204 research outputs found
Asynchronous Gossip for Averaging and Spectral Ranking
We consider two variants of the classical gossip algorithm. The first variant
is a version of asynchronous stochastic approximation. We highlight a
fundamental difficulty associated with the classical asynchronous gossip
scheme, viz., that it may not converge to a desired average, and suggest an
alternative scheme based on reinforcement learning that has guaranteed
convergence to the desired average. We then discuss a potential application to
a wireless network setting with simultaneous link activation constraints. The
second variant is a gossip algorithm for distributed computation of the
Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant
draws upon a reinforcement learning algorithm for an average cost controlled
Markov decision problem, the second variant draws upon a reinforcement learning
algorithm for risk-sensitive control. We then discuss potential applications of
the second variant to ranking schemes, reputation networks, and principal
component analysis.Comment: 14 pages, 7 figures. Minor revisio
Spectral Ranking in Complex Networks Using Memristor Crossbars
Various centrality measures have been proposed to identify the influence of each node in a complex network. Among the most popular ranking metrics, spectral measures stand out from the crowd. They rely on the computation of the dominant eigenvector of suitable matrices related to the graph: EigenCentrality, PageRank, Hyperlink Induced Topic Search (HITS) and Stochastic Approach for Link-Structure Analysis (SALSA). The simplest algorithm used to solve this linear algebra computation is the Power Method. It consists of multiple Matrix-Vector Multiplications (MVMs) and a normalization step to avoid divergent behaviours. In this work, we present an analog circuit used to accelerate the Power Iteration algorithm including current-mode termination for the memristor crossbars and a normalization circuit. The normalization step together with the feedback loop of the complete circuit ensure stability and convergence of the dominant eigenvector. We implement a transistor level peripheral circuitry around the memristor crossbar and take non-idealities such as wire parasitics, source driver resistance and finite memristor precision into account. We compute the different spectral centralities to demonstrate the performance of the system. We compare our results to the ones coming from the conventional digital computers and observe significant energy savings while maintaining a competitive accuracy
Spectral Ranking Inferences based on General Multiway Comparisons
This paper studies the performance of the spectral method in the estimation
and uncertainty quantification of the unobserved preference scores of compared
entities in a very general and more realistic setup in which the comparison
graph consists of hyper-edges of possible heterogeneous sizes and the number of
comparisons can be as low as one for a given hyper-edge. Such a setting is
pervasive in real applications, circumventing the need to specify the graph
randomness and the restrictive homogeneous sampling assumption imposed in the
commonly-used Bradley-Terry-Luce (BTL) or Plackett-Luce (PL) models.
Furthermore, in the scenarios when the BTL or PL models are appropriate, we
unravel the relationship between the spectral estimator and the Maximum
Likelihood Estimator (MLE). We discover that a two-step spectral method, where
we apply the optimal weighting estimated from the equal weighting vanilla
spectral method, can achieve the same asymptotic efficiency as the MLE. Given
the asymptotic distributions of the estimated preference scores, we also
introduce a comprehensive framework to carry out both one-sample and two-sample
ranking inferences, applicable to both fixed and random graph settings. It is
noteworthy that it is the first time effective two-sample rank testing methods
are proposed. Finally, we substantiate our findings via comprehensive numerical
simulations and subsequently apply our developed methodologies to perform
statistical inferences on statistics journals and movie rankings
Approximating Spectral Impact of Structural Perturbations in Large Networks
Determining the effect of structural perturbations on the eigenvalue spectra
of networks is an important problem because the spectra characterize not only
their topological structures, but also their dynamical behavior, such as
synchronization and cascading processes on networks. Here we develop a theory
for estimating the change of the largest eigenvalue of the adjacency matrix or
the extreme eigenvalues of the graph Laplacian when small but arbitrary set of
links are added or removed from the network. We demonstrate the effectiveness
of our approximation schemes using both real and artificial networks, showing
in particular that we can accurately obtain the spectral ranking of small
subgraphs. We also propose a local iterative scheme which computes the relative
ranking of a subgraph using only the connectivity information of its neighbors
within a few links. Our results may not only contribute to our theoretical
understanding of dynamical processes on networks, but also lead to practical
applications in ranking subgraphs of real complex networks.Comment: 9 pages, 3 figures, 2 table
- …