Title: Time Series Prediction for Graphs in Kernel and Dissimilarity Spaces,
Abstract: Graph models are relevant in many fields, such as distributed computing,
intelligent tutoring systems or social network analysis. In many cases, such
models need to take changes in the graph structure into account, i.e. a varying
number of nodes or edges. Predicting such changes within graphs can be expected
to yield important insight with respect to the underlying dynamics, e.g. with
respect to user behaviour. However, predictive techniques in the past have
almost exclusively focused on single edges or nodes. In this contribution, we
attempt to predict the future state of a graph as a whole. We propose to phrase
time series prediction as a regression problem and apply dissimilarity- or
kernel-based regression techniques, such as 1-nearest neighbor, kernel
regression and Gaussian process regression, which can be applied to graphs via
graph kernels. The output of the regression is a point embedded in a
pseudo-Euclidean space, which can be analyzed using subsequent dissimilarity-
or kernel-based processing methods. We discuss strategies to speed up Gaussian
Processes regression from cubic to linear time and evaluate our approach on two
well-established theoretical models of graph evolution as well as two real data
sets from the domain of intelligent tutoring systems. We find that simple
regression methods, such as kernel regression, are sufficient to capture the
dynamics in the theoretical models, but that Gaussian process regression
significantly improves the prediction error for real-world data.