15,963 research outputs found
Outlier Detection from Network Data with Subnetwork Interpretation
Detecting a small number of outliers from a set of data observations is
always challenging. This problem is more difficult in the setting of multiple
network samples, where computing the anomalous degree of a network sample is
generally not sufficient. In fact, explaining why the network is exceptional,
expressed in the form of subnetwork, is also equally important. In this paper,
we develop a novel algorithm to address these two key problems. We treat each
network sample as a potential outlier and identify subnetworks that mostly
discriminate it from nearby regular samples. The algorithm is developed in the
framework of network regression combined with the constraints on both network
topology and L1-norm shrinkage to perform subnetwork discovery. Our method thus
goes beyond subspace/subgraph discovery and we show that it converges to a
global optimum. Evaluation on various real-world network datasets demonstrates
that our algorithm not only outperforms baselines in both network and high
dimensional setting, but also discovers highly relevant and interpretable local
subnetworks, further enhancing our understanding of anomalous networks
Augmented Sparse Reconstruction of Protein Signaling Networks
The problem of reconstructing and identifying intracellular protein signaling
and biochemical networks is of critical importance in biology today. We sought
to develop a mathematical approach to this problem using, as a test case, one
of the most well-studied and clinically important signaling networks in biology
today, the epidermal growth factor receptor (EGFR) driven signaling cascade.
More specifically, we suggest a method, augmented sparse reconstruction, for
the identification of links among nodes of ordinary differential equation (ODE)
networks from a small set of trajectories with different initial conditions.
Our method builds a system of representation by using a collection of integrals
of all given trajectories and by attenuating block of terms in the
representation itself. The system of representation is then augmented with
random vectors, and minimization of the 1-norm is used to find sparse
representations for the dynamical interactions of each node. Augmentation by
random vectors is crucial, since sparsity alone is not able to handle the large
error-in-variables in the representation. Augmented sparse reconstruction
allows to consider potentially very large spaces of models and it is able to
detect with high accuracy the few relevant links among nodes, even when
moderate noise is added to the measured trajectories. After showing the
performance of our method on a model of the EGFR protein network, we sketch
briefly the potential future therapeutic applications of this approach.Comment: 24 pages, 6 figure
Spectral identification of networks with inputs
We consider a network of interconnected dynamical systems. Spectral network
identification consists in recovering the eigenvalues of the network Laplacian
from the measurements of a very limited number (possibly one) of signals. These
eigenvalues allow to deduce some global properties of the network, such as
bounds on the node degree.
Having recently introduced this approach for autonomous networks of nonlinear
systems, we extend it here to treat networked systems with external inputs on
the nodes, in the case of linear dynamics. This is more natural in several
applications, and removes the need to sometimes use several independent
trajectories. We illustrate our framework with several examples, where we
estimate the mean, minimum, and maximum node degree in the network. Inferring
some information on the leading Laplacian eigenvectors, we also use our
framework in the context of network clustering.Comment: 8 page
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