  In this thesis, we propose several modelling strategies to tackle evolving
data in different contexts. In the framework of static clustering, we start by
introducing a soft kernel spectral clustering (SKSC) algorithm, which can
better deal with overlapping clusters with respect to kernel spectral
clustering (KSC) and provides more interpretable outcomes. Afterwards, a whole
strategy based upon KSC for community detection of static networks is proposed,
where the extraction of a high quality training sub-graph, the choice of the
kernel function, the model selection and the applicability to large-scale data
are key aspects. This paves the way for the development of a novel clustering
algorithm for the analysis of evolving networks called kernel spectral
clustering with memory effect (MKSC), where the temporal smoothness between
clustering results in successive time steps is incorporated at the level of the
primal optimization problem, by properly modifying the KSC formulation. Later
on, an application of KSC to fault detection of an industrial machine is
presented. Here, a smart pre-processing of the data by means of a proper
windowing operation is necessary to catch the ongoing degradation process
affecting the machine. In this way, in a genuinely unsupervised manner, it is
possible to raise an early warning when necessary, in an online fashion.
Finally, we propose a new algorithm called incremental kernel spectral
clustering (IKSC) for online learning of non-stationary data. This ambitious
challenge is faced by taking advantage of the out-of-sample property of kernel
spectral clustering (KSC) to adapt the initial model, in order to tackle
merging, splitting or drifting of clusters across time. Real-world applications
considered in this thesis include image segmentation, time-series clustering,
community detection of static and evolving networks.
