18,938 research outputs found
Different approaches to community detection
A precise definition of what constitutes a community in networks has remained
elusive. Consequently, network scientists have compared community detection
algorithms on benchmark networks with a particular form of community structure
and classified them based on the mathematical techniques they employ. However,
this comparison can be misleading because apparent similarities in their
mathematical machinery can disguise different reasons for why we would want to
employ community detection in the first place. Here we provide a focused review
of these different motivations that underpin community detection. This
problem-driven classification is useful in applied network science, where it is
important to select an appropriate algorithm for the given purpose. Moreover,
highlighting the different approaches to community detection also delineates
the many lines of research and points out open directions and avenues for
future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in
network clustering and blockmodeling, and based on an extended version of The
many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4
(2017) by the same author
Coarse-to-Fine Lifted MAP Inference in Computer Vision
There is a vast body of theoretical research on lifted inference in
probabilistic graphical models (PGMs). However, few demonstrations exist where
lifting is applied in conjunction with top of the line applied algorithms. We
pursue the applicability of lifted inference for computer vision (CV), with the
insight that a globally optimal (MAP) labeling will likely have the same label
for two symmetric pixels. The success of our approach lies in efficiently
handling a distinct unary potential on every node (pixel), typical of CV
applications. This allows us to lift the large class of algorithms that model a
CV problem via PGM inference. We propose a generic template for coarse-to-fine
(C2F) inference in CV, which progressively refines an initial coarsely lifted
PGM for varying quality-time trade-offs. We demonstrate the performance of C2F
inference by developing lifted versions of two near state-of-the-art CV
algorithms for stereo vision and interactive image segmentation. We find that,
against flat algorithms, the lifted versions have a much superior anytime
performance, without any loss in final solution quality.Comment: Published in IJCAI 201
Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation
The detection of community structure in networks is intimately related to
finding a concise description of the network in terms of its modules. This
notion has been recently exploited by the Map equation formalism (M. Rosvall
and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an
information-theoretic description of the process of coding inter- and
intra-community transitions of a random walker in the network at stationarity.
However, a thorough study of the relationship between the full Markov dynamics
and the coding mechanism is still lacking. We show here that the original Map
coding scheme, which is both block-averaged and one-step, neglects the internal
structure of the communities and introduces an upper scale, the `field-of-view'
limit, in the communities it can detect. As a consequence, Map is well tuned to
detect clique-like communities but can lead to undesirable overpartitioning
when communities are far from clique-like. We show that a signature of this
behavior is a large compression gap: the Map description length is far from its
ideal limit. To address this issue, we propose a simple dynamic approach that
introduces time explicitly into the Map coding through the analysis of the
weighted adjacency matrix of the time-dependent multistep transition matrix of
the Markov process. The resulting Markov time sweeping induces a dynamical
zooming across scales that can reveal (potentially multiscale) community
structure above the field-of-view limit, with the relevant partitions indicated
by a small compression gap.Comment: 10 pages, 6 figure
Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models
Graphical models use graphs to compactly capture stochastic dependencies
amongst a collection of random variables. Inference over graphical models
corresponds to finding marginal probability distributions given joint
probability distributions. In general, this is computationally intractable,
which has led to a quest for finding efficient approximate inference
algorithms. We propose a framework for generalized inference over graphical
models that can be used as a wrapper for improving the estimates of approximate
inference algorithms. Instead of applying an inference algorithm to the
original graph, we apply the inference algorithm to a block-graph, defined as a
graph in which the nodes are non-overlapping clusters of nodes from the
original graph. This results in marginal estimates of a cluster of nodes, which
we further marginalize to get the marginal estimates of each node. Our proposed
block-graph construction algorithm is simple, efficient, and motivated by the
observation that approximate inference is more accurate on graphs with longer
cycles. We present extensive numerical simulations that illustrate our
block-graph framework with a variety of inference algorithms (e.g., those in
the libDAI software package). These simulations show the improvements provided
by our framework.Comment: Extended the previous version to include extensive numerical
simulations. See http://www.ima.umn.edu/~dvats/GeneralizedInference.html for
code and dat
Enhancing hyperspectral image unmixing with spatial correlations
