Beyond FCM: Graph-theoretic post-processing algorithms for learning and representing the data structure

We show that when fuzzy C-means (FCM) algorithm is used in an over-partitioning mode, the resulting membership values can be further utilized for building a connectivity graph   that represents the relative distribution of the computed centroids. Standard graph-theoretic procedures and recent algorithms from manifold learning theory are subsequently applied to this graph. This facilitates the accomplishment of a great variety of data-analysis tasks. The definition of optimal cluster number CoCo, the detection of intrinsic geometrical constraints within the data, and the faithful low-dimensional representation of the original structure are all performed efficiently, by working with just a down-sampled version (comprised of the centroids) of the data. Our approach is extensively demonstrated using synthetic data and actual brain signals.