23,551 research outputs found
Studying the properties of galaxy cluster morphology estimators
X-ray observations of galaxy clusters reveal a large range of morphologies
with various degrees of disturbance, showing that the assumptions of
hydrostatic equilibrium and spherical shape which are used to determine the
cluster mass from X-ray data are not always satisfied. It is therefore
important for the understanding of cluster properties as well as for
cosmological applications to detect and quantify substructure in X-ray images
of galaxy clusters. Two promising methods to do so are power ratios and center
shifts. Since these estimators can be heavily affected by Poisson noise and
X-ray background, we performed an extensive analysis of their statistical
properties using a large sample of simulated X-ray observations of clusters
from hydrodynamical simulations. We quantify the measurement bias and error in
detail and give ranges where morphological analysis is feasible. A new,
computationally fast method to correct for the Poisson bias and the X-ray
background contribution in power ratio and center shift measurements is
presented and tested for typical XMM-Newton observational data sets. We studied
the morphology of 121 simulated cluster images and establish structure
boundaries to divide samples into relaxed, mildly disturbed and disturbed
clusters. In addition, we present a new morphology estimator - the peak of the
0.3-1 r500 P3/P0 profile to better identify merging clusters. The analysis
methods were applied to a sample of 80 galaxy clusters observed with
XMM-Newton. We give structure parameters (P3/P0 in r500, w and P3/P0_max) for
all 80 observed clusters. Using our definition of the P3/P0 (w) substructure
boundary, we find 41% (47%) of our observed clusters to be disturbed.Comment: Replaced to match version published in A&A, Eq. 1 correcte
Hashing with binary autoencoders
An attractive approach for fast search in image databases is binary hashing,
where each high-dimensional, real-valued image is mapped onto a
low-dimensional, binary vector and the search is done in this binary space.
Finding the optimal hash function is difficult because it involves binary
constraints, and most approaches approximate the optimization by relaxing the
constraints and then binarizing the result. Here, we focus on the binary
autoencoder model, which seeks to reconstruct an image from the binary code
produced by the hash function. We show that the optimization can be simplified
with the method of auxiliary coordinates. This reformulates the optimization as
alternating two easier steps: one that learns the encoder and decoder
separately, and one that optimizes the code for each image. Image retrieval
experiments, using precision/recall and a measure of code utilization, show the
resulting hash function outperforms or is competitive with state-of-the-art
methods for binary hashing.Comment: 22 pages, 11 figure
Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm
The nuclear norm is widely used as a convex surrogate of the rank function in
compressive sensing for low rank matrix recovery with its applications in image
recovery and signal processing. However, solving the nuclear norm based relaxed
convex problem usually leads to a suboptimal solution of the original rank
minimization problem. In this paper, we propose to perform a family of
nonconvex surrogates of -norm on the singular values of a matrix to
approximate the rank function. This leads to a nonconvex nonsmooth minimization
problem. Then we propose to solve the problem by Iteratively Reweighted Nuclear
Norm (IRNN) algorithm. IRNN iteratively solves a Weighted Singular Value
Thresholding (WSVT) problem, which has a closed form solution due to the
special properties of the nonconvex surrogate functions. We also extend IRNN to
solve the nonconvex problem with two or more blocks of variables. In theory, we
prove that IRNN decreases the objective function value monotonically, and any
limit point is a stationary point. Extensive experiments on both synthesized
data and real images demonstrate that IRNN enhances the low-rank matrix
recovery compared with state-of-the-art convex algorithms
Improved variable selection with Forward-Lasso adaptive shrinkage
Recently, considerable interest has focused on variable selection methods in
regression situations where the number of predictors, , is large relative to
the number of observations, . Two commonly applied variable selection
approaches are the Lasso, which computes highly shrunk regression coefficients,
and Forward Selection, which uses no shrinkage. We propose a new approach,
"Forward-Lasso Adaptive SHrinkage" (FLASH), which includes the Lasso and
Forward Selection as special cases, and can be used in both the linear
regression and the Generalized Linear Model domains. As with the Lasso and
Forward Selection, FLASH iteratively adds one variable to the model in a
hierarchical fashion but, unlike these methods, at each step adjusts the level
of shrinkage so as to optimize the selection of the next variable. We first
present FLASH in the linear regression setting and show that it can be fitted
using a variant of the computationally efficient LARS algorithm. Then, we
extend FLASH to the GLM domain and demonstrate, through numerous simulations
and real world data sets, as well as some theoretical analysis, that FLASH
generally outperforms many competing approaches.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS375 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The cluster Abell 780: an optical view
The Abell 780 cluster, better known as the Hydra A cluster, has been
thouroughly analyzed in X-rays. However, little is known on its optical
properties. We derive the galaxy luminosity function (GLF) in this apparently
relaxed cluster, and search for possible environmental effects by comparing the
GLFs in various regions, and by looking at the galaxy distribution at large
scale around Abell 780. Our study is based on optical images obtained with the
ESO 2.2m telescope and WFI camera in the B and R bands, covering a total region
of 67.22x32.94 arcmin^2, or 4.235x2.075 Mpc^2 for a cluster redshift of 0.0539.
In a region of 500 kpc radius around the cluster centre, the GLF in the R band
shows a double structure, with a broad and flat bright part and a flat faint
end that can be fit by a power law with an index alpha=-0.85+-0.12 in the
20.25<R<21.75 interval. If we divide this 500 kpc radius region in North+South
or East+West halves, we find no clear difference between the GLFs in these
smaller regions. No obvious large scale structure is apparent within 5 Mpc from
the cluster, based on galaxy redshifts and magnitudes collected from the NED
database in a much larger region than that covered by our data, suggesting that
there is no major infall of material in any preferential direction. However,
the Serna-Gerbal method reveals the presence of a gravitationally bound
structure of 27 galaxies, which includes the cD, and of a more strongly
gravitationally bound structure of 14 galaxies. These optical results agree
with the overall relaxed structure of Abell 780 previously derived from X-ray
analyses.Comment: Accepted for publication in Astronomy & Astrophysic
Generalized Nonconvex Nonsmooth Low-Rank Minimization
As surrogate functions of -norm, many nonconvex penalty functions have
been proposed to enhance the sparse vector recovery. It is easy to extend these
nonconvex penalty functions on singular values of a matrix to enhance low-rank
matrix recovery. However, different from convex optimization, solving the
nonconvex low-rank minimization problem is much more challenging than the
nonconvex sparse minimization problem. We observe that all the existing
nonconvex penalty functions are concave and monotonically increasing on
. Thus their gradients are decreasing functions. Based on this
property, we propose an Iteratively Reweighted Nuclear Norm (IRNN) algorithm to
solve the nonconvex nonsmooth low-rank minimization problem. IRNN iteratively
solves a Weighted Singular Value Thresholding (WSVT) problem. By setting the
weight vector as the gradient of the concave penalty function, the WSVT problem
has a closed form solution. In theory, we prove that IRNN decreases the
objective function value monotonically, and any limit point is a stationary
point. Extensive experiments on both synthetic data and real images demonstrate
that IRNN enhances the low-rank matrix recovery compared with state-of-the-art
convex algorithms.Comment: IEEE International Conference on Computer Vision and Pattern
Recognition, 201
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