A new validity function of FCM clustering algorithm based on intra-class compactness and inter-class separation

2021 ◽  
pp. 1-22
Author(s):  
H.Y. Wang ◽  
J.S. Wang ◽  
L.F. Zhu
Keyword(s):  
Clustering Algorithm ◽  
Optimal Number ◽  
Data Sets ◽  
Data Set ◽  
Class Separation ◽  
Data Similarity ◽  
Fcm Clustering ◽  
Membership Matrix ◽  
Clustering Validity ◽  
Optimal Number Of Clusters

Fuzzy C-means (FCM) clustering algorithm is a widely used method in data mining. However, there is a big limitation that the predefined number of clustering must be given. So it is very important to find an optimal number of clusters. Therefore, a new validity function of FCM clustering algorithm is proposed to verify the validity of the clustering results. This function is defined based on the intra-class compactness and inter-class separation from the fuzzy membership matrix, the data similarity between classes and the geometric structure of the data set, whose minimum value represents the optimal clustering partition result. The proposed clustering validity function and seven traditional clustering validity functions are experimentally verified on four artificial data sets and six UCI data sets. The simulation results show that the proposed validity function can obtain the optimal clustering number of the data set more accurately, and can still find the more accurate clustering number under the condition of changing the fuzzy weighted index, which has strong adaptability and robustness.

Improved Fuzzy C-Means Based on the Optimal Number of Clusters

2013 ◽  
Vol 392 ◽  
pp. 803-807 ◽  
Author(s):  
Xue Bo Feng ◽  
Fang Yao ◽  
Zhi Gang Li ◽  
Xiao Jing Yang
Keyword(s):  
Convergence Rate ◽  
Clustering Algorithm ◽  
Optimal Number ◽  
Data Set ◽  
Number Of Clusters ◽  
Fuzzy C Means ◽  
Initial Cluster ◽  
Fuzzy C Means Clustering ◽  
Fcm Clustering ◽  
Optimal Number Of Clusters

According to the number of cluster centers, initial cluster centers, fuzzy factor, iterations and threshold, Fuzzy C-means clustering algorithm (FCM) clusters the data set. FCM will encounter the initialization problem of clustering prototype. Firstly, the article combines the maximum and minimum distance algorithm and K-means algorithm to determine the number of clusters and the initial cluster centers. Secondly, the article determines the optimal number of clusters with Silhouette indicators. Finally, the article improves the convergence rate of FCM by revising membership constantly. The improved FCM has good clustering effect, enhances the optimized capability, and improves the efficiency and effectiveness of the clustering. It has better tightness in the class, scatter among classes and cluster stability and faster convergence rate than the traditional FCM clustering method.

A classification approach based on variable precision rough sets and cluster validity index function

2014 ◽  
Vol 31 (8) ◽  
pp. 1778-1789
Author(s):  
Hongkang Lin
Keyword(s):  
Optimal Number ◽  
Data Sets ◽  
Cluster Validity ◽  
Cluster Validity Index ◽  
Index Method ◽  
Data Set ◽  
Content Type ◽  
The Individual ◽  
Variable Precision Rough Sets ◽  
Optimal Number Of Clusters

Purpose – The clustering/classification method proposed in this study, designated as the PFV-index method, provides the means to solve the following problems for a data set characterized by imprecision and uncertainty: first, discretizing the continuous values of all the individual attributes within a data set; second, evaluating the optimality of the discretization results; third, determining the optimal number of clusters per attribute; and fourth, improving the classification accuracy (CA) of data sets characterized by uncertainty. The paper aims to discuss these issues. Design/methodology/approach – The proposed method for the solution of the clustering/classifying problem, designated as PFV-index method, combines a particle swarm optimization algorithm, fuzzy C-means method, variable precision rough sets theory, and a new cluster validity index function. Findings – This method could cluster the values of the individual attributes within the data set and achieves both the optimal number of clusters and the optimal CA. Originality/value – The validity of the proposed approach is investigated by comparing the classification results obtained for UCI data sets with those obtained by supervised classification BPNN, decision-tree methods.

