Related papers: Threshold-Based Graph Reconstruction Using Discret…
Signal processing on graph is attracting more and more attentions. For a graph signal in the low-frequency subspace, the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the…
The Reeb graph is a construction which originated in Morse theory to study a real valued function defined on a topological space. More recently, it has been used in various applications to study noisy data which creates a desire to define a…
We consider the problem of reconstructing an undirected graph $G$ on $n$ vertices given multiple random noisy subgraphs or "traces". Specifically, a trace is generated by sampling each vertex with probability $p_v$, then taking the…
Graph theory is increasingly commonly utilised in genetics, proteomics and neuroimaging. In such fields, the data of interest generally constitute weighted graphs. Analysis of such weighted graphs often require the integration of…
We study the problem of reconstructing a hidden graph given access to a distance oracle. We design randomized algorithms for the following problems: reconstruction of a degree bounded graph with query complexity $\tilde{O}(n^{3/2})$;…
Limited data and low dose constraints are common problems in a variety of tomographic reconstruction paradigms which lead to noisy and incomplete data. Over the past few years sinogram denoising has become an essential pre-processing step…
The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree depth. In this paper we survey results related to this concept…
In this paper, the focus is on the reconstruction of a diffusive field and the localization of the underlying driving sources on arbitrary graphs by observing a significantly smaller subset of vertices of the graph uniformly in time.…
The basic inverse problem in spectral graph theory consists in determining the graph given its eigenvalue spectrum. In this paper, we are interested in a network of technological agents whose graph is unknown, communicating by means of a…
In this paper, we provide a Graph Fourier Transform based approach to downsample signals on graphs. For bandlimited signals on a graph, a test is provided to identify whether signal reconstruction is possible from the given downsampled…
Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…
We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
Neuroscientific data analysis has classically involved methods for statistical signal and image processing, drawing on linear algebra and stochastic process theory. However, digitized neuroanatomical data sets containing labelled neurons,…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Sensing the fluid flow around an arbitrary geometry entails extrapolating from the physical quantities perceived at its surface in order to reconstruct the features of the surrounding fluid. This is a challenging inverse problem, yet one…
We introduce a new deep generative model useful for uncertainty quantification: the Morse neural network, which generalizes the unnormalized Gaussian densities to have modes of high-dimensional submanifolds instead of just discrete points.…
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. In this paper, we study the embedded homology as well as the homology of the (lower-)associated simplicial complexes for hypergraphs. We…
We reconstruct a closed denoised curve from an unstructured and highly noisy 2D point cloud. Our proposed method uses a two- pass approach: Previously recovered manifold connectivity is used for ordering noisy samples along this manifold…
We consider the problem of constructing embeddings of large attributed graphs and supporting multiple downstream learning tasks. We develop a graph embedding method, which is based on extending deep metric and unbiased contrastive learning…