1,099 research outputs found
Accelerating Consensus by Spectral Clustering and Polynomial Filters
It is known that polynomial filtering can accelerate the convergence towards
average consensus on an undirected network. In this paper the gain of a
second-order filtering is investigated. A set of graphs is determined for which
consensus can be attained in finite time, and a preconditioner is proposed to
adapt the undirected weights of any given graph to achieve fastest convergence
with the polynomial filter. The corresponding cost function differs from the
traditional spectral gap, as it favors grouping the eigenvalues in two
clusters. A possible loss of robustness of the polynomial filter is also
highlighted
Consensus State Gram Matrix Estimation for Stochastic Switching Networks from Spectral Distribution Moments
Reaching distributed average consensus quickly and accurately over a network
through iterative dynamics represents an important task in numerous distributed
applications. Suitably designed filters applied to the state values can
significantly improve the convergence rate. For constant networks, these
filters can be viewed in terms of graph signal processing as polynomials in a
single matrix, the consensus iteration matrix, with filter response evaluated
at its eigenvalues. For random, time-varying networks, filter design becomes
more complicated, involving eigendecompositions of sums and products of random,
time-varying iteration matrices. This paper focuses on deriving an estimate for
the Gram matrix of error in the state vectors over a filtering window for
large-scale, stationary, switching random networks. The result depends on the
moments of the empirical spectral distribution, which can be estimated through
Monte-Carlo simulation. This work then defines a quadratic objective function
to minimize the expected consensus estimate error norm. Simulation results
provide support for the approximation.Comment: 52nd Asilomar Conference on Signals, Systems, and Computers (Asilomar
2017
Hybrid Approach of Relation Network and Localized Graph Convolutional Filtering for Breast Cancer Subtype Classification
Network biology has been successfully used to help reveal complex mechanisms
of disease, especially cancer. On the other hand, network biology requires
in-depth knowledge to construct disease-specific networks, but our current
knowledge is very limited even with the recent advances in human cancer
biology. Deep learning has shown a great potential to address the difficult
situation like this. However, deep learning technologies conventionally use
grid-like structured data, thus application of deep learning technologies to
the classification of human disease subtypes is yet to be explored. Recently,
graph based deep learning techniques have emerged, which becomes an opportunity
to leverage analyses in network biology. In this paper, we proposed a hybrid
model, which integrates two key components 1) graph convolution neural network
(graph CNN) and 2) relation network (RN). We utilize graph CNN as a component
to learn expression patterns of cooperative gene community, and RN as a
component to learn associations between learned patterns. The proposed model is
applied to the PAM50 breast cancer subtype classification task, the standard
breast cancer subtype classification of clinical utility. In experiments of
both subtype classification and patient survival analysis, our proposed method
achieved significantly better performances than existing methods. We believe
that this work is an important starting point to realize the upcoming
personalized medicine.Comment: 8 pages, To be published in proceeding of IJCAI 201
DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning
toolbox and have led to many breakthroughs in Artificial Intelligence. These
networks have mostly been developed for regular Euclidean domains such as those
supporting images, audio, or video. Because of their success, CNN-based methods
are becoming increasingly popular in Cosmology. Cosmological data often comes
as spherical maps, which make the use of the traditional CNNs more complicated.
The commonly used pixelization scheme for spherical maps is the Hierarchical
Equal Area isoLatitude Pixelisation (HEALPix). We present a spherical CNN for
analysis of full and partial HEALPix maps, which we call DeepSphere. The
spherical CNN is constructed by representing the sphere as a graph. Graphs are
versatile data structures that can act as a discrete representation of a
continuous manifold. Using the graph-based representation, we define many of
the standard CNN operations, such as convolution and pooling. With filters
restricted to being radial, our convolutions are equivariant to rotation on the
sphere, and DeepSphere can be made invariant or equivariant to rotation. This
way, DeepSphere is a special case of a graph CNN, tailored to the HEALPix
sampling of the sphere. This approach is computationally more efficient than
using spherical harmonics to perform convolutions. We demonstrate the method on
a classification problem of weak lensing mass maps from two cosmological models
and compare the performance of the CNN with that of two baseline classifiers.
The results show that the performance of DeepSphere is always superior or equal
to both of these baselines. For high noise levels and for data covering only a
smaller fraction of the sphere, DeepSphere achieves typically 10% better
classification accuracy than those baselines. Finally, we show how learned
filters can be visualized to introspect the neural network.Comment: arXiv admin note: text overlap with arXiv:astro-ph/0409513 by other
author
Deep Learning-Based Average Consensus
In this study, we analyzed the problem of accelerating the linear average
consensus algorithm for complex networks. We propose a data-driven approach to
tuning the weights of temporal (i.e., time-varying) networks using deep
learning techniques. Given a finite-time window, the proposed approach first
unfolds the linear average consensus protocol to obtain a feedforward
signal-flow graph, which is regarded as a neural network. The edge weights of
the obtained neural network are then trained using standard deep learning
techniques to minimize consensus error over a given finite-time window. Through
this training process, we obtain a set of optimized time-varying weights, which
yield faster consensus for a complex network. We also demonstrate that the
proposed approach can be extended for infinite-time window problems. Numerical
experiments revealed that our approach can achieve a significantly smaller
consensus error compared to baseline strategies
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