A Frequency-Structure Approach for Link Stream Analysis
This work addresses a fundamental gap in link stream analysis for researchers and practitioners in network science and signal processing, though it appears incremental by building on existing linear methods.
The paper tackles the problem of understanding how dynamical and structural information from raw link streams carries into transformed objects like time series or graphs, by introducing a novel linear matrix framework that enables analysis in a frequency-structure domain, showing that transformations such as aggregation or embedding can be viewed as simple filters in this domain.
A link stream is a set of triplets $(t, u, v)$ indicating that $u$ and $v$ interacted at time $t$. Link streams model numerous datasets and their proper study is crucial in many applications. In practice, raw link streams are often aggregated or transformed into time series or graphs where decisions are made. Yet, it remains unclear how the dynamical and structural information of a raw link stream carries into the transformed object. This work shows that it is possible to shed light into this question by studying link streams via algebraically linear graph and signal operators, for which we introduce a novel linear matrix framework for the analysis of link streams. We show that, due to their linearity, most methods in signal processing can be easily adopted by our framework to analyze the time/frequency information of link streams. However, the availability of linear graph methods to analyze relational/structural information is limited. We address this limitation by developing (i) a new basis for graphs that allow us to decompose them into structures at different resolution levels; and (ii) filters for graphs that allow us to change their structural information in a controlled manner. By plugging-in these developments and their time-domain counterpart into our framework, we are able to (i) obtain a new basis for link streams that allow us to represent them in a frequency-structure domain; and (ii) show that many interesting transformations to link streams, like the aggregation of interactions or their embedding into a euclidean space, can be seen as simple filters in our frequency-structure domain.