A MULTI-CLUSTERING FUSION SCHEME FOR DATA PARTITIONING

2005 ◽  
Vol 15 (05) ◽  
pp. 391-401 ◽  
Author(s):  
DIMITRIOS S. FROSSYNIOTIS ◽  
CHRISTOS PATERITSAS ◽  
ANDREAS STAFYLOPATIS
Keyword(s):  
Clustering Algorithm ◽  
Optimal Number ◽  
Data Partitioning ◽  
Clustering Methods ◽  
Data Set ◽  
Fusion Procedure ◽  
Distinct Partition ◽  
Fusion Scheme ◽  
Previous Phase ◽  
Optimal Number Of Clusters

A multi-clustering fusion method is presented based on combining several runs of a clustering algorithm resulting in a common partition. More specifically, the results of several independent runs of the same clustering algorithm are appropriately combined to obtain a distinct partition of the data which is not affected by initialization and overcomes the instabilities of clustering methods. Subsequently, a fusion procedure is applied to the clusters generated during the previous phase to determine the optimal number of clusters in the data set according to some predefined criteria.

A new cluster validity index using maximum cluster spread based compactness measure

2016 ◽  
Vol 9 (2) ◽  
pp. 179-204 ◽  
Author(s):  
M. Arif Wani ◽  
Romana Riyaz
Keyword(s):  
Optimal Number ◽  
Data Sets ◽  
Cluster Validity ◽  
Cluster Validity Index ◽  
Validity Index ◽  
Data Set ◽  
Number Of Clusters ◽  
Content Type ◽  
Validity Indices ◽  
Optimal Number Of Clusters

Purpose – The most commonly used approaches for cluster validation are based on indices but the majority of the existing cluster validity indices do not work well on data sets of different complexities. The purpose of this paper is to propose a new cluster validity index (ARSD index) that works well on all types of data sets. Design/methodology/approach – The authors introduce a new compactness measure that depicts the typical behaviour of a cluster where more points are located around the centre and lesser points towards the outer edge of the cluster. A novel penalty function is proposed for determining the distinctness measure of clusters. Random linear search-algorithm is employed to evaluate and compare the performance of the five commonly known validity indices and the proposed validity index. The values of the six indices are computed for all nc ranging from (nc min, nc max) to obtain the optimal number of clusters present in a data set. The data sets used in the experiments include shaped, Gaussian-like and real data sets. Findings – Through extensive experimental study, it is observed that the proposed validity index is found to be more consistent and reliable in indicating the correct number of clusters compared to other validity indices. This is experimentally demonstrated on 11 data sets where the proposed index has achieved better results. Originality/value – The originality of the research paper includes proposing a novel cluster validity index which is used to determine the optimal number of clusters present in data sets of different complexities.

Different Approaches for Missing Data Handling in Fuzzy Clustering: A Review

2020 ◽  
Vol 13 (6) ◽  
pp. 833-846
Author(s):  
Sonia Goel ◽  
Meena Tushir
Keyword(s):  
Missing Data ◽  
Fuzzy Clustering ◽  
Incomplete Data ◽  
Clustering Algorithm ◽  
Linear Interpolation ◽  
Performance Criteria ◽  
Data Sets ◽  
Data Set ◽  
Fcm Clustering ◽  
Missing Attributes

Introduction: Incomplete data sets containing some missing attributes is a prevailing problem in many research areas. The reasons for the lack of missing attributes may be several; human error in tabulating/recording the data, machine failure, errors in data acquisition or refusal of a patient/customer to answer few questions in a questionnaire or survey. Further, clustering of such data sets becomes a challenge. Objective: In this paper, we presented a critical review of various methodologies proposed for handling missing data in clustering. The focus of this paper is the comparison of various imputation techniques based FCM clustering and the four clustering strategies proposed by Hathway and Bezdek. Methods: In this paper, we imputed the missing values in incomplete datasets by various imputation/ non-imputation techniques to complete the data set and then conventional fuzzy clustering algorithm is applied to get the clustering results. Results: Experiments on various synthetic data sets and real data sets from UCI repository are carried out. To evaluate the performance of the various imputation/ non-imputation based FCM clustering algorithm, several performance criteria and statistical tests are considered. Experimental results on various data sets show that the linear interpolation based FCM clustering performs significantly better than other imputation as well as non-imputation techniques. Conclusion: It is concluded that the clustering algorithm is data specific, no clustering technique can give good results on all data sets. It depends upon both the data type and the percentage of missing attributes in the dataset. Through this study, we have shown that the linear interpolation based FCM clustering algorithm can be used effectively for clustering of incomplete data set.

scholarly journals A SELF-ORGANIZING MAP FOR MIXED CONTINUOUS AND CATEGORICAL DATA

2011 ◽  
pp. 24-32 ◽  
Author(s):  
Nicoleta Rogovschi ◽  
Mustapha Lebbah ◽  
Younès Bennani
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Mixed Data ◽  
Categorical Variables ◽  
Data Sets ◽  
Self Organizing Map ◽  
Data Set ◽  
Public Data ◽  
Self Organizing

Most traditional clustering algorithms are limited to handle data sets that contain either continuous or categorical variables. However data sets with mixed types of variables are commonly used in data mining field. In this paper we introduce a weighted self-organizing map for clustering, analysis and visualization mixed data (continuous/binary). The learning of weights and prototypes is done in a simultaneous manner assuring an optimized data clustering. More variables has a high weight, more the clustering algorithm will take into account the informations transmitted by these variables. The learning of these topological maps is combined with a weighting process of different variables by computing weights which influence the quality of clustering. We illustrate the power of this method with data sets taken from a public data set repository: a handwritten digit data set, Zoo data set and other three mixed data sets. The results show a good quality of the topological ordering and homogenous clustering.

scholarly journals Improved Bidirectional CABOSFV Based on Multi-Adjustment Clustering and Simulated Annealing

2016 ◽  
Vol 16 (6) ◽  
pp. 27-42 ◽  
Author(s):  
Minghan Yang ◽  
Xuedong Gao ◽  
Ling Li
Keyword(s):  
Simulated Annealing ◽  
Data Clustering ◽  
Time Complexity ◽  
Clustering Algorithm ◽  
Feature Vector ◽  
Parameter Determination ◽  
Data Sets ◽  
Parameter Vector ◽  
Clustering Validity

Abstract Although Clustering Algorithm Based on Sparse Feature Vector (CABOSFV) and its related algorithms are efficient for high dimensional sparse data clustering, there exist several imperfections. Such imperfections as subjective parameter designation and order sensibility of clustering process would eventually aggravate the time complexity and quality of the algorithm. This paper proposes a parameter adjustment method of Bidirectional CABOSFV for optimization purpose. By optimizing Parameter Vector (PV) and Parameter Selection Vector (PSV) with the objective function of clustering validity, an improved Bidirectional CABOSFV algorithm using simulated annealing is proposed, which circumvents the requirement of initial parameter determination. The experiments on UCI data sets show that the proposed algorithm, which can perform multi-adjustment clustering, has a higher accurateness than single adjustment clustering, along with a decreased time complexity through iterations.

The Application of Probabilistic Neural Network in Speech Recognition Based on Partition Clustering

2012 ◽  
Vol 263-266 ◽  
pp. 2173-2178
Author(s):  
Xin Guang Li ◽  
Min Feng Yao ◽  
Li Rui Jian ◽  
Zhen Jiang Li
Keyword(s):  
Neural Network ◽  
Speech Recognition ◽  
Clustering Algorithm ◽  
Probabilistic Neural Network ◽  
Back Propagation ◽  
Back Propagation Neural Network ◽  
Data Sets ◽  
Data Set ◽  
Proposed Model ◽  
Partition Clustering

A probabilistic neural network (PNN) speech recognition model based on the partition clustering algorithm is proposed in this paper. The most important advantage of PNN is that training is easy and instantaneous. Therefore, PNN is capable of dealing with real time speech recognition. Besides, in order to increase the performance of PNN, the selection of data set is one of the most important issues. In this paper, using the partition clustering algorithm to select data is proposed. The proposed model is tested on two data sets from the field of spoken Arabic numbers, with promising results. The performance of the proposed model is compared to single back propagation neural network and integrated back propagation neural network. The final comparison result shows that the proposed model performs better than the other two neural networks, and has an accuracy rate of 92.41%.

Sign in / Sign up

Export Citation Format

Share Document