16,441 research outputs found
Brain covariance selection: better individual functional connectivity models using population prior
Spontaneous brain activity, as observed in functional neuroimaging, has been
shown to display reproducible structure that expresses brain architecture and
carries markers of brain pathologies. An important view of modern neuroscience
is that such large-scale structure of coherent activity reflects modularity
properties of brain connectivity graphs. However, to date, there has been no
demonstration that the limited and noisy data available in spontaneous activity
observations could be used to learn full-brain probabilistic models that
generalize to new data. Learning such models entails two main challenges: i)
modeling full brain connectivity is a difficult estimation problem that faces
the curse of dimensionality and ii) variability between subjects, coupled with
the variability of functional signals between experimental runs, makes the use
of multiple datasets challenging. We describe subject-level brain functional
connectivity structure as a multivariate Gaussian process and introduce a new
strategy to estimate it from group data, by imposing a common structure on the
graphical model in the population. We show that individual models learned from
functional Magnetic Resonance Imaging (fMRI) data using this population prior
generalize better to unseen data than models based on alternative
regularization schemes. To our knowledge, this is the first report of a
cross-validated model of spontaneous brain activity. Finally, we use the
estimated graphical model to explore the large-scale characteristics of
functional architecture and show for the first time that known cognitive
networks appear as the integrated communities of functional connectivity graph.Comment: in Advances in Neural Information Processing Systems, Vancouver :
Canada (2010
Communities in Networks
We survey some of the concepts, methods, and applications of community
detection, which has become an increasingly important area of network science.
To help ease newcomers into the field, we provide a guide to available
methodology and open problems, and discuss why scientists from diverse
backgrounds are interested in these problems. As a running theme, we emphasize
the connections of community detection to problems in statistical physics and
computational optimization.Comment: survey/review article on community structure in networks; published
version is available at
http://people.maths.ox.ac.uk/~porterm/papers/comnotices.pd
Graphs in machine learning: an introduction
Graphs are commonly used to characterise interactions between objects of
interest. Because they are based on a straightforward formalism, they are used
in many scientific fields from computer science to historical sciences. In this
paper, we give an introduction to some methods relying on graphs for learning.
This includes both unsupervised and supervised methods. Unsupervised learning
algorithms usually aim at visualising graphs in latent spaces and/or clustering
the nodes. Both focus on extracting knowledge from graph topologies. While most
existing techniques are only applicable to static graphs, where edges do not
evolve through time, recent developments have shown that they could be extended
to deal with evolving networks. In a supervised context, one generally aims at
inferring labels or numerical values attached to nodes using both the graph
and, when they are available, node characteristics. Balancing the two sources
of information can be challenging, especially as they can disagree locally or
globally. In both contexts, supervised and un-supervised, data can be
relational (augmented with one or several global graphs) as described above, or
graph valued. In this latter case, each object of interest is given as a full
graph (possibly completed by other characteristics). In this context, natural
tasks include graph clustering (as in producing clusters of graphs rather than
clusters of nodes in a single graph), graph classification, etc. 1 Real
networks One of the first practical studies on graphs can be dated back to the
original work of Moreno [51] in the 30s. Since then, there has been a growing
interest in graph analysis associated with strong developments in the modelling
and the processing of these data. Graphs are now used in many scientific
fields. In Biology [54, 2, 7], for instance, metabolic networks can describe
pathways of biochemical reactions [41], while in social sciences networks are
used to represent relation ties between actors [66, 56, 36, 34]. Other examples
include powergrids [71] and the web [75]. Recently, networks have also been
considered in other areas such as geography [22] and history [59, 39]. In
machine learning, networks are seen as powerful tools to model problems in
order to extract information from data and for prediction purposes. This is the
object of this paper. For more complete surveys, we refer to [28, 62, 49, 45].
In this section, we introduce notations and highlight properties shared by most
real networks. In Section 2, we then consider methods aiming at extracting
information from a unique network. We will particularly focus on clustering
methods where the goal is to find clusters of vertices. Finally, in Section 3,
techniques that take a series of networks into account, where each network i
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
Network Community Detection on Metric Space
Community detection in a complex network is an important problem of much
interest in recent years. In general, a community detection algorithm chooses
an objective function and captures the communities of the network by optimizing
the objective function, and then, one uses various heuristics to solve the
optimization problem to extract the interesting communities for the user. In
this article, we demonstrate the procedure to transform a graph into points of
a metric space and develop the methods of community detection with the help of
a metric defined for a pair of points. We have also studied and analyzed the
community structure of the network therein. The results obtained with our
approach are very competitive with most of the well-known algorithms in the
literature, and this is justified over the large collection of datasets. On the
other hand, it can be observed that time taken by our algorithm is quite less
compared to other methods and justifies the theoretical findings
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