Related papers: Statistical ranking and combinatorial Hodge theory
The quest for efficient sorting is ongoing, and we will explore a graph-based stable sorting strategy, in particular employing comparison graphs. We use the topological sort to map the comparison graph to a linear domain, and we can…
We consider the problem of ranking $n$ experts according to their abilities, based on the correctness of their answers to $d$ questions. This is modeled by the so-called crowd-sourcing model, where the answer of expert $i$ on question $k$…
We propose a novel combinatorial inference framework to conduct general uncertainty quantification in ranking problems. We consider the widely adopted Bradley-Terry-Luce (BTL) model, where each item is assigned a positive preference score…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
The traditional methods of finding mixture components of rank data are mostly based on distance and latent class models; these models may exhibit the phenomenon of masking of groups of small sizes; probably due to the spherical nature of…
Bipartite graphs are a fundamental concept in graph theory with diverse applications. A graph is bipartite iff it contains no odd cycles, a characteristic that has many implications in diverse fields ranging from matching problems to the…
Recent years have witnessed the remarkable success of applying Graph machine learning (GML) to node/graph classification and link prediction. However, edge classification task that enjoys numerous real-world applications such as social…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
In this paper, we will investigate a harmonic cycle (discrete harmonic form). With a CW-complex, we can construct the combinatorial Laplacian operator. The kernel of the operator is the harmonic space, the set of harmonic cycles, and is…
Knot theory is an active field of mathematics, in which combinatorial and computational methods play an important role. One side of computational knot theory, that has gained interest in recent years, both for complexity analysis and…
Structural balance theory studies stability in networks. Given a $n$-vertex complete graph $G=(V,E)$ whose edges are labeled positive or negative, the graph is considered \emph{balanced} if every triangle either consists of three positive…
We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…
We investigate how sorting algorithms efficiently overcome the exponential size of the permutation space. Our main contribution is a new continuous-time formulation of sorting as a gradient flow on the permutohedron, yielding an independent…
"Concurrence topology" (Ellis and Klein \emph{Homology, Homotopy, and Applications,} \textbf{16}) is a TDA method for binary data. The idea is to construct a filtration consisting of Dowker complexes then compute persistent homology.…
This paper shows that pairwise PageRank orders emerge from two-hop walks. The main tool used here refers to a specially designed sign-mirror function and a parameter curve, whose low-order derivative information implies pairwise PageRank…
We consider estimation of worker skills from worker-task interaction data (with unknown labels) for the single-coin crowd-sourcing binary classification model in symmetric noise. We define the (worker) interaction graph whose nodes are…
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…
Ranking sectors and countries within global value chains is of paramount importance to estimate risks and forecast growth in large economies. However, this task is often non-trivial due to the lack of complete and accurate information on…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…