Fuzzy Possibility C-Mean Based on Complete Mahalanobis Distance and Separable Criterion

Abstract

Two well known fuzzy partition clustering algorithms, FCM and FPCM are based on Euclidean distance function, which can only be used to detect spherical structural clusters. GK clustering algorithm and GG clustering algorithm, were developed to detect non-spherical structural clusters, but both of them need additional prior information. In our previous studies, we developed four improved algorithms, FCM-M, FPCM-M, FCM-CM and FPCM-CM based on unsupervised Mahalanobis distance without any additional prior information. In first two algorithms, only the local covariance matrix of each cluster was considered, In last two algorithms, not only the local covariance matrix of each cluster but also the overall covariance matrix was considered, and FPCM-CM is the better one. In this paper, a more information about "separable criterion" is considered, and the further improved new algorithm, "fuzzy possibility c-mean based on complete Mahalanobis distance and separable criterion, (FPCM-CMS)" is proposed. It can get more information and higher accuracy by considering the additional separable criterion than FPCM-CM. A real data set was applied to prove that the performance of the FPCM-CMS algorithm is better than those of above six algorithms.

Improved FCM Algorithm Based on K-Means and Granular Computing

“…The varying range of the cluster number was taken as c ∈ [2,12] in the simulation tests. The validity function values for difference cluster numbers are listed in Table 4.…”

“…Its main advantage is the ability to convert the problem of clustering to the related mathematical problems. However, FCM algorithm also has some shortcomings [12][13][14], such as the definition of weighted number and cluster size, and it is easily falling into local optimum. These problems are likely to affect the classification results and reduce the efficiency of FCM algorithm.…”

Clustering and Detecting Network Intrusion Based on Fuzzy Algorithms

“…The Fuzzy C-Means algorithm (FCM) is introduced by Bezdek [12]. Fuzzy cmeans is based on Euclidean distance function [9]. It is a data clustering technique where each data point belongs to a cluster to some degree that is specified by membership grade [18].…”

“…The same data set (494020) records were used after preprocessing it in the training stage to classify it into 5 classes, Table (8) shows the results of experiment for FCM, GK and PCM. While table (9) shows the results after applying these three fuzzy clustering algorithms FCM, PCM and GK to classify data set into 5 classes. As shown in table (9) PCM was classified data set faster than other two algorithms, because PCM takes a number of iterations and time less than other algorithms, but FCM take a number of iteration greater than GK and PCM algorithms.…”