Bezdek-Type Fuzzified Co-Clustering Algorithm

2015 ◽  
Vol 19 (6) ◽  
pp. 852-860 ◽  
Author(s):  
Yuchi Kanzawa ◽  
Keyword(s):  
Fuzzy Clustering ◽  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Clustering Methods ◽  
Suitable Parameter ◽  
Fuzzy Clustering Methods ◽  
Clustering Approach ◽  
Parameter Values ◽  
Vectorial Data

In this study, two co-clustering algorithms based on Bezdek-type fuzzification of fuzzy clustering are proposed for categorical multivariate data. The two proposed algorithms are motivated by the fact that there are only two fuzzy co-clustering methods currently available – entropy regularization and quadratic regularization – whereas there are three fuzzy clustering methods for vectorial data: entropy regularization, quadratic regularization, and Bezdek-type fuzzification. The first proposed algorithm forms the basis of the second algorithm. The first algorithm is a variant of a spherical clustering method, with the kernelization of a maximizing model of Bezdek-type fuzzy clustering with multi-medoids. By interpreting the first algorithm in this way, the second algorithm, a spectral clustering approach, is obtained. Numerical examples demonstrate that the proposed algorithms can produce satisfactory results when suitable parameter values are selected.

Fuzzy Clustering Methods for Categorical Multivariate Data Based on q-Divergence

2018 ◽  
Vol 22 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Tadafumi Kondo ◽  
◽  
Yuchi Kanzawa
Keyword(s):  
Conventional Method ◽  
Fuzzy Clustering ◽  
Optimization Problems ◽  
Clustering Algorithms ◽  
Multivariate Data ◽  
Clustering Methods ◽  
Kl Divergence ◽  
Fuzzy Clustering Methods ◽  
Conventional Methods ◽  
Vectorial Data

This paper presents two fuzzy clustering algorithms for categorical multivariate data based on q-divergence. First, this study shows that a conventional method for vectorial data can be explained as regularizing another conventional method using q-divergence. Second, based on the known results that Kullback-Leibler (KL)-divergence is generalized into the q-divergence, and two conventional fuzzy clustering methods for categorical multivariate data adopt KL-divergence, two fuzzy clustering algorithms for categorical multivariate data that are based on q-divergence are derived from two optimization problems built by extending the KL-divergence in these conventional methods to the q-divergence. Through numerical experiments using real datasets, the proposed methods outperform the conventional methods in term of clustering accuracy.

scholarly journals VDPC: Variational Density Peak Clustering Algorithm

2021 ◽  
Author(s):  
Yizhang Wang ◽  
Di Wang ◽  
You Zhou ◽  
Chai Quek ◽  
Xiaofeng Zhang
Keyword(s):  
Clustering Algorithm ◽  
Cluster Formation ◽  
Clustering Algorithms ◽  
Data Distribution ◽  
Distribution Patterns ◽  
Clustering Methods ◽  
Density Peak ◽  
Global Parameter ◽  
Density Peak Clustering ◽  
Parameter Values

<div>Clustering is an important unsupervised knowledge acquisition method, which divides the unlabeled data into different groups \cite{atilgan2021efficient,d2021automatic}. Different clustering algorithms make different assumptions on the cluster formation, thus, most clustering algorithms are able to well handle at least one particular type of data distribution but may not well handle the other types of distributions. For example, K-means identifies convex clusters well \cite{bai2017fast}, and DBSCAN is able to find clusters with similar densities \cite{DBSCAN}. </div><div>Therefore, most clustering methods may not work well on data distribution patterns that are different from the assumptions being made and on a mixture of different distribution patterns. Taking DBSCAN as an example, it is sensitive to the loosely connected points between dense natural clusters as illustrated in Figure~\ref{figconnect}. The density of the connected points shown in Figure~\ref{figconnect} is different from the natural clusters on both ends, however, DBSCAN with fixed global parameter values may wrongly assign these connected points and consider all the data points in Figure~\ref{figconnect} as one big cluster.</div>

scholarly journals Comparison of Fuzzy Clustering Methods and Their Applications to Geophysics Data

