53,921 research outputs found
Map equation for link community
Community structure exists in many real-world networks and has been reported
being related to several functional properties of the networks. The
conventional approach was partitioning nodes into communities, while some
recent studies start partitioning links instead of nodes to find overlapping
communities of nodes efficiently. We extended the map equation method, which
was originally developed for node communities, to find link communities in
networks. This method is tested on various kinds of networks and compared with
the metadata of the networks, and the results show that our method can identify
the overlapping role of nodes effectively. The advantage of this method is that
the node community scheme and link community scheme can be compared
quantitatively by measuring the unknown information left in the networks
besides the community structure. It can be used to decide quantitatively
whether or not the link community scheme should be used instead of the node
community scheme. Furthermore, this method can be easily extended to the
directed and weighted networks since it is based on the random walk.Comment: 9 pages,5 figure
Cross-Entropy Clustering
We construct a cross-entropy clustering (CEC) theory which finds the optimal
number of clusters by automatically removing groups which carry no information.
Moreover, our theory gives simple and efficient criterion to verify cluster
validity.
Although CEC can be build on an arbitrary family of densities, in the most
important case of Gaussian CEC:
{\em -- the division into clusters is affine invariant;
-- the clustering will have the tendency to divide the data into
ellipsoid-type shapes;
-- the approach is computationally efficient as we can apply Hartigan
approach.}
We study also with particular attention clustering based on the Spherical
Gaussian densities and that of Gaussian densities with covariance s \I. In
the letter case we show that with converging to zero we obtain the
classical k-means clustering
A Review of Codebook Models in Patch-Based Visual Object Recognition
The codebook model-based approach, while ignoring any structural aspect in vision, nonetheless provides state-of-the-art performances on current datasets. The key role of a visual codebook is to provide a way to map the low-level features into a fixed-length vector in histogram space to which standard classifiers can be directly applied. The discriminative power of such a visual codebook determines the quality of the codebook model, whereas the size of the codebook controls the complexity of the model. Thus, the construction of a codebook is an important step which is usually done by cluster analysis. However, clustering is a process that retains regions of high density in a distribution and it follows that the resulting codebook need not have discriminant properties. This is also recognised as a computational bottleneck of such systems. In our recent work, we proposed a resource-allocating codebook, to constructing a discriminant codebook in a one-pass design procedure that slightly outperforms more traditional approaches at drastically reduced computing times. In this review we survey several approaches that have been proposed over the last decade with their use of feature detectors, descriptors, codebook construction schemes, choice of classifiers in recognising objects, and datasets that were used in evaluating the proposed methods
Adaptive gravitational softening in GADGET
Cosmological simulations of structure formation follow the collisionless
evolution of dark matter starting from a nearly homogeneous field at early
times down to the highly clustered configuration at redshift zero. The density
field is sampled by a number of particles in number infinitely smaller than
those believed to be its actual components and this limits the mass and spatial
scales over which we can trust the results of a simulation. Softening of the
gravitational force is introduced in collisionless simulations to limit the
importance of close encounters between these particles. The scale of softening
is generally fixed and chosen as a compromise between the need for high spatial
resolution and the need to limit the particle noise. In the scenario of
cosmological simulations, where the density field evolves to a highly
inhomogeneous state, this compromise results in an appropriate choice only for
a certain class of objects, the others being subject to either a biased or a
noisy dynamical description. We have implemented adaptive gravitational
softening lengths in the cosmological simulation code GADGET; the formalism
allows the softening scale to vary in space and time according to the density
of the environment, at the price of modifying the equation of motion for the
particles in order to be consistent with the new dependencies introduced in the
system's Lagrangian. We have applied the technique to a number of test cases
and to a set of cosmological simulations of structure formation. We conclude
that the use of adaptive softening enhances the clustering of particles at
small scales, a result visible in the amplitude of the correlation function and
in the inner profile of massive objects, thereby anticipating the results
expected from much higher resolution simulations.Comment: 15 pages, 21 figures, 1 table. Accepted for publication in MNRA
Dynamic Zoom Simulations: a fast, adaptive algorithm for simulating lightcones
The advent of a new generation of large-scale galaxy surveys is pushing
cosmological numerical simulations in an uncharted territory. The simultaneous
requirements of high resolution and very large volume pose serious technical
challenges, due to their computational and data storage demand. In this paper,
we present a novel approach dubbed Dynamic Zoom Simulations -- or DZS --
developed to tackle these issues. Our method is tailored to the production of
lightcone outputs from N-body numerical simulations, which allow for a more
efficient storage and post-processing compared to standard comoving snapshots,
and more directly mimic the format of survey data. In DZS, the resolution of
the simulation is dynamically decreased outside the lightcone surface, reducing
the computational work load, while simultaneously preserving the accuracy
inside the lightcone and the large-scale gravitational field. We show that our
approach can achieve virtually identical results to traditional simulations at
half of the computational cost for our largest box. We also forecast this
speedup to increase up to a factor of 5 for larger and/or higher-resolution
simulations. We assess the accuracy of the numerical integration by comparing
pairs of identical simulations run with and without DZS. Deviations in the
lightcone halo mass function, in the sky-projected lightcone, and in the 3D
matter lightcone always remain below 0.1%. In summary, our results indicate
that the DZS technique may provide a highly-valuable tool to address the
technical challenges that will characterise the next generation of large-scale
cosmological simulations.Comment: 17 pages, 13 figures, version accepted for publication in MNRA
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