7,706 research outputs found
Functional PCA for Remotely Sensed Lake Surface Water Temperature Data
Functional principal component analysis is used to investigate a high-dimensional surface water temperature data set of Lake Victoria, which has been produced in the ARC-Lake project. Two different perspectives are adopted in the analysis: modelling temperature curves (univariate functions) and temperature surfaces (bivariate functions). The latter proves to be a better approach in the sense of both dimension reduction and pattern detection. Computational details and some results from an application to Lake Victoria data are presented
N-Dimensional Principal Component Analysis
In this paper, we first briefly introduce the multidimensional Principal Component Analysis (PCA) techniques, and then amend our previous N-dimensional PCA (ND-PCA) scheme by introducing multidirectional decomposition into ND-PCA implementation. For the case of high dimensionality, PCA technique is usually extended to an arbitrary n-dimensional space by the Higher-Order Singular Value Decomposition (HO-SVD) technique. Due to the size of tensor, HO-SVD implementation usually leads to a huge matrix along some direction of tensor, which is always beyond the capacity of an ordinary PC. The novelty of this paper is to amend our previous ND-PCA scheme to deal with this challenge and further prove that the revised ND-PCA scheme can provide a near optimal linear solution under the given error bound. To evaluate the numerical property of the revised ND-PCA scheme, experiments are performed on a set of 3D volume datasets
PCA consistency in high dimension, low sample size context
Principal Component Analysis (PCA) is an important tool of dimension
reduction especially when the dimension (or the number of variables) is very
high. Asymptotic studies where the sample size is fixed, and the dimension
grows [i.e., High Dimension, Low Sample Size (HDLSS)] are becoming increasingly
relevant. We investigate the asymptotic behavior of the Principal Component
(PC) directions. HDLSS asymptotics are used to study consistency, strong
inconsistency and subspace consistency. We show that if the first few
eigenvalues of a population covariance matrix are large enough compared to the
others, then the corresponding estimated PC directions are consistent or
converge to the appropriate subspace (subspace consistency) and most other PC
directions are strongly inconsistent. Broad sets of sufficient conditions for
each of these cases are specified and the main theorem gives a catalogue of
possible combinations. In preparation for these results, we show that the
geometric representation of HDLSS data holds under general conditions, which
includes a -mixing condition and a broad range of sphericity measures of
the covariance matrix.Comment: Published in at http://dx.doi.org/10.1214/09-AOS709 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Parametrization of stochastic inputs using generative adversarial networks with application in geology
We investigate artificial neural networks as a parametrization tool for
stochastic inputs in numerical simulations. We address parametrization from the
point of view of emulating the data generating process, instead of explicitly
constructing a parametric form to preserve predefined statistics of the data.
This is done by training a neural network to generate samples from the data
distribution using a recent deep learning technique called generative
adversarial networks. By emulating the data generating process, the relevant
statistics of the data are replicated. The method is assessed in subsurface
flow problems, where effective parametrization of underground properties such
as permeability is important due to the high dimensionality and presence of
high spatial correlations. We experiment with realizations of binary
channelized subsurface permeability and perform uncertainty quantification and
parameter estimation. Results show that the parametrization using generative
adversarial networks is very effective in preserving visual realism as well as
high order statistics of the flow responses, while achieving a dimensionality
reduction of two orders of magnitude
PynPoint: a modular pipeline architecture for processing and analysis of high-contrast imaging data
The direct detection and characterization of planetary and substellar
companions at small angular separations is a rapidly advancing field. Dedicated
high-contrast imaging instruments deliver unprecedented sensitivity, enabling
detailed insights into the atmospheres of young low-mass companions. In
addition, improvements in data reduction and PSF subtraction algorithms are
equally relevant for maximizing the scientific yield, both from new and
archival data sets. We aim at developing a generic and modular data reduction
pipeline for processing and analysis of high-contrast imaging data obtained
with pupil-stabilized observations. The package should be scalable and robust
for future implementations and in particular well suitable for the 3-5 micron
wavelength range where typically (ten) thousands of frames have to be processed
and an accurate subtraction of the thermal background emission is critical.
PynPoint is written in Python 2.7 and applies various image processing
techniques, as well as statistical tools for analyzing the data, building on
open-source Python packages. The current version of PynPoint has evolved from
an earlier version that was developed as a PSF subtraction tool based on PCA.
The architecture of PynPoint has been redesigned with the core functionalities
decoupled from the pipeline modules. Modules have been implemented for
dedicated processing and analysis steps, including background subtraction,
frame registration, PSF subtraction, photometric and astrometric measurements,
and estimation of detection limits. The pipeline package enables end-to-end
data reduction of pupil-stabilized data and supports classical dithering and
coronagraphic data sets. As an example, we processed archival VLT/NACO L' and
M' data of beta Pic b and reassessed the planet's brightness and position with
an MCMC analysis, and we provide a derivation of the photometric error budget.Comment: 16 pages, 9 figures, accepted for publication in A&A, PynPoint is
available at https://github.com/PynPoint/PynPoin
Fast Mixing for the Low Temperature 2D Ising Model Through Irreversible Parallel Dynamics
We study tunneling and mixing time for a non-reversible probabilistic cellular automaton. With a suitable choice of the parameters, we first show that the stationary distribution is close in total variation to a low temperature Ising model. Then we prove that both the mixing time and the time to exit a metastable state grow polynomially in the size of the system, while this growth is exponential in reversible dynamics. In this model, non-reversibility, parallel updatings and a suitable choice of boundary conditions combine to produce an efficient dynamical stability
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