2,086 research outputs found
Time scale modeling for consensus in sparse directed networks with time-varying topologies
The paper considers the consensus problem in large networks represented by
time-varying directed graphs. A practical way of dealing with large-scale
networks is to reduce their dimension by collapsing the states of nodes
belonging to densely and intensively connected clusters into aggregate
variables. It will be shown that under suitable conditions, the states of the
agents in each cluster converge fast toward a local agreement. Local agreements
correspond to aggregate variables which slowly converge to consensus. Existing
results concerning the time-scale separation in large networks focus on fixed
and undirected graphs. The aim of this work is to extend these results to the
more general case of time-varying directed topologies. It is noteworthy that in
the fixed and undirected graph case the average of the states in each cluster
is time-invariant when neglecting the interactions between clusters. Therefore,
they are good candidates for the aggregate variables. This is no longer
possible here. Instead, we find suitable time-varying weights to compute the
aggregate variables as time-invariant weighted averages of the states in each
cluster. This allows to deal with the more challenging time-varying directed
graph case. We end up with a singularly perturbed system which is analyzed by
using the tools of two time-scales averaging which seem appropriate to this
system
Spectral identification of networks using sparse measurements
We propose a new method to recover global information about a network of
interconnected dynamical systems based on observations made at a small number
(possibly one) of its nodes. In contrast to classical identification of full
graph topology, we focus on the identification of the spectral graph-theoretic
properties of the network, a framework that we call spectral network
identification.
The main theoretical results connect the spectral properties of the network
to the spectral properties of the dynamics, which are well-defined in the
context of the so-called Koopman operator and can be extracted from data
through the Dynamic Mode Decomposition algorithm. These results are obtained
for networks of diffusively-coupled units that admit a stable equilibrium
state. For large networks, a statistical approach is considered, which focuses
on spectral moments of the network and is well-suited to the case of
heterogeneous populations.
Our framework provides efficient numerical methods to infer global
information on the network from sparse local measurements at a few nodes.
Numerical simulations show for instance the possibility of detecting the mean
number of connections or the addition of a new vertex using measurements made
at one single node, that need not be representative of the other nodes'
properties.Comment: 3
Distributed Big-Data Optimization via Block-Iterative Convexification and Averaging
In this paper, we study distributed big-data nonconvex optimization in
multi-agent networks. We consider the (constrained) minimization of the sum of
a smooth (possibly) nonconvex function, i.e., the agents' sum-utility, plus a
convex (possibly) nonsmooth regularizer. Our interest is in big-data problems
wherein there is a large number of variables to optimize. If treated by means
of standard distributed optimization algorithms, these large-scale problems may
be intractable, due to the prohibitive local computation and communication
burden at each node. We propose a novel distributed solution method whereby at
each iteration agents optimize and then communicate (in an uncoordinated
fashion) only a subset of their decision variables. To deal with non-convexity
of the cost function, the novel scheme hinges on Successive Convex
Approximation (SCA) techniques coupled with i) a tracking mechanism
instrumental to locally estimate gradient averages; and ii) a novel block-wise
consensus-based protocol to perform local block-averaging operations and
gradient tacking. Asymptotic convergence to stationary solutions of the
nonconvex problem is established. Finally, numerical results show the
effectiveness of the proposed algorithm and highlight how the block dimension
impacts on the communication overhead and practical convergence speed
Graph Summarization
The continuous and rapid growth of highly interconnected datasets, which are
both voluminous and complex, calls for the development of adequate processing
and analytical techniques. One method for condensing and simplifying such
datasets is graph summarization. It denotes a series of application-specific
algorithms designed to transform graphs into more compact representations while
preserving structural patterns, query answers, or specific property
distributions. As this problem is common to several areas studying graph
topologies, different approaches, such as clustering, compression, sampling, or
influence detection, have been proposed, primarily based on statistical and
optimization methods. The focus of our chapter is to pinpoint the main graph
summarization methods, but especially to focus on the most recent approaches
and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie
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