A Robust Process to Identify Pivots Inside Sub-communities in Social Networks

In this work, we extend a previous work where we proposed a suitable state model built from a Karhunen-Loeve Transformation to build a new decision process from which, we can extract useful knowledge and information about the identified underlying sub-communities from an initial network. The aim of the method is to build a framework for a multi-level knowledge retrieval. Besides the capacity of the methodology to reduce the high dimensionality of the data, the new detection scheme is able to extract, from the sub-communities, the dense sub-groups with the definition and formulation of new quantities related to the notions of energy and co-energy. The energy of a node is defined as the rate of its participation to the set of activities while the notion of co-energy defines the rate of interaction/link between two nodes. These two important features are used to make each link weighted and bounded, so that we are able to perform a thorough refinement of the sub-community discovery. This study allows to perform a multi-level analysis by extracting information either per-link or per-intra-sub-community. As an improvement of this work, we define the notion of pivot to relate the node(s) with the greatest influence in the network. We propose the use of a thorough tool based on the formulation of the transformation of a suitable probabilistic model into a possibilistic model to extract these pivot(s) which are the nodes that control the evolution of the community.