Fuzzy Clustering Via Proportional Membership Model

Development of models with explicit mechanisms for data generation from cluster structures is of major interest in order to provide a theoretical framework for cluster structures found in data. Especially appealing in this regard are the so-called typological structures in which observed entities relate in various degrees to one or several prototypes. Such structures are relevant in many areas such as medicine or marketing, where any entity (patient/consumer) may adhere, with different degrees, to one or several prototypes (clinical scenario/consumer behavior), modelling a typological classification. In fuzzy clustering, the fuzzy c-means (FCM) method has become one of the most popular techniques. As a fuzzy analogue of c-means crisp clustering, FCM models a typological classification, much the same way as c-means. However, FCM does not adhere to the statistical paradigm at which the data are considered generated by a cluster structure, while crisp c-means does. The present work proposes a framework for typological classification based on a fuzzy clustering model of data generation.