P-FCM: a proximity—based fuzzy clustering

In this study, we introduce and study a proximity-based fuzzy clustering. As the name stipulates, in this mode of clustering, a structure “discovery” in the data is realized in an unsupervised manner and becomes augmented by a certain auxiliary supervision mechanism. The supervision mechanism introduced in this algorithm is realized via a number of proximity “hints” (constraints) that specify an extent to which some pairs of patterns are regarded similar or different. They are provided externally to the clustering algorithm and help in the navigation of the search through the set of patterns and this gives rise to a two-phase optimization process. Its first phase is the standard FCM while the second step is concerned with the gradient-driven minimization of the differences between the provided proximity values and those computed on a basis of the partition matrix computed at the first phase of the algorithm. The proximity type of auxiliary information is discussed in the context of Web mining where clusters of Web pages are built in presence of some proximity information provided by a user who assesses (assigns) these degrees on a basis of some personal preferences. Numeric studies involve experiments with several synthetic data and Web data (pages).