Clustering data over time using kernel spectral clustering with memory

This paper discusses the problem of clustering data changing over time, a research domain that is attracting increasing attention due to the increased availability of streaming data in the Web 2.0 era. In the analysis conducted throughout the paper we make use of the kernel spectral clustering with memory (MKSC) algorithm, which is developed in a constrained optimization setting. Since the objective function of the MKSC model is designed to explicitly incorporate temporal smoothness, the algorithm belongs to the family of evolutionary clustering methods. Experiments over a number of real and synthetic datasets provide very interesting insights in the dynamics of the clusters evolution. Specifically, MKSC is able to handle objects leaving and entering over time, and recognize events like continuing, shrinking, growing, splitting, merging, dissolving and forming of clusters. Moreover, we discover how one of the regularization constants of the MKSC model, referred as the smoothness parameter, can be used as a change indicator measure. Finally, some possible visualizations of the cluster dynamics are proposed.