10 research outputs found
Network-based ranking in social systems: three challenges
Ranking algorithms are pervasive in our increasingly digitized societies,
with important real-world applications including recommender systems, search
engines, and influencer marketing practices. From a network science
perspective, network-based ranking algorithms solve fundamental problems
related to the identification of vital nodes for the stability and dynamics of
a complex system. Despite the ubiquitous and successful applications of these
algorithms, we argue that our understanding of their performance and their
applications to real-world problems face three fundamental challenges: (i)
Rankings might be biased by various factors; (2) their effectiveness might be
limited to specific problems; and (3) agents' decisions driven by rankings
might result in potentially vicious feedback mechanisms and unhealthy systemic
consequences. Methods rooted in network science and agent-based modeling can
help us to understand and overcome these challenges.Comment: Perspective article. 9 pages, 3 figure
Estimating network dimension when the spectrum struggles
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 and extremely efficient algorithm for data clouds, based on computing first- and second-nearest neighbour distances, can be used as the basis of an approach for estimating the dimension of a network with weighted edges. We also show how the algorithm can be extended to unweighted networks when combined with spectral embedding. We illustrate the advantages of this technique over the widely used approach of characterizing dimension by visually searching for a suitable gap in the spectrum of the Laplacian
Ranking a set of objects: a graph based least-square approach
We consider the problem of ranking objects starting from a set of noisy
pairwise comparisons provided by a crowd of equal workers. We assume that
objects are endowed with intrinsic qualities and that the probability with
which an object is preferred to another depends only on the difference between
the qualities of the two competitors. We propose a class of non-adaptive
ranking algorithms that rely on a least-squares optimization criterion for the
estimation of qualities. Such algorithms are shown to be asymptotically optimal
(i.e., they require comparisons
to be -PAC). Numerical results show that our schemes are
very efficient also in many non-asymptotic scenarios exhibiting a performance
similar to the maximum-likelihood algorithm. Moreover, we show how they can be
extended to adaptive schemes and test them on real-world datasets
An extension of the angular synchronization problem to the heterogeneous setting
Given an undirected measurement graph G = ([n], E), the classical angular synchronization problem consists of recovering unknown angles Ξ1,. .. , Ξn from a collection of noisy pairwise measurements of the form (Ξi â Ξj) mod 2Ï, for each {i, j} â E. This problem arises in a variety of applications, including computer vision, time synchronization of distributed networks, and ranking from preference relationships. In this paper, we consider a generalization to the setting where there exist k unknown groups of angles Ξ_{l,1} ,. .. , Ξ_{l,n} , for l = 1,. .. , k. For each {i, j} â E, we are given noisy pairwise measurements of the form Ξ ,i â Ξ ,j for an unknown â {1, 2,. .. , k}. This can be thought of as a natural extension of the angular synchronization problem to the heterogeneous setting of multiple groups of angles, where the measurement graph has an unknown edge-disjoint decomposition G = G1 âȘ G2. .. âȘ G k , where the Gi's denote the subgraphs of edges corresponding to each group. We propose a probabilistic generative model for this problem, along with a spectral algorithm for which we provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise. The theoretical findings are complemented by a comprehensive set of numerical experiments, showcasing the efficacy of our algorithm under various parameter regimes. Finally, we consider an application of bi-synchronization to the graph realization problem, and provide along the way an iterative graph disentangling procedure that uncovers the subgraphs Gi, i = 1,. .. , k which is of independent interest, as it is shown to improve the final recovery accuracy across all the experiments considered
Ranking and synchronization from pairwise measurements via SVD
International audienceGiven a measurement graph and an unknown signal , we investigate algorithms for recovering from pairwise measurements of the form ; . This problem arises in a variety of applications, such as ranking teams in sports data and time synchronization of distributed networks. Framed in the context of ranking, the task is to recover the ranking of teams (induced by ) given a small subset of noisy pairwise rank offsets. We propose a simple SVD-based algorithmic pipeline for both the problem of time synchronization and ranking. We provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise perturbations with outliers, using results from matrix perturbation and random matrix theory. Our theoretical findings are complemented by a detailed set of numerical experiments on both synthetic and real data, showcasing the competitiveness of our proposed algorithms with other state-of-the-art methods
Ranking and synchronization from pairwise measurements via SVD
42 pages, 9 figuresGiven a measurement graph and an unknown signal , we investigate algorithms for recovering from pairwise measurements of the form ; . This problem arises in a variety of applications, such as ranking teams in sports data and time synchronization of distributed networks. Framed in the context of ranking, the task is to recover the ranking of teams (induced by ) given a small subset of noisy pairwise rank offsets. We propose a simple SVD-based algorithmic pipeline for both the problem of time synchronization and ranking. We provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise perturbations with outliers, using results from matrix perturbation and random matrix theory. Our theoretical findings are complemented by a detailed set of numerical experiments on both synthetic and real data, showcasing the competitiveness of our proposed algorithms with other state-of-the-art methods
Ranking and synchronization from pairwise measurements via SVD
Given a measurement graph and an unknown signal , we investigate algorithms for recovering from pairwise
measurements of the form ; . This problem arises in a
variety of applications, such as ranking teams in sports data and time
synchronization of distributed networks. Framed in the context of ranking, the
task is to recover the ranking of teams (induced by ) given a small
subset of noisy pairwise rank offsets. We propose a simple SVD-based
algorithmic pipeline for both the problem of time synchronization and ranking.
We provide a detailed theoretical analysis in terms of robustness against both
sampling sparsity and noise perturbations with outliers, using results from
matrix perturbation and random matrix theory. Our theoretical findings are
complemented by a detailed set of numerical experiments on both synthetic and
real data, showcasing the competitiveness of our proposed algorithms with other
state-of-the-art methods