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
David J. Miller ◽  
Carl A. Nelson ◽  
Molly Boeka Cannon ◽  
Kenneth P. Cannon
Keyword(s):  
Fuzzy Clustering ◽  
Real World ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Optimal Number ◽  
Optimum Number ◽  
Clustering Methods ◽  
Real World Data ◽  
Data Set ◽  
World Data

Fuzzy clustering algorithms are helpful when there exists a dataset with subgroupings of points having indistinct boundaries and overlap between the clusters. Traditional methods have been extensively studied and used on real-world data, but require users to have some knowledge of the outcome a priori in order to determine how many clusters to look for. Additionally, iterative algorithms choose the optimal number of clusters based on one of several performance measures. In this study, the authors compare the performance of three algorithms (fuzzy c-means, Gustafson-Kessel, and an iterative version of Gustafson-Kessel) when clustering a traditional data set as well as real-world geophysics data that were collected from an archaeological site in Wyoming. Areas of interest in the were identified using a crisp cutoff value as well as a fuzzyα-cut to determine which provided better elimination of noise and non-relevant points. Results indicate that theα-cut method eliminates more noise than the crisp cutoff values and that the iterative version of the fuzzy clustering algorithm is able to select an optimum number of subclusters within a point set (in both the traditional and real-world data), leading to proper indication of regions of interest for further expert analysis

scholarly journals VDPC: Variational Density Peak Clustering Algorithm

2021 ◽  
Author(s):  
Yizhang Wang ◽  
Di Wang ◽  
You Zhou ◽  
Chai Quek ◽  
Xiaofeng Zhang
Keyword(s):  
Clustering Algorithm ◽  
Cluster Formation ◽  
Clustering Algorithms ◽  
Data Distribution ◽  
Distribution Patterns ◽  
Clustering Methods ◽  
Density Peak ◽  
Global Parameter ◽  
Density Peak Clustering ◽  
Parameter Values

<div>Clustering is an important unsupervised knowledge acquisition method, which divides the unlabeled data into different groups \cite{atilgan2021efficient,d2021automatic}. Different clustering algorithms make different assumptions on the cluster formation, thus, most clustering algorithms are able to well handle at least one particular type of data distribution but may not well handle the other types of distributions. For example, K-means identifies convex clusters well \cite{bai2017fast}, and DBSCAN is able to find clusters with similar densities \cite{DBSCAN}. </div><div>Therefore, most clustering methods may not work well on data distribution patterns that are different from the assumptions being made and on a mixture of different distribution patterns. Taking DBSCAN as an example, it is sensitive to the loosely connected points between dense natural clusters as illustrated in Figure~\ref{figconnect}. The density of the connected points shown in Figure~\ref{figconnect} is different from the natural clusters on both ends, however, DBSCAN with fixed global parameter values may wrongly assign these connected points and consider all the data points in Figure~\ref{figconnect} as one big cluster.</div>

Analysis of Fuzzy Clustering for the Adoption in Data Mining

2014 ◽  
Vol 989-994 ◽  
pp. 2047-2050
Author(s):  
Ying Jie Wang
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Mathematical Method ◽  
Big Data ◽  
Fuzzy Clustering ◽  
Clustering Analysis ◽  
Data Clustering ◽  
Clustering Algorithm ◽  
Clustering Methods ◽  
Fuzzy Clustering Methods

Data mining is the general methodology for retrieving useful information from big data. Clustering analysis is a mathematical method of classification for unsupervised machine learning. It can be adopted for data classification in Data mining. This paper combines the clustering process by fuzzy way and then deduces a special clustering algorithm with fast fuzzy c-means (FFCM) method. In summary, the paper illustrates the adoption of a series of fuzzy clustering methods in Data Mining. These methods have improved the computational efficiency with learning as the convergence speed is fast. The methodology of this paper presents significantly meaningful for information retrieval of big data.

