Research On Possibilistic Clustering Algorithms

Fuzzy C- Means (FCM) clustering algorithm is one of the widely applied algorithms in unsupervised model recognition field. FCM based on the least-square error clustering criterion uses probabilistic constraints that the memberships of a data point across classes sum to 1. However, memberships do not always correspond to the intuitive concept of degree of belonging or compatibility. Furthermore, FCM is sensitive to noises or outliers. To overcome these disadvantages, the Possibilistic C- Means clustering (PCM) algorithm was proposed by R. Krishnapuram and J.Keller by abandoning the constraint of FCM and constructing a novel objective function in 1993. But PCM tends to find identical clusters and is very sensitive to initializations.Now the Possibilistic C-means clustering algorithm and its modified version are referred to as PCM₁ algorithm and PCM₂ algorithm respectively. Three main questions have been researched in this thesis in order to solve the problem existed in PCM.1. In this thesis, some familiar fuzzy clustering algorithms are analyzed. The fuzzy clustering algorithms are introduced in this thesis including Hard C-Means (HCM) clustering algorithm,Fuzzy C-Means (FCM) clustering algorithm,Possibilistic C- Means (PCM₁) clustering algorithm and Possibilistic C- Means (PCM₂ ) clustering algorithm. The thesis compared four algorithms respectively by simulating experiment.2. In PCM₂ algorithm, it does not involve the weighting exponent for the possibilistic membership. Therefore, it is not necessary to select a value for this parameter. Nevertheless, when the PCM₂ algorithm cannot determine proper clusters, we cannot tune any parameter to attempt alternative clustering. To overcome PCM₂'s disadvantages, the improved Possibilistic C- Means clustering (IPCM₂ ) algorithm was proposed by Zhang and Leung based on the FCM and PCM₂ . IPCM₂ can solve the sensitivity of FCM and the identity of PCM₂ . But the objective functions of FCM,PCM₂ and IPCM₂ use the Euclidean distance. In reality, the situation does not exist. The non-Euclidean type of Possibilistic C-Means clustering (NIPCM₂ ) is introduced in the thesis. At the same time, the results of simulating experiment show that NIPCM₂ can overcome the noise sensitivity and obtain more appropriate cluster centers.3. A hybrid C-means clustering algorithm based on the kernel function was presented in this thesis. Firstly, the advantages of FCM and PCM₂ were utilized to design a new hybrid C-means clustering algorithm accordingly in this thesis. And then on account of the lack of the algorithm, this thesis would introduce Mercer kernel function into the algorithm, so the clustering was better performed. The results of simulation experiments show the feasibility and effectiveness of the hybrid C-means clustering based on the kernel function.