Outlier detection with Possibilistic Exponential Fuzzy Clustering

Generally, impact of noise and outliers cause cluster analysis to produce low accuracy. Especially in fuzzy clustering where one data is assigned to all clusters. The centroids are influenced by shifting to another position to include those abnormal points. Therefore, traditional fuzzy clustering like Fuzzy C-Means (FCM) produces the different of membership between data and outliers in polynomial which is not enough to differentiate noise and outliers from normal data. By reformulating objective function in Exponential equation, the algorithm does widen the different gap in exponential. However noise and outliers do not removed by clustering process therefore they are forced to belong in one cluster because of general probabilistic constraint that sum of membership degree of a data across all clusters to 1. By integrating the Possibilistic approach, it allows algorithm to detect outliers. In this paper, we propose Possibilistic Exponential Fuzzy Clustering (PXFCM) that is not only minimizing but cease impact of outliers during the clustering process. Additionally, they are detected and removed for further outlier mining. The comprehensive experiments show that PXFCM produces accurate result for outlier detection while clustering quality is retained.