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 An Enhanced Spectral Clustering Algorithm with S-Distance

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 596
Author(s):  
Krishna Kumar Sharma ◽  
Ayan Seal ◽  
Enrique Herrera-Viedma ◽  
Ondrej Krejcar
Keyword(s):  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Spatial Clustering ◽  
Clustering Algorithms ◽  
Rank Test ◽  
Customer Churn ◽  
Signed Rank ◽  
Signed Rank Test ◽  
Spectral Clustering Algorithm ◽  
Industrial Databases

Calculating and monitoring customer churn metrics is important for companies to retain customers and earn more profit in business. In this study, a churn prediction framework is developed by modified spectral clustering (SC). However, the similarity measure plays an imperative role in clustering for predicting churn with better accuracy by analyzing industrial data. The linear Euclidean distance in the traditional SC is replaced by the non-linear S-distance (Sd). The Sd is deduced from the concept of S-divergence (SD). Several characteristics of Sd are discussed in this work. Assays are conducted to endorse the proposed clustering algorithm on four synthetics, eight UCI, two industrial databases and one telecommunications database related to customer churn. Three existing clustering algorithms—k-means, density-based spatial clustering of applications with noise and conventional SC—are also implemented on the above-mentioned 15 databases. The empirical outcomes show that the proposed clustering algorithm beats three existing clustering algorithms in terms of its Jaccard index, f-score, recall, precision and accuracy. Finally, we also test the significance of the clustering results by the Wilcoxon’s signed-rank test, Wilcoxon’s rank-sum test, and sign tests. The relative study shows that the outcomes of the proposed algorithm are interesting, especially in the case of clusters of arbitrary shape.

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.

A Hard C-Means Clustering Algorithm Incorporating Membership KL Divergence and Local Data Information for Noisy Image Segmentation

2017 ◽  
Vol 32 (04) ◽  
pp. 1850012 ◽  
Author(s):  
R. R. Gharieb ◽  
G. Gendy ◽  
H. Selim
Keyword(s):  
Image Segmentation ◽  
Membership Function ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Cluster Center ◽  
Local Data ◽  
Cluster Membership ◽  
Kl Divergence ◽  
Clustering Approach ◽  
Center Distance

In this paper, the standard hard C-means (HCM) clustering approach to image segmentation is modified by incorporating weighted membership Kullback–Leibler (KL) divergence and local data information into the HCM objective function. The membership KL divergence, used for fuzzification, measures the proximity between each cluster membership function of a pixel and the locally-smoothed value of the membership in the pixel vicinity. The fuzzification weight is a function of the pixel to cluster-centers distances. The used pixel to a cluster-center distance is composed of the original pixel data distance plus a fraction of the distance generated from the locally-smoothed pixel data. It is shown that the obtained membership function of a pixel is proportional to the locally-smoothed membership function of this pixel multiplied by an exponentially distributed function of the minus pixel distance relative to the minimum distance provided by the nearest cluster-center to the pixel. Therefore, since incorporating the locally-smoothed membership and data information in addition to the relative distance, which is more tolerant to additive noise than the absolute distance, the proposed algorithm has a threefold noise-handling process. The presented algorithm, named local data and membership KL divergence based fuzzy C-means (LDMKLFCM), is tested by synthetic and real-world noisy images and its results are compared with those of several FCM-based clustering algorithms.

Research on Spectral Clustering

2014 ◽  
Vol 687-691 ◽  
pp. 1350-1353
Author(s):  
Li Li Fu ◽  
Yong Li Liu ◽  
Li Jing Hao
Keyword(s):  
Spectral Clustering ◽  
Clustering Algorithm ◽  
Theoretical Foundation ◽  
Clustering Algorithms ◽  
Spectral Graph Theory ◽  
Graph Partition ◽  
Mining Areas ◽  
Spectral Graph ◽  
Definition Of ◽  
Spectral Clustering Algorithm

Spectral clustering algorithm is a kind of clustering algorithm based on spectral graph theory. As spectral clustering has deep theoretical foundation as well as the advantage in dealing with non-convex distribution, it has received much attention in machine learning and data mining areas. The algorithm is easy to implement, and outperforms traditional clustering algorithms such as K-means algorithm. This paper aims to give some intuitions on spectral clustering. We describe different graph partition criteria, the definition of spectral clustering, and clustering steps, etc. Finally, in order to solve the disadvantage of spectral clustering, some improvements are introduced briefly.

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