4,068 research outputs found
Simultaneous Matrix Diagonalization for Structural Brain Networks Classification
This paper considers the problem of brain disease classification based on
connectome data. A connectome is a network representation of a human brain. The
typical connectome classification problem is very challenging because of the
small sample size and high dimensionality of the data. We propose to use
simultaneous approximate diagonalization of adjacency matrices in order to
compute their eigenstructures in more stable way. The obtained approximate
eigenvalues are further used as features for classification. The proposed
approach is demonstrated to be efficient for detection of Alzheimer's disease,
outperforming simple baselines and competing with state-of-the-art approaches
to brain disease classification
Discriminating different classes of biological networks by analyzing the graphs spectra distribution
The brain's structural and functional systems, protein-protein interaction,
and gene networks are examples of biological systems that share some features
of complex networks, such as highly connected nodes, modularity, and
small-world topology. Recent studies indicate that some pathologies present
topological network alterations relative to norms seen in the general
population. Therefore, methods to discriminate the processes that generate the
different classes of networks (e.g., normal and disease) might be crucial for
the diagnosis, prognosis, and treatment of the disease. It is known that
several topological properties of a network (graph) can be described by the
distribution of the spectrum of its adjacency matrix. Moreover, large networks
generated by the same random process have the same spectrum distribution,
allowing us to use it as a "fingerprint". Based on this relationship, we
introduce and propose the entropy of a graph spectrum to measure the
"uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon
divergences between graph spectra to compare networks. We also introduce
general methods for model selection and network model parameter estimation, as
well as a statistical procedure to test the nullity of divergence between two
classes of complex networks. Finally, we demonstrate the usefulness of the
proposed methods by applying them on (1) protein-protein interaction networks
of different species and (2) on networks derived from children diagnosed with
Attention Deficit Hyperactivity Disorder (ADHD) and typically developing
children. We conclude that scale-free networks best describe all the
protein-protein interactions. Also, we show that our proposed measures
succeeded in the identification of topological changes in the network while
other commonly used measures (number of edges, clustering coefficient, average
path length) failed
A generative model for protein contact networks
In this paper we present a generative model for protein contact networks. The
soundness of the proposed model is investigated by focusing primarily on
mesoscopic properties elaborated from the spectra of the graph Laplacian. To
complement the analysis, we study also classical topological descriptors, such
as statistics of the shortest paths and the important feature of modularity.
Our experiments show that the proposed model results in a considerable
improvement with respect to two suitably chosen generative mechanisms,
mimicking with better approximation real protein contact networks in terms of
diffusion properties elaborated from the Laplacian spectra. However, as well as
the other considered models, it does not reproduce with sufficient accuracy the
shortest paths structure. To compensate this drawback, we designed a second
step involving a targeted edge reconfiguration process. The ensemble of
reconfigured networks denotes improvements that are statistically significant.
As a byproduct of our study, we demonstrate that modularity, a well-known
property of proteins, does not entirely explain the actual network architecture
characterizing protein contact networks. In fact, we conclude that modularity,
intended as a quantification of an underlying community structure, should be
considered as an emergent property of the structural organization of proteins.
Interestingly, such a property is suitably optimized in protein contact
networks together with the feature of path efficiency.Comment: 18 pages, 67 reference
Characterization of complex networks: A survey of measurements
Each complex network (or class of networks) presents specific topological
features which characterize its connectivity and highly influence the dynamics
of processes executed on the network. The analysis, discrimination, and
synthesis of complex networks therefore rely on the use of measurements capable
of expressing the most relevant topological features. This article presents a
survey of such measurements. It includes general considerations about complex
network characterization, a brief review of the principal models, and the
presentation of the main existing measurements. Important related issues
covered in this work comprise the representation of the evolution of complex
networks in terms of trajectories in several measurement spaces, the analysis
of the correlations between some of the most traditional measurements,
perturbation analysis, as well as the use of multivariate statistics for
feature selection and network classification. Depending on the network and the
analysis task one has in mind, a specific set of features may be chosen. It is
hoped that the present survey will help the proper application and
interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of
measurements for inclusion are welcomed by the author
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