اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSupracentrality Analysis of Temporal Networks with Directed Interlayer Coupling
57
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based centralities, a family of centrality measures for time-independent networks that includes PageRank, hub and authority scores, and eigenvector centrality. We start with a sequence of adjacency matrices, each of which represents a time layer of a network at a different point or interval of time. Coupling centrality matrices across time layers with weighted interlayer edges yields a emph{supracentrality matrix} $mathbb{C}(omega)$, where $omega$ controls the extent to which centrality trajectories change over time. We can flexibly tune the weight and topology of the interlayer coupling to cater to different scientific applications. The entries of the dominant eigenvector of $mathbb{C}(omega)$ represent emph{joint centralities}, which simultaneously quantify the importance of every node in every time layer. Inspired by probability theory, we also compute emph{marginal} and emph{conditional centralities}. We illustrate how to adjust the coupling between time layers to tune the extent to which nodes centrality trajectories are influenced by the oldest and newest time layers. We support our findings by analysis in the limits of small and large $omega$.
قيم البحث
اقرأ أيضاً
Characterizing the importances (i.e., centralities) of nodes in social, biological, and technological networks is a core topic in both network science and data science. We present a linear-algebraic framework that generalizes eigenvector-based centra
lities, including PageRank and hub/authority scores, to provide a common framework for two popular classes of multilayer networks: multiplex networks (which have layers that encode different types of relationships) and temporal networks (in which the relationships change over time). Our approach involves the study of joint, marginal, and conditional supracentralities that one can calculate from the dominant eigenvector of a supracentrality matrix [Taylor et al., 2017], which couples centrality matrices that are associated with individual network layers. We extend this prior work (which was restricted to temporal networks with layers that are coupled by adjacent-in-time coupling) by allowing the layers to be coupled through a (possibly asymmetric) interlayer-adjacency matrix $tilde{{bf A}}$, where the entry $tilde{A}_{tt} geq 0$ encodes the coupling between layers $t$ and $t$. Our framework provides a unifying foundation for centrality analysis of multiplex and temporal networks; it also illustrates a complicated dependency of the supracentralities on the topology and weights of interlayer coupling. By scaling $tilde{{bf A}}$ by an interlayer-coupling strength $omegage0$ and developing a singular perturbation theory for the limits of weak ($omegato0^+$) and strong coupling ($omegatoinfty$), we also reveal an interesting dependence of supracentralities on the dominant left and right eigenvectors of $tilde{{bf A}}$.
We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve some partia
l differential equations, mostly in high dimensions in practical applications. In this work, we introduce a general framework to analyze the generalization error of regularized networks. The error estimate relies on two assumptions on the approximation error and the quadrature error. Moreover, we conduct some experiments on the image classification tasks to show that gradient-based methods can significantly improve the generalization ability and adversarial robustness of neural networks. A graphical extension of the gradient-based methods are also considered in the experiments.
Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partitio
n of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.
Estimating distributions of node characteristics (labels) such as number of connections or citizenship of users in a social network via edge and node sampling is a vital part of the study of complex networks. Due to its low cost, sampling via a rando
m walk (RW) has been proposed as an attractive solution to this task. Most RW methods assume either that the network is undirected or that walkers can traverse edges regardless of their direction. Some RW methods have been designed for directed networks where edges coming into a node are not directly observable. In this work, we propose Directed Unbiased Frontier Sampling (DUFS), a sampling method based on a large number of coordinated walkers, each starting from a node chosen uniformly at random. It is applicable to directed networks with invisible incoming edges because it constructs, in real-time, an undirected graph consistent with the walkers trajectories, and due to the use of random jumps which prevent walkers from being trapped. DUFS generalizes previous RW methods and is suited for undirected networks and to directed networks regardless of in-edges visibility. We also propose an improved estimator of node label distributions that combines information from the initial walker locations with subsequent RW observations. We evaluate DUFS, compare it to other RW methods, investigate the impact of its parameters on estimation accuracy and provide practical guidelines for choosing them. In estimating out-degree distributions, DUFS yields significantly better estimates of the head of the distribution than other methods, while matching or exceeding estimation accuracy of the tail. Last, we show that DUFS outperforms uniform node sampling when estimating distributions of node labels of the top 10% largest degree nodes, even when sampling a node uniformly has the same cost as RW steps.
A weighted directed network (WDN) is a directed graph in which each edge is associated to a unique value called weight. These networks are very suitable for modeling real-world social networks in which there is an assessment of one vertex toward othe
r vertices. One of the main problems studied in this paper is prediction of edge weights in such networks. We introduce, for the first time, a metric geometry approach to studying edge weight prediction in WDNs. We modify a usual notion of WDNs, and introduce a new type of WDNs which we coin the term textit{almost-weighted directed networks} (AWDNs). AWDNs can capture the weight information of a network from a given training set. We then construct a class of metrics (or distances) for AWDNs which equips such networks with a metric space structure. Using the metric geometry structure of AWDNs, we propose modified $k$ nearest neighbors (kNN) methods and modified support-vector machine (SVM) methods which will then be used to predict edge weights in AWDNs. In many real-world datasets, in addition to edge weights, one can also associate weights to vertices which capture information of vertices; association of weights to vertices especially plays an important role in graph embedding problems. Adopting a similar approach, we introduce two new types of directed networks in which weights are associated to either a subset of origin vertices or a subset of terminal vertices . We, for the first time, construct novel classes of metrics on such networks, and based on these new metrics propose modified $k$NN and SVM methods for predicting weights of origins and terminals in these networks. We provide experimental results on several real-world datasets, using our geometric methodologies.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
