# A Frequency-Structure Approach for Link Stream Analysis

arXiv: https://arxiv.org/abs/2212.03804 · HTML: https://mlsanity.com/paper/2212.03804/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 7 Dec 2022.

## Builds on (most cited first, 13 of 13)

- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Know-Evolve: Deep Temporal Reasoning for Dynamic Knowledge Graphs](https://mlsanity.com/paper/1705.05742/) (2017)
- [Motifs in Temporal Networks](https://mlsanity.com/paper/1612.09259/) (2016)
- [Attributed Network Embedding for Learning in a Dynamic Environment](https://mlsanity.com/paper/1706.01860/) (2017)
- [dynnode2vec: Scalable Dynamic Network Embedding](https://mlsanity.com/paper/1812.02356/) (2018)
- [MIDAS: Microcluster-Based Detector of Anomalies in Edge Streams](https://mlsanity.com/paper/1911.04464/) (2019)
- [F-FADE: Frequency Factorization for Anomaly Detection in Edge Streams](https://mlsanity.com/paper/2011.04723/) (2020)
- [Stream Graphs and Link Streams for the Modeling of Interactions over Time](https://mlsanity.com/paper/1710.04073/) (2017)
- [Quantitative Evaluation of Snapshot Graphs for the Analysis of Temporal Networks](https://mlsanity.com/paper/2110.13466/) (2021)
- [Scaling in Internet Traffic: a 14 year and 3 day longitudinal study, with multiscale analyses and random projections](https://mlsanity.com/paper/1703.02005/) (2017)
- [Weighted, Bipartite, or Directed Stream Graphs for the Modeling of Temporal Networks](https://mlsanity.com/paper/1906.04840/) (2019)

## Abstract (arXiv)

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.