336,241 research outputs found
Reduction of Spin Glasses applied to the Migdal-Kadanoff Hierarchical Lattice
A reduction procedure to obtain ground states of spin glasses on sparse
graphs is developed and tested on the hierarchical lattice associated with the
Migdal-Kadanoff approximation for low-dimensional lattices. While more
generally applicable, these rules here lead to a complete reduction of the
lattice. The stiffness exponent governing the scaling of the defect energy
with system size , , is obtained as
by reducing the equivalent of lattices up to in
, and as for up to in . The reduction
rules allow the exact determination of the ground state energy, entropy, and
also provide an approximation to the overlap distribution. With these methods,
some well-know and some new features of diluted hierarchical lattices are
calculated.Comment: 7 pages, RevTex, 6 figures (postscript), added results for d=4, some
corrections; final version, as to appear in EPJ
Recherche et représentation de communautés dans des grands graphes
15 pagesNational audienceThis paper deals with the analysis and the visualization of large graphs. Our interest in such a subject-matter is related to the fact that graphs are convenient widespread data structures. Indeed, this type of data can be encountered in a growing number of concrete problems: Web, information retrieval, social networks, biological interaction networks... Furthermore, the size of these graphs becomes increasingly large as the progression of the means for data gathering and storage steadily strengthens. This calls for new methods in graph analysis and visualization which are now important and dynamic research fields at the interface of many disciplines such as mathematics, statistics, computer science and sociology. In this paper, we propose a method for graphs representation and visualization based on a prior clustering of the vertices. Newman and Girvan (2004) points out that âreducing [the] level of complexity [of a network] to one that can be interpreted readily by the human eye, will be invaluable in helping us to understand the large-scale structure of these new network dataâ: we rely on this assumption to use a priori a clustering of the vertices as a preliminary step for simplifying the representation of the graphs - as a whole. The clustering phase consists in optimizing a quality measure specifically suitable for the research of dense groups in graphs. This quality measure is the modularity and expresses the âdistanceâ to a null model in which the graph edges do not depend on the clustering. The modularity has shown its relevance in solving the problem of uncovering dense groups in a graph. Optimization of the modularity is done through a stochastic simulated annealing algorithm. The visualization/representation phase, as such, is based on a force-directed algorithm described in Truong et al. (2007). After giving a short introduction to the problem and detailing the vertices clustering and representation algorithms, the paper will introduce and discuss two applications from the social network field
Enumerating Maximal Bicliques from a Large Graph using MapReduce
We consider the enumeration of maximal bipartite cliques (bicliques) from a
large graph, a task central to many practical data mining problems in social
network analysis and bioinformatics. We present novel parallel algorithms for
the MapReduce platform, and an experimental evaluation using Hadoop MapReduce.
Our algorithm is based on clustering the input graph into smaller sized
subgraphs, followed by processing different subgraphs in parallel. Our
algorithm uses two ideas that enable it to scale to large graphs: (1) the
redundancy in work between different subgraph explorations is minimized through
a careful pruning of the search space, and (2) the load on different reducers
is balanced through the use of an appropriate total order among the vertices.
Our evaluation shows that the algorithm scales to large graphs with millions of
edges and tens of mil- lions of maximal bicliques. To our knowledge, this is
the first work on maximal biclique enumeration for graphs of this scale.Comment: A preliminary version of the paper was accepted at the Proceedings of
the 3rd IEEE International Congress on Big Data 201
Scene Graph Lossless Compression with Adaptive Prediction for Objects and Relations
The scene graph is a new data structure describing objects and their pairwise
relationship within image scenes. As the size of scene graph in vision
applications grows, how to losslessly and efficiently store such data on disks
or transmit over the network becomes an inevitable problem. However, the
compression of scene graph is seldom studied before because of the complicated
data structures and distributions. Existing solutions usually involve
general-purpose compressors or graph structure compression methods, which is
weak at reducing redundancy for scene graph data. This paper introduces a new
lossless compression framework with adaptive predictors for joint compression
of objects and relations in scene graph data. The proposed framework consists
of a unified prior extractor and specialized element predictors to adapt for
different data elements. Furthermore, to exploit the context information within
and between graph elements, Graph Context Convolution is proposed to support
different graph context modeling schemes for different graph elements. Finally,
a learned distribution model is devised to predict numerical data under
complicated conditional constraints. Experiments conducted on labeled or
generated scene graphs proves the effectiveness of the proposed framework in
scene graph lossless compression task
Pre-processing for Triangulation of Probabilistic Networks
The currently most efficient algorithm for inference with a probabilistic
network builds upon a triangulation of a network's graph. In this paper, we
show that pre-processing can help in finding good triangulations
forprobabilistic networks, that is, triangulations with a minimal maximum
clique size. We provide a set of rules for stepwise reducing a graph, without
losing optimality. This reduction allows us to solve the triangulation problem
on a smaller graph. From the smaller graph's triangulation, a triangulation of
the original graph is obtained by reversing the reduction steps. Our
experimental results show that the graphs of some well-known real-life
probabilistic networks can be triangulated optimally just by preprocessing; for
other networks, huge reductions in their graph's size are obtained.Comment: Appears in Proceedings of the Seventeenth Conference on Uncertainty
in Artificial Intelligence (UAI2001
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