Graph Signal Processing: Introduction and Research at SPS
Speaker: Geert Leus
Abstract: Although processing and analyzing audio, images and video is still of great importance in current society, more and more data is originating from networks with an irregular structure, e.g., social networks, brain networks, sensor networks, and communications networks to name a few. To handle such signals, graph signal processing (GSP) has recently been coined as a proper tool set. In GSP the irregular structure of the network is captured by means of a graph, and the data is viewed as a signal on top of this graph, i.e., a graph signal. GSP extends concepts and tools from classical signal processing to the field of graph signals, e.g., the Fourier transform, filtering, sampling, stationarity, etc. In this talk, we introduce the field of graph signal processing and mainly focus on the graph Fourier transform and graph filters. The latter find applications in image denoising, network data interpolation, distributed optimization and learning of graph signals. After this introduction, we will focus on some of the more specific GSP topics that are being investigated in the Signal Processing Systems (SPS) group.
Learning (Time-Varying) Graphs from (Online) Data
Speaker: Alberto Natali
Abstract: Learning network topologies from data is very appealing. On the interpretable side, the structure of a network reveals important descriptors of the network itself, providing to humans a prompt and explainable decision support system; on the operative side, it is a requirement for processing and learning architectures operating on graph data, such as graph filters. When this structure is not readily available from the application, a fundamental question is how to learn it from data. The class of problems and the associated techniques concerning the identification of a network structure (from data) are known as graph topology identification (GTI), graph learning, or network topology inference. In this talk I will provide a mathematical description of the problem with possible algorithmic solutions. Finally, I will outline recent advances to learn network topologies which vary over time.
Uncovering Temporal Networks through Tensor-like Decompositions
Speaker: Bishwadeep Das
Abstract: Temporal network evolution can be algebraically represented by tensors, which lends itself to using multi-way decompositions to study the underpinning factors driving the network evolution. Low-rank tensor decompositions have been used on such representations but mostly with a focus on downstream tasks. Moreover, they have seldom been used to study the change of structure and the underlying factors influencing it. Here, we use a two-way decomposition to identify a limited number of key mode graphs that can explain the temporal network evolution. The temporal network at a time instant is expressed as a linear combination of these graphs. For this, we put forward a novel graph-based tensor decomposition approach, where we impose a graph structure on the first factor and temporal smoothness on the second, as one instance of a more general formulation. We investigate these mode graphs and use them for tasks such as network reconstruction and link prediction.