A New Credibilistic Clustering Method with Mahalanobis Distance

fuzzy c-means (FCM)

Table of Contents


The fuzzy c-means (FCM) is the best-known clustering and use the degree of membership fuzzy to data clustering. But the membership is not always for all data correctly. That is, at scattered dataset belonging is less and noisy dataset belonging is more assigned and local optimization problem occurs. Possibility c-means (PCM) were introduced to correspond to weaknesses FCM approach. In PCM was not a self-duality property. In other words, a sample membership for all clusters is assigned more than one and basic condition FCM was violated. One of the new methods is Credibilistic clustering and based on the credibility theory proposed that is used to study the behavior of the fuzzy phenomenon. The aim is to provide a new Credibilistic clustering approach with replacing credibility measure instead of the fuzzy membership and Mahalanobis distance use in FCM objective function. Credibility measure has a self-duality property and solves a coincident clustering problem. Mahalanobis distance used instead of Euclidian distance to separate cluster centers from each other and dens samples of each cluster. The result of the proposed method is evaluated with three numeric datasets and the Iris dataset. The most important challenge will be how to choose the initial cluster centers in the noisy dataset. In the future, we can be used FCM combined with particle swarm optimization.

KEY words:

Credibility clustering, Fuzzy C-Means, Data Mining, Possibility C-Means, Credibility measure, Mahalanobis Distance

Conclusion and Further researches

The advantage of the presented method was the elimination of the problems of Coincident clusters in PCM methods and the avoiding of local optimization in fuzzy c-means FCM methods. The evaluation measures of obtained presented and concluded that the results in terms of the clusters average error`s center was minimum. Also, the cluster’s center is very close in comparison with the previous methods. Then the number of clusters obtained in the presented method is done correctly. Another measure was the average distance of clusters which shows that in the method, the clusters have the highest distance in comparison with the other methods. And finally, the repetition times of frequency are lower and reaching the answers is more quickly. On the contrary, there are still challenges and problems in Fuzzy clustering and Credibilistic clustering. When the datasets have different features, choosing the initial cluster center is one of the most important challenging. Choosing the number of clusters is another challenge in such ways. For further researches, Credebilistic clustering algorithms with the particle swarm methods and the ways of the developments can be analyzed and studied. The new objective can be proposed and the application of those in all of the other sets can be analyzed by changing the distance measuring function, the use of other evaluation distance measures

Authors’ Profiles 1

Shahin Akbarpour

Shahin Akbarpour was born in Iran in 1972. He received the B.S. degree in Computer science from the University of Isfahan, Iran, in 1996; the M.Sc. degree in Mathematics applied in O.R. from the Islamic Azad University, Iran, in 1999, and the Ph.D. degree in Intelligent Computing from the University Putra Malaysia, Malaysia, in 2011. He joined Islamic Azad University, Shabestar, Iran, in 1999. His main areas of research interest are computer vision, data mining, and web mining.

Authors’ Profiles 2

Ahad Rafati

Ahad Rafati was born in Tabriz, Azarbayjan Sharghi, Iran in 1985. He received his BSc. degree in 2010 and MSc. Degree in software engineering from Islamic Azad University of Shabestar, in 2016. He is a member of Young Researchers and Elite Club Ilkhchi Branch, Islamic Azad University, Ilkhchi, Iran. He is working on many projects in the field of data mining and he has oracle certification. In addition, he published many papers in journals and conferences that are related to data mining approaches. Generally, most like researching and working with expert teams related to data mining, mobile programming with Xamarin.

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Professor Siavosh Kaviani was born in 1961 in Tehran. He had a professorship. He holds a Ph.D. in Software Engineering from the QL University of Software Development Methodology and an honorary Ph.D. from the University of Chelsea.