally distant from each other. Before analysis, clusterability of the dataset was evaluated with Hopkins statistic which resulted in 0.4371, a value &lt; 0.5, indicating that the data is highly clusterable. The optimal clusters were determined using NbClust package, where it is evidenced that 9 various indices proposed 3 cluster solutions as best clusters. Further, appropriate value of fuzziness parameter <em>m</em> was evaluated to determine the distribution of membership values with variation in <em>m</em> from 1 to 2. Coefficient of variation (CV), also known as relative variability was evaluated to study the spread of data. The time complexity of fuzzy clustering (fanny) and fuzzy c-means algorithms were evaluated by keeping data points constant and varying number of clusters.

Sign in / Sign up

Export Citation Format

Share Document