Abstract
Many fields, like physics, neuroscience, chemistry, and sociology, investigate phenomena by processing multivariate measurementsadvantageously represented as a sequence of attributed graphs. Graphs come in different forms, with variable attributes, topology, and ordering, making it difficult to perform a mathematical analysis in the graph space. Within this framework, we are interested in processing graph datastreams to solve applications e.g., detect structural changes in the graphsequence, a situation associated with time variance, faults, anomalies or events of interestas well as design sophisticated processing like those requested by predictors. On the change detection front, theoretic results show that, under mild hypotheses, the confidence level of an event detected in the graph domain can be associated with another confidence level inan embedding space; this enables the identification of events in the graph domain by investigating embedded data. The opposite holds. However, evaluation of distances between graphs and identification of an appropriate embedding for the problem at hand are far from being trivial tasks with deep adversarial learning approaches and constant curvature manifold transformation showing to be appropriate transformations able to solve the problem. Deep autoregressive predictive models can then be designed to operate directly on graphs, hence providing the building blocks for other future sophisticated neural processing.
