429 research outputs found
A Connectedness Constraint for Learning Sparse Graphs
Graphs are naturally sparse objects that are used to study many problems
involving networks, for example, distributed learning and graph signal
processing. In some cases, the graph is not given, but must be learned from the
problem and available data. Often it is desirable to learn sparse graphs.
However, making a graph highly sparse can split the graph into several
disconnected components, leading to several separate networks. The main
difficulty is that connectedness is often treated as a combinatorial property,
making it hard to enforce in e.g. convex optimization problems. In this
article, we show how connectedness of undirected graphs can be formulated as an
analytical property and can be enforced as a convex constraint. We especially
show how the constraint relates to the distributed consensus problem and graph
Laplacian learning. Using simulated and real data, we perform experiments to
learn sparse and connected graphs from data.Comment: 5 pages, presented at the European Signal Processing Conference
(EUSIPCO) 201
Approximate nonnegative matrix factorization algorithm for the analysis of angular differential imaging data
The angular differential imaging (ADI) is used to improve contrast in high
resolution astronomical imaging. An example is the direct imaging of exoplanet
in camera fed by Extreme Adaptive Optics. The subtraction of the main dazzling
object to observe the faint companion was improved using Principal Component
Analysis (PCA). It factorizes the positive astronomical frames into positive
and negative components. On the contrary, the Nonnegative Matrix Factorization
(NMF) uses only positive components, mimicking the actual composition of the
long exposure images.Comment: 9 pages, 7 Figures, Proceeding of the SPIE Conference Adaptive Optics
Systems VI, SPIE Astronomical Telescopes + Instrumentation, Austin Convention
Center Austin, Texas, United States 10 - 15 June 201
Trilogy on Computing Maximal Eigenpair
The eigenpair here means the twins consist of eigenvalue and its eigenvector.
This paper introduces the three steps of our study on computing the maximal
eigenpair. In the first two steps, we construct efficient initials for a known
but dangerous algorithm, first for tridiagonal matrices and then for
irreducible matrices, having nonnegative off-diagonal elements. In the third
step, we present two global algorithms which are still efficient and work well
for a quite large class of matrices, even complex for instance.Comment: Updated versio
Delocalization transition for the Google matrix
We study the localization properties of eigenvectors of the Google matrix,
generated both from the World Wide Web and from the Albert-Barabasi model of
networks. We establish the emergence of a delocalization phase for the PageRank
vector when network parameters are changed. In the phase of localized PageRank,
a delocalization takes place in the complex plane of eigenvalues of the matrix,
leading to delocalized relaxation modes. We argue that the efficiency of
information retrieval by Google-type search is strongly affected in the phase
of delocalized PageRank.Comment: 4 pages, 5 figures. Research done at
http://www.quantware.ups-tlse.fr
Reducing the Effects of Unequal Number of Games on Rankings
Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In such settings, the standard derivations of the methods can produce nonsensical rankings. This paper introduces the idea of including a super-user into the rankings and considers the effect of this fictitious player on the ratings. We apply such techniques to rank batters and pitchers in Major League baseball, professional tennis players, and participants in a free online social game. The ideas introduced in this paper can further the scope that such methods are applied and the depth of insight they offer
Ranking and clustering of nodes in networks with smart teleportation
Random teleportation is a necessary evil for ranking and clustering directed
networks based on random walks. Teleportation enables ergodic solutions, but
the solutions must necessarily depend on the exact implementation and
parametrization of the teleportation. For example, in the commonly used
PageRank algorithm, the teleportation rate must trade off a heavily biased
solution with a uniform solution. Here we show that teleportation to links
rather than nodes enables a much smoother trade-off and effectively more robust
results. We also show that, by not recording the teleportation steps of the
random walker, we can further reduce the effect of teleportation with dramatic
effects on clustering.Comment: 10 pages, 7 figure
Influence, originality and similarity in directed acyclic graphs
We introduce a framework for network analysis based on random walks on
directed acyclic graphs where the probability of passing through a given node
is the key ingredient. We illustrate its use in evaluating the mutual influence
of nodes and discovering seminal papers in a citation network. We further
introduce a new similarity metric and test it in a simple personalized
recommendation process. This metric's performance is comparable to that of
classical similarity metrics, thus further supporting the validity of our
framework.Comment: 6 pages, 4 figure
Thermodynamic formalism for dissipative quantum walks
We consider the dynamical properties of dissipative continuous-time quantum
walks on directed graphs. Using a large-deviation approach we construct a
thermodynamic formalism allowing us to define a dynamical order parameter, and
to identify transitions between dynamical regimes. For a particular class of
dissipative quantum walks we propose a quantum generalization of the the
classical PageRank vector, used to rank the importance of nodes in a directed
graph. We also provide an example where one can characterize the dynamical
transition from an effective classical random walk to a dissipative quantum
walk as a thermodynamic crossover between distinct dynamical regimes.Comment: 8 page
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