Discovering cluster dynamics using kernel spectral methods

Abstract

Networks represent patterns of interactions between components of complex systems present in nature, science, technology and society. Furthermore, graph theory allows to perform insightful analysis for different kinds of data by representing the instances as nodes of a weighted network, where the weights characterize similarity between the data points. In this chapter we describe a number of algorithms to perform cluster analysis, that is finding groups of similar items (called clusters or communities) and understand their evolution over time. These algorithms are designed in a kernel-based framework: the original data are mapped into an high dimensional feature space; linear models are designed in this space; complex nonlinear relationships between the data in the original input space can then be detected. Applications like fault detection in industrial machines, community detection of static and evolving networks, image segmentation, incremental time-series clustering and text clustering are considered.