This paper describes a new algorithm for hyperspectral image unmixing. Most
of the unmixing algorithms proposed in the literature do not take into account
the possible spatial correlations between the pixels. In this work, a Bayesian
model is introduced to exploit these correlations. The image to be unmixed is
assumed to be partitioned into regions (or classes) where the statistical
properties of the abundance coefficients are homogeneous. A Markov random field
is then proposed to model the spatial dependency of the pixels within any
class. Conditionally upon a given class, each pixel is modeled by using the
classical linear mixing model with additive white Gaussian noise. This strategy
is investigated the well known linear mixing model. For this model, the
posterior distributions of the unknown parameters and hyperparameters allow
ones to infer the parameters of interest. These parameters include the
abundances for each pixel, the means and variances of the abundances for each
class, as well as a classification map indicating the classes of all pixels in
the image. To overcome the complexity of the posterior distribution of
interest, we consider Markov chain Monte Carlo methods that generate samples
distributed according to the posterior of interest. The generated samples are
then used for parameter and hyperparameter estimation. The accuracy of the
proposed algorithms is illustrated on synthetic and real data.Comment: Manuscript accepted for publication in IEEE Trans. Geoscience and
Remote Sensin
A Statistical Modeling Approach to Computer-Aided Quantification of Dental Biofilm
Biofilm is a formation of microbial material on tooth substrata. Several
methods to quantify dental biofilm coverage have recently been reported in the
literature, but at best they provide a semi-automated approach to
quantification with significant input from a human grader that comes with the
graders bias of what are foreground, background, biofilm, and tooth.
Additionally, human assessment indices limit the resolution of the
quantification scale; most commercial scales use five levels of quantification
for biofilm coverage (0%, 25%, 50%, 75%, and 100%). On the other hand, current
state-of-the-art techniques in automatic plaque quantification fail to make
their way into practical applications owing to their inability to incorporate
human input to handle misclassifications. This paper proposes a new interactive
method for biofilm quantification in Quantitative light-induced fluorescence
(QLF) images of canine teeth that is independent of the perceptual bias of the
grader. The method partitions a QLF image into segments of uniform texture and
intensity called superpixels; every superpixel is statistically modeled as a
realization of a single 2D Gaussian Markov random field (GMRF) whose parameters
are estimated; the superpixel is then assigned to one of three classes
(background, biofilm, tooth substratum) based on the training set of data. The
quantification results show a high degree of consistency and precision. At the
same time, the proposed method gives pathologists full control to post-process
the automatic quantification by flipping misclassified superpixels to a
different state (background, tooth, biofilm) with a single click, providing
greater usability than simply marking the boundaries of biofilm and tooth as
done by current state-of-the-art methods.Comment: 10 pages, 7 figures, Journal of Biomedical and Health Informatics
2014. keywords: {Biomedical imaging;Calibration;Dentistry;Estimation;Image
segmentation;Manuals;Teeth},
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6758338&isnumber=636350
The stability of a graph partition: A dynamics-based framework for community detection
Recent years have seen a surge of interest in the analysis of complex
networks, facilitated by the availability of relational data and the
increasingly powerful computational resources that can be employed for their
analysis. Naturally, the study of real-world systems leads to highly complex
networks and a current challenge is to extract intelligible, simplified
descriptions from the network in terms of relevant subgraphs, which can provide
insight into the structure and function of the overall system.
Sparked by seminal work by Newman and Girvan, an interesting line of research
has been devoted to investigating modular community structure in networks,
revitalising the classic problem of graph partitioning.
However, modular or community structure in networks has notoriously evaded
rigorous definition. The most accepted notion of community is perhaps that of a
group of elements which exhibit a stronger level of interaction within
themselves than with the elements outside the community. This concept has
resulted in a plethora of computational methods and heuristics for community
detection. Nevertheless a firm theoretical understanding of most of these
methods, in terms of how they operate and what they are supposed to detect, is
still lacking to date.
Here, we will develop a dynamical perspective towards community detection
enabling us to define a measure named the stability of a graph partition. It
will be shown that a number of previously ad-hoc defined heuristics for
community detection can be seen as particular cases of our method providing us
with a dynamic reinterpretation of those measures. Our dynamics-based approach
thus serves as a unifying framework to gain a deeper understanding of different
aspects and problems associated with community detection and allows us to
propose new dynamically-inspired criteria for community structure.Comment: 3 figures; published as book chapte
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