Related papers: Latent Distance Estimation for Random Geometric Gr…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
The primary objective of this thesis is to develop novel algorithmic approaches for Graph Representation Learning of static and single-event dynamic networks. In such a direction, we focus on the family of Latent Space Models, and more…
As a fundamental challenge in vast disciplines, link prediction aims to identify potential links in a network based on the incomplete observed information, which has broad applications ranging from uncovering missing protein-protein…
In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the…
Many popular dimensionality reduction procedures have out-of-sample extensions, which allow a practitioner to apply a learned embedding to observations not seen in the initial training sample. In this work, we consider the problem of…
Measuring the distances between vertices on graphs is one of the most fundamental components in network analysis. Since finding shortest paths requires traversing the graph, it is challenging to obtain distance information on large graphs…
The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness…
Many functions have been recently defined to assess the similarity among networks as tools for quantitative comparison. They stem from very different frameworks - and they are tuned for dealing with different situations. Here we show an…
The random geometric graph $\mathsf{RGG}(n,\mathbb{S}^{d-1}, p)$ is formed by sampling $n$ i.i.d. vectors $\{V_i\}_{i = 1}^n$ uniformly on $\mathbb{S}^{d-1}$ and placing an edge between pairs of vertices $i$ and $j$ for which $\langle…
Geodesic distances on manifolds have numerous applications in image processing, computer graphics and computer vision. In this work, we introduce an approach called `LGGD' (Learned Generalized Geodesic Distances). This method involves…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
The unit ball random geometric graph $G=G^d_p(\lambda,n)$ has as its vertices $n$ points distributed independently and uniformly in the $d$-dimensional unit ball, with two vertices adjacent if and only if their $l_p$-distance is at most…
What is the dimension of a network? Here, we view it as the smallest dimension of Euclidean space into which nodes can be embedded so that pairwise distances accurately reflect the connectivity structure. We show that a recently proposed…
We study the problem of reconstructing the latent geometry of a $d$-dimensional Riemannian manifold from a random geometric graph. While recent works have made significant progress in manifold recovery from random geometric graphs, and more…
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…