A new possibilistic-based clustering method for probability density functions and its application to detecting abnormal elements.

Cluster analysis can also detect abnormalities besides building a basis for identifying elements into clusters. Detecting abnormalities is a highly developed feature in the field of unsupervised learning. However, existing studies have mainly focused on discrete data, not probability density functions. This paper enables a possibilistic approach to solving the clustering for probability density functions dealing with abnormal elements. First, the data are extracted using the density function. Then, they are passed through the proposed algorithm to produce a possibilistic partition. Finally, a decision rule is established to recognize which function is abnormal. We compare the proposed algorithm with baseline algorithms in clustering PDFs, such as k-means, FCF, and Self-Updated Clustering. The results of three numerical examples applied to the image are typical for this new method. Furthermore, The proposed algorithm reaches accuracy at 100% over simulated benchmark data and outperforms baseline methods. Additionally, two last examples apply to image data reaching G-mean up from 96 to 100% (Sensitivity: 92-100% and Specificity: 100%). The proposed method can be researched and used to understand the internal structures of big data in the digital age through the probability density functions.