606 research outputs found
A Web Aggregation Approach for Distributed Randomized PageRank Algorithms
The PageRank algorithm employed at Google assigns a measure of importance to
each web page for rankings in search results. In our recent papers, we have
proposed a distributed randomized approach for this algorithm, where web pages
are treated as agents computing their own PageRank by communicating with linked
pages. This paper builds upon this approach to reduce the computation and
communication loads for the algorithms. In particular, we develop a method to
systematically aggregate the web pages into groups by exploiting the sparsity
inherent in the web. For each group, an aggregated PageRank value is computed,
which can then be distributed among the group members. We provide a distributed
update scheme for the aggregated PageRank along with an analysis on its
convergence properties. The method is especially motivated by results on
singular perturbation techniques for large-scale Markov chains and multi-agent
consensus.Comment: To appear in the IEEE Transactions on Automatic Control, 201
Ergodic Randomized Algorithms and Dynamics over Networks
Algorithms and dynamics over networks often involve randomization, and
randomization may result in oscillating dynamics which fail to converge in a
deterministic sense. In this paper, we observe this undesired feature in three
applications, in which the dynamics is the randomized asynchronous counterpart
of a well-behaved synchronous one. These three applications are network
localization, PageRank computation, and opinion dynamics. Motivated by their
formal similarity, we show the following general fact, under the assumptions of
independence across time and linearities of the updates: if the expected
dynamics is stable and converges to the same limit of the original synchronous
dynamics, then the oscillations are ergodic and the desired limit can be
locally recovered via time-averaging.Comment: 11 pages; submitted for publication. revised version with fixed
technical flaw and updated reference
FrogWild! -- Fast PageRank Approximations on Graph Engines
We propose FrogWild, a novel algorithm for fast approximation of high
PageRank vertices, geared towards reducing network costs of running traditional
PageRank algorithms. Our algorithm can be seen as a quantized version of power
iteration that performs multiple parallel random walks over a directed graph.
One important innovation is that we introduce a modification to the GraphLab
framework that only partially synchronizes mirror vertices. This partial
synchronization vastly reduces the network traffic generated by traditional
PageRank algorithms, thus greatly reducing the per-iteration cost of PageRank.
On the other hand, this partial synchronization also creates dependencies
between the random walks used to estimate PageRank. Our main theoretical
innovation is the analysis of the correlations introduced by this partial
synchronization process and a bound establishing that our approximation is
close to the true PageRank vector.
We implement our algorithm in GraphLab and compare it against the default
PageRank implementation. We show that our algorithm is very fast, performing
each iteration in less than one second on the Twitter graph and can be up to 7x
faster compared to the standard GraphLab PageRank implementation
Distributed estimation and control of node centrality in undirected asymmetric networks
Measures of node centrality that describe the importance of a node within a
network are crucial for understanding the behavior of social networks and
graphs. In this paper, we address the problems of distributed estimation and
control of node centrality in undirected graphs with asymmetric weight values.
In particular, we focus our attention on -centrality, which can be seen
as a generalization of eigenvector centrality. In this setting, we first
consider a distributed protocol where agents compute their -centrality,
focusing on the convergence properties of the method; then, we combine the
estimation method with a consensus algorithm to achieve a consensus value
weighted by the influence of each node in the network. Finally, we formulate an
-centrality control problem which is naturally decoupled and, thus,
suitable for a distributed setting and we apply this formulation to protect the
most valuable nodes in a network against a targeted attack, by making every
node in the network equally important in terms of {\alpha}-centrality.
Simulations results are provided to corroborate the theoretical findings.Comment: published on IEEE Transactions on Automatic Control
https://ieeexplore.ieee.org/abstract/document/912618
Efficient Numerical Methods to Solve Sparse Linear Equations with Application to PageRank
In this paper, we propose three methods to solve the PageRank problem for the
transition matrices with both row and column sparsity. Our methods reduce the
PageRank problem to the convex optimization problem over the simplex. The first
algorithm is based on the gradient descent in L1 norm instead of the Euclidean
one. The second algorithm extends the Frank-Wolfe to support sparse gradient
updates. The third algorithm stands for the mirror descent algorithm with a
randomized projection. We proof converges rates for these methods for sparse
problems as well as numerical experiments support their effectiveness.Comment: 26 page
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