1,961 research outputs found
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
3D Human Activity Recognition with Reconfigurable Convolutional Neural Networks
Human activity understanding with 3D/depth sensors has received increasing
attention in multimedia processing and interactions. This work targets on
developing a novel deep model for automatic activity recognition from RGB-D
videos. We represent each human activity as an ensemble of cubic-like video
segments, and learn to discover the temporal structures for a category of
activities, i.e. how the activities to be decomposed in terms of
classification. Our model can be regarded as a structured deep architecture, as
it extends the convolutional neural networks (CNNs) by incorporating structure
alternatives. Specifically, we build the network consisting of 3D convolutions
and max-pooling operators over the video segments, and introduce the latent
variables in each convolutional layer manipulating the activation of neurons.
Our model thus advances existing approaches in two aspects: (i) it acts
directly on the raw inputs (grayscale-depth data) to conduct recognition
instead of relying on hand-crafted features, and (ii) the model structure can
be dynamically adjusted accounting for the temporal variations of human
activities, i.e. the network configuration is allowed to be partially activated
during inference. For model training, we propose an EM-type optimization method
that iteratively (i) discovers the latent structure by determining the
decomposed actions for each training example, and (ii) learns the network
parameters by using the back-propagation algorithm. Our approach is validated
in challenging scenarios, and outperforms state-of-the-art methods. A large
human activity database of RGB-D videos is presented in addition.Comment: This manuscript has 10 pages with 9 figures, and a preliminary
version was published in ACM MM'14 conferenc
Detecting highly overlapping community structure by greedy clique expansion
In complex networks it is common for each node to belong to several
communities, implying a highly overlapping community structure. Recent advances
in benchmarking indicate that existing community assignment algorithms that are
capable of detecting overlapping communities perform well only when the extent
of community overlap is kept to modest levels. To overcome this limitation, we
introduce a new community assignment algorithm called Greedy Clique Expansion
(GCE). The algorithm identifies distinct cliques as seeds and expands these
seeds by greedily optimizing a local fitness function. We perform extensive
benchmarks on synthetic data to demonstrate that GCE's good performance is
robust across diverse graph topologies. Significantly, GCE is the only
algorithm to perform well on these synthetic graphs, in which every node
belongs to multiple communities. Furthermore, when put to the task of
identifying functional modules in protein interaction data, and college dorm
assignments in Facebook friendship data, we find that GCE performs
competitively.Comment: 10 pages, 7 Figures. Implementation source and binaries available at
http://sites.google.com/site/greedycliqueexpansion
A Novel Approach to Finding Near-Cliques: The Triangle-Densest Subgraph Problem
Many graph mining applications rely on detecting subgraphs which are
near-cliques. There exists a dichotomy between the results in the existing work
related to this problem: on the one hand the densest subgraph problem (DSP)
which maximizes the average degree over all subgraphs is solvable in polynomial
time but for many networks fails to find subgraphs which are near-cliques. On
the other hand, formulations that are geared towards finding near-cliques are
NP-hard and frequently inapproximable due to connections with the Maximum
Clique problem.
In this work, we propose a formulation which combines the best of both
worlds: it is solvable in polynomial time and finds near-cliques when the DSP
fails. Surprisingly, our formulation is a simple variation of the DSP.
Specifically, we define the triangle densest subgraph problem (TDSP): given
, find a subset of vertices such that , where is the number of triangles induced
by the set . We provide various exact and approximation algorithms which the
solve the TDSP efficiently. Furthermore, we show how our algorithms adapt to
the more general problem of maximizing the -clique average density. Finally,
we provide empirical evidence that the TDSP should be used whenever the output
of the DSP fails to output a near-clique.Comment: 42 page
Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?
Correlations in the signal observed via functional Magnetic Resonance Imaging
(fMRI), are expected to reveal the interactions in the underlying neural
populations through hemodynamic response. In particular, they highlight
distributed set of mutually correlated regions that correspond to brain
networks related to different cognitive functions. Yet graph-theoretical
studies of neural connections give a different picture: that of a highly
integrated system with small-world properties: local clustering but with short
pathways across the complete structure. We examine the conditional independence
properties of the fMRI signal, i.e. its Markov structure, to find realistic
assumptions on the connectivity structure that are required to explain the
observed functional connectivity. In particular we seek a decomposition of the
Markov structure into segregated functional networks using decomposable graphs:
a set of strongly-connected and partially overlapping cliques. We introduce a
new method to efficiently extract such cliques on a large, strongly-connected
graph. We compare methods learning different graph structures from functional
connectivity by testing the goodness of fit of the model they learn on new
data. We find that summarizing the structure as strongly-connected networks can
give a good description only for very large and overlapping networks. These
results highlight that Markov models are good tools to identify the structure
of brain connectivity from fMRI signals, but for this purpose they must reflect
the small-world properties of the underlying neural systems
Structural matching by discrete relaxation
This paper describes a Bayesian framework for performing relational graph matching by discrete relaxation. Our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching. Broadly speaking there are two main aspects to this study. Firstly we locus on the issue of how relational inexactness may be quantified. We illustrate that several popular relational distance measures can be recovered as specific limiting cases of the Bayesian consistency measure. The second aspect of our comparison concerns the way in which structural inexactness is controlled. We investigate three different realizations ai the matching process which draw on contrasting control models. The main conclusion of our study is that the active process of graph-editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter
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