An Analysis of Fuzzy Clustering Methods

Data Mining is the process of obtaining or exploring data from the large amount of raw data. It produces the meaningful information. To obtain the information data mining has multiple techniques such as classification, regression, prediction, clustering, and summarization. There are multiple tasks in data mining to obtain the information such as cleaning, integrating, selection, transformation, pattern evaluation. One of the challenging techniques in the data mining is clustering. Clustering is the process of grouping the data under some condition. The main aim of the paper is to describe about the Fuzzy C-Means Clustering (FCM) and compared with K-Means clustering. The pitfalls overcome by the FCM are also measured theoretically.

Pattern Recognition, 1999

Fuzzy cluster-validity criterion tends to evaluate the quality of fuzzy c-partitions produced by fuzzy clustering algorithms. Many functions have been proposed. Some methods use only the properties of fuzzy membership degrees to evaluate partitions. Others techniques combine the properties of membership degrees and the structure of data. In this paper a new heuristic method is based on the combination of two functions. The search of good clustering is measured by a fuzzy compactness}separation ratio. The "rst function calculates this ratio by considering geometrical properties and membership degrees of data. The second function evaluates it by using only the properties of membership degrees. Four numerical examples are used to illustrate its use as a validity functional. Its e!ectiveness is compared to some existing cluster-validity criterion.

Soft Computing, 2015

Fuzzy clustering especially fuzzy C-means (FCM) is considered as a useful tool in the processes of pattern recognition and knowledge discovery from a database; thus being applied to various crucial, socioeconomic applications. Nevertheless, the clustering quality of FCM is not high since this algorithm is deployed on the basis of the traditional fuzzy sets, which have some limitations in the membership representation, the determination of hesitancy and the vagueness of prototype parameters. Various improvement versions of FCM on some extensions of the traditional fuzzy sets have been proposed to tackle with those limitations. In this paper, we consider another improvement of FCM on the picture fuzzy sets, which is a generalization of the traditional fuzzy sets and the intuitionistic fuzzy sets, and present a novel picture fuzzy clustering algorithm, the so-called FC-PFS. A numerical example on the IRIS dataset is conducted to illustrate the activities of the proposed algorithm. The experimental results on various benchmark datasets of UCI Machine Learning Repository under different scenarios of parameters of the algorithm reveal that FC-PFS has better Communicated by V. Loia.

Computers & Geosciences, 1984

AbstractnThis paper transmits a FORTRAN-IV coding of the fuzzy c-means (FCM) clustering program. The FCM program is applicable to a wide variety of geostatistical data analysis problems. This program generates fuzzy partitions and prototypes for any set of numerical data. These partitions are useful for corroborating known substructures or suggesting substructure in unexplored data. The clustering criterion used to aggregate subsets is a generalized least-squares objective function. Features of this program include a choice of three norms (Euclidean, Diagonal, or Mahalonobis), an adjustable weighting factor that essentially controls sensitivity to noise, acceptance of variable numbers of clusters, and outputs that include several measures of cluster validity.

Control, Automation, Robotics and Vision …

In fuzzy neural network systems, fuzzy membership functions play a key role in making the fuzzy sets organize the input data knowledge in an appropriate and representative manner. Earlier clustering techniques exploit some uniform, convex algebraic functions, such as Gaussian, Triangular or Trapezoidal to represent the fuzzy sets. However, due to the irregularity of the input data, regular and uniform fuzzy sets may not be able to represent the exact feature information of input data. In order to address this issue, a clustering method called Modified Discrete Clustering Technique (MDCT) is proposed in this paper. MDCT represents non-uniform, and normal fuzzy sets with a set of irregular sampling points. The sampling points learn the knowledge of data feature in an irregular and flexible manner. Thus, the fuzzy membership functions generated using these sampling points can provide a better representation of the actual input data.

Fuzzy Sets and Systems, 1991

A number of hard clustering algorithms have been shown to be derivable from the maximum likelihood principle. The only corresponding fuzzy algorithm are the well known fuzzy k-means or FUZZY 1SODATA of Dunn and its generalizations by Bezdek and by Gustafson and Kessel. The authors show how to generate two other fuzzy algorithms which are the analogous of known hard algorithms: the minimization of the fuzzy determinant and of the product of fuzzy determinants. By comparison between the hard and fuzzy methods it appears that the latter yield more often the global optimum, rather than merely a local optimum. This result and the comparison between the different algorithms, together with their specific domains of application, are illustrated by a few numerical examples.

International Journal of Circuits, Systems and Signal Processing, 2021

The Fuzzy C-means (FCM) algorithm has been widely used in the field of clustering and classification but has encountered difficulties with noisy data and outliers. Other versions of algorithms related to possibilistic theory have given good results, such as Fuzzy C- Means(FCM), possibilistic C-means (PCM), Fuzzy possibilistic C-means (FPCM) and possibilistic fuzzy C- Means algorithm (PFCM).This last algorithm works effectively in some environments but encountered more shortcomings with noisy databases. To solve this problem, we propose in this manuscript, a new algorithm named Improved Possibilistic Fuzzy C-Means (ImPFCM) by combining the PFCM algorithm with a very powerful statistical method. The properties of this new ImPFCM algorithm show that it is not only applicable on clusters of spherical shapes, but also on clusters of different sizes and densities. The results of the comparative study with very recent algorithms indicate the performance and the superiority of the proposed ...

Clustering technique challenges to find classes of patterns using some measure of similarity. Fuzzy clustering belongs to a group of soft computing techniques which includes Artificial Neural Networks (ANN) and Fuzzy Systems (FS). The Fuzzy K-means algorithm is one of the simplest unsupervised algorithms that solve a clustering problem. This procedure classifies a given data set through a certain number of cluster priorities. Neural network model attempts to emulate architecture and information representation scheme of the human brain. A class of NN, Self Organizing Feature Map (SOFM) is a clustering algorithm developed by Kohonen. Both Fuzzy Systems and Artificial Neural Networks have advantages when unclear or prior knowledge is required. A comparative study is proposed on clustering algorithm with FS and ANN. The various drawbacks with their performance are analyzed and therefore a combination of FS and ANN has been proposed. Thus this paper brings out the concept referred as Hybrid network or Fuzzy Artificial Neural Networks (FANN) which offers few new features to overcome the individual weakness of both the approaches.

International journal of performability engineering, 2006

Performance testing of an algorithm is necessary to ascertain its applicability in real data and to evolve software. Clustering of a data set could be either fuzzy (having vague boundaries among the clusters) or crisp (having welldefined fixed boundaries) in nature. The present work is focused on the performance measure of some similarity-based fuzzy clustering algorithms, where three methods and each method having three different approaches are developed. In the first method, cluster centers are decided based on the minimum of entropy (probability) values of different data points [10]. In the second method, cluster centers are selected based on the maximum of total similarity values of data points and in the third method, a ratio of dissimilarity to similarity is considered to determine the cluster centers. Performances of these methods and approaches are compared on three standard data sets, such as IRIS, WINES, and OLITOS. Experimental results show that entropy-based method is able to generate better quality clusters but at the cost of little more computations. Finally, the best sets of clusters are mapped to 2-D using a self-organizing map (SOM) for visualization.

Fuzzy Systems, IEEE …, 2005

In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification.