977 research outputs found
Cosmic Ray Rejection by Linear Filtering of Single Images
We present a convolution-based algorithm for finding cosmic rays in single
well-sampled astronomical images. The spatial filter used is the point spread
function (approximated by a Gaussian) minus a scaled delta function, and cosmic
rays are identified by thresholding the filtered image. This filter searches
for features with significant power at spatial frequencies too high for
legitimate objects. Noise properties of the filtered image are readily
calculated, which allows us to compute the probability of rejecting a pixel not
contaminated by a cosmic ray (the false alarm probability). We demonstrate that
the false alarm probability for a pixel containing object flux will never
exceed the corresponding probability for a blank sky pixel, provided we choose
the convolution kernel appropriately. This allows confident rejection of cosmic
rays superposed on real objects. Identification of multiple-pixel cosmic ray
hits can be enhanced by running the algorithm iteratively, replacing flagged
pixels with the background level at each iteration.Comment: Accepted for publication in PASP (May 2000 issue). An iraf script
implementing the algorithm is available from the author, or from
http://sol.stsci.edu/~rhoads/ . 16 pages including 3 figures. Uses AASTeX
aaspp4 styl
Latitude: A Model for Mixed Linear-Tropical Matrix Factorization
Nonnegative matrix factorization (NMF) is one of the most frequently-used
matrix factorization models in data analysis. A significant reason to the
popularity of NMF is its interpretability and the `parts of whole'
interpretation of its components. Recently, max-times, or subtropical, matrix
factorization (SMF) has been introduced as an alternative model with equally
interpretable `winner takes it all' interpretation. In this paper we propose a
new mixed linear--tropical model, and a new algorithm, called Latitude, that
combines NMF and SMF, being able to smoothly alternate between the two. In our
model, the data is modeled using the latent factors and latent parameters that
control whether the factors are interpreted as NMF or SMF features, or their
mixtures. We present an algorithm for our novel matrix factorization. Our
experiments show that our algorithm improves over both baselines, and can yield
interpretable results that reveal more of the latent structure than either NMF
or SMF alone.Comment: 14 pages, 6 figures. To appear in 2018 SIAM International Conference
on Data Mining (SDM '18). For the source code, see
https://people.mpi-inf.mpg.de/~pmiettin/linear-tropical
Max-Plus Algebraic Statistical Leverage Scores
The statistical leverage scores of a matrix A ∈ Rn×d record the degree of alignment between col(A) and the coordinate axes in Rn. These scores are used in random sampling algorithms for solving certain numerical linear algebra problems. In this paper we present a max-plus algebraic analogue of statistical leverage scores. We show that max-plus statistical leverage scores can be used to calculate the exact asymptotic behavior of the conventional statistical leverage scores of a generic radial basis function network (RBFN) matrix. We also show how max-plus statistical leverage scores can provide a novel way to approximate the conventional statistical leverage scores of a fixed, nonparametrized matrix
Max-plus linear inverse problems:2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise
In this paper we present new theory and algorithms for 2-norm regression over
the max-plus semiring. As an application we also show how max-plus 2-norm
regression can be used in system identification of max-plus linear dynamical
systems with Gaussian noise. We also introduce and provide methods for solving
a max-plus linear inverse problem with regularization, which can be used when
the the original problem is not well posed.Comment: arXiv admin note: substantial text overlap with arXiv:1712.0349
As goes the seminary : how seminaries are intentionally producing spiritually alive pastors
https://place.asburyseminary.edu/ecommonsatsdissertations/1232/thumbnail.jp
Performance analysis of asynchronous parallel Jacobi
The directed acyclic graph (DAG) associated with a parallel algorithm captures the partial order in which separaT.L.cal computations are completed and how their outputs are subsequently used in further computations. Unlike in a synchronous parallel algorithm, the DAG associated with an asynchronous parallel algorithm is not predetermined. Instead, it is a product of the asynchronous timing dynamics of the machine and cannot be known in advance, as such it is best thought of as a pseudorandom variable. In this paper, we present a formalism for analyzing the performance of asynchronous parallel Jacobi’s method in terms of its DAG. We use this app.roach to prove error bounds and bounds on the rate of convergence. The rate of convergence bounds is based on the statistical properties of the DAG and is valid for systems with a non-negative iteration matrix. We supp.ort our theoretical results with a suit of numerical examples, where we compare the performance of synchronous and asynchronous parallel Jacobi to certain statistical properties of the DAGs associated with the computations. We also present some examples of small matrices with elements of mixed sign, which demonstrate that determining whether a system will converge under asynchronous iteration in this more general setting is a far more difficult problem
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