14 research outputs found
Line Graphs of Weighted Networks for Overlapping Communities
In this paper, we develop the idea to partition the edges of a weighted graph
in order to uncover overlapping communities of its nodes. Our approach is based
on the construction of different types of weighted line graphs, i.e. graphs
whose nodes are the links of the original graph, that encapsulate differently
the relations between the edges. Weighted line graphs are argued to provide an
alternative, valuable representation of the system's topology, and are shown to
have important applications in community detection, as the usual node partition
of a line graph naturally leads to an edge partition of the original graph.
This identification allows us to use traditional partitioning methods in order
to address the long-standing problem of the detection of overlapping
communities. We apply it to the analysis of different social and geographical
networks.Comment: 8 Pages. New title and text revisions to emphasise differences from
earlier paper
Kernel Spectral Clustering and applications
In this chapter we review the main literature related to kernel spectral
clustering (KSC), an approach to clustering cast within a kernel-based
optimization setting. KSC represents a least-squares support vector machine
based formulation of spectral clustering described by a weighted kernel PCA
objective. Just as in the classifier case, the binary clustering model is
expressed by a hyperplane in a high dimensional space induced by a kernel. In
addition, the multi-way clustering can be obtained by combining a set of binary
decision functions via an Error Correcting Output Codes (ECOC) encoding scheme.
Because of its model-based nature, the KSC method encompasses three main steps:
training, validation, testing. In the validation stage model selection is
performed to obtain tuning parameters, like the number of clusters present in
the data. This is a major advantage compared to classical spectral clustering
where the determination of the clustering parameters is unclear and relies on
heuristics. Once a KSC model is trained on a small subset of the entire data,
it is able to generalize well to unseen test points. Beyond the basic
formulation, sparse KSC algorithms based on the Incomplete Cholesky
Decomposition (ICD) and , , Group Lasso regularization are
reviewed. In that respect, we show how it is possible to handle large scale
data. Also, two possible ways to perform hierarchical clustering and a soft
clustering method are presented. Finally, real-world applications such as image
segmentation, power load time-series clustering, document clustering and big
data learning are considered.Comment: chapter contribution to the book "Unsupervised Learning Algorithms
Modern temporal network theory: A colloquium
The power of any kind of network approach lies in the ability to simplify a
complex system so that one can better understand its function as a whole.
Sometimes it is beneficial, however, to include more information than in a
simple graph of only nodes and links. Adding information about times of
interactions can make predictions and mechanistic understanding more accurate.
The drawback, however, is that there are not so many methods available, partly
because temporal networks is a relatively young field, partly because it more
difficult to develop such methods compared to for static networks. In this
colloquium, we review the methods to analyze and model temporal networks and
processes taking place on them, focusing mainly on the last three years. This
includes the spreading of infectious disease, opinions, rumors, in social
networks; information packets in computer networks; various types of signaling
in biology, and more. We also discuss future directions.Comment: Final accepted versio
Stable biomarker identification for predicting schizophrenia in the human connectome.
Schizophrenia, as a psychiatric disorder, has recognized brain alterations both at the structural and at the functional magnetic resonance imaging level. The developing field of connectomics has attracted much attention as it allows researchers to take advantage of powerful tools of network analysis in order to study structural and functional connectivity abnormalities in schizophrenia. Many methods have been proposed to identify biomarkers in schizophrenia, focusing mainly on improving the classification performance or performing statistical comparisons between groups. However, the stability of biomarkers selection has been for long overlooked in the connectomics field. In this study, we follow a machine learning approach where the identification of biomarkers is addressed as a feature selection problem for a classification task. We perform a recursive feature elimination and support vector machines (RFE-SVM) approach to identify the most meaningful biomarkers from the structural, functional, and multi-modal connectomes of healthy controls and patients. Furthermore, the stability of the retrieved biomarkers is assessed across different subsamplings of the dataset, allowing us to identify the affected core of the pathology. Considering our technique altogether, it demonstrates a principled way to achieve both accurate and stable biomarkers while highlighting the importance of multi-modal approaches to brain pathology as they tend to reveal complementary information
On Immortal Configurations in Turing Machines
Abstract We investigate the immortality problem for Turing machines and prove that there exists a Turing Machine that is immortal but halts on every recursive configuration. The result is obtained by combining a new proof of Hooper’s theorem [11] with recent results on effective symbolic dynamics