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Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
We develop a systematic approach for resolving the analytic wave front set for a class of integral geometry transforms appearing in various tomography problems. Combined with microlocal analytic continuation, this leads to uniqueness and…
Graph sampling addresses the problem of selecting a node subset in a graph to collect samples, so that a K-bandlimited signal can be reconstructed in high fidelity. Assuming an independent and identically distributed (i.i.d.) noise model,…
Some microfluidic lab-on-chip devices contain modules whose function is to mix two fluids, called reactant and buffer, in desired proportions. In one of the technologies for fluid mixing the process can be represented by a directed acyclic…
Construction of multivariate tight framelets is known to be a challenging problem. Multivariate dual framelets with vanishing moments generalize tight framelets and are not easy to be constructed either. Compactly supported multivariate…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…
Recent studies have indicated that Graph Convolutional Networks (GCNs) act as a \emph{low pass} filter in spectral domain and encode smoothed node representations. In this paper, we consider their opposite, namely Graph Deconvolutional…
Wireless sensor networks (WSNs) are considered as a major technology enabling the Internet of Things (IoT) paradigm. The recent emerging Graph Signal Processing field can also contribute to enabling the IoT by providing key tools, such as…
We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the…
Graph Neural Networks (GNNs) have emerged as powerful tools for analyzing and learning representations from graph-structured data. A crucial prerequisite for the outstanding performance of GNNs is the availability of complete graph…
Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its…
\emph{Bidirected graphs} (a sort of nonstandard graphs introduced by Edmonds and Johnson) provide a natural generalization to the notions of directed and undirected graphs. By a \emph{weakly (node- or edge-) acyclic} bidirected graph we…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
Graph Neural Networks (GNNs) are gaining increasing attention on graph data learning tasks in recent years. However, in many applications, graph may be coming in an incomplete form where attributes of graph nodes are partially…
We study the clustering of bipartite graphs and Boolean matrix factorization in data streams. We consider a streaming setting in which the vertices from the left side of the graph arrive one by one together with all of their incident edges.…
Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…
In machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…
Bipartite best match graphs (BMG) and their generalizations arise in mathematical phylogenetics as combinatorial models describing evolutionary relationships among related genes in a pair of species. In this work, we characterize the class…