1,054 research outputs found
A Robust Classification of Galaxy Spectra: Dealing with Noisy and Incomplete Data
Over the next few years new spectroscopic surveys (from the optical surveys
of the Sloan Digital Sky Survey and the 2 degree Field survey through to
space-based ultraviolet satellites such as GALEX) will provide the opportunity
and challenge of understanding how galaxies of different spectral type evolve
with redshift. Techniques have been developed to classify galaxies based on
their continuum and line spectra. Some of the most promising of these have used
the Karhunen and Loeve transform (or Principal Component Analysis) to separate
galaxies into distinct classes. Their limitation has been that they assume that
the spectral coverage and quality of the spectra are constant for all galaxies
within a given sample. In this paper we develop a general formalism that
accounts for the missing data within the observed spectra (such as the removal
of sky lines or the effect of sampling different intrinsic rest wavelength
ranges due to the redshift of a galaxy). We demonstrate that by correcting for
these gaps we can recover an almost redshift independent classification scheme.
From this classification we can derive an optimal interpolation that
reconstructs the underlying galaxy spectral energy distributions in the regions
of missing data. This provides a simple and effective mechanism for building
galaxy spectral energy distributions directly from data that may be noisy,
incomplete or drawn from a number of different sources.Comment: 20 pages, 8 figures. Accepted for publication in A
Determining the Spectral Signature of Spatial Coherent Structures
We applied to an open flow a proper orthogonal decomposition (pod) technique,
on 2D snapshots of the instantaneous velocity field, to reveal the spatial
coherent structures responsible of the self-sustained oscillations observed in
the spectral distribution of time series. We applied the technique to 2D planes
out of 3D direct numerical simulations on an open cavity flow. The process can
easily be implemented on usual personal computers, and might bring deep
insights on the relation between spatial events and temporal signature in (both
numerical or experimental) open flows.Comment: 4 page
An extension of Wiener integration with the use of operator theory
With the use of tensor product of Hilbert space, and a diagonalization
procedure from operator theory, we derive an approximation formula for a
general class of stochastic integrals. Further we establish a generalized
Fourier expansion for these stochastic integrals. In our extension, we
circumvent some of the limitations of the more widely used stochastic integral
due to Wiener and Ito, i.e., stochastic integration with respect to Brownian
motion. Finally we discuss the connection between the two approaches, as well
as a priori estimates and applications.Comment: 13 page
On dimension reduction in Gaussian filters
A priori dimension reduction is a widely adopted technique for reducing the
computational complexity of stationary inverse problems. In this setting, the
solution of an inverse problem is parameterized by a low-dimensional basis that
is often obtained from the truncated Karhunen-Loeve expansion of the prior
distribution. For high-dimensional inverse problems equipped with smoothing
priors, this technique can lead to drastic reductions in parameter dimension
and significant computational savings.
In this paper, we extend the concept of a priori dimension reduction to
non-stationary inverse problems, in which the goal is to sequentially infer the
state of a dynamical system. Our approach proceeds in an offline-online
fashion. We first identify a low-dimensional subspace in the state space before
solving the inverse problem (the offline phase), using either the method of
"snapshots" or regularized covariance estimation. Then this subspace is used to
reduce the computational complexity of various filtering algorithms - including
the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within
a novel subspace-constrained Bayesian prediction-and-update procedure (the
online phase). We demonstrate the performance of our new dimension reduction
approach on various numerical examples. In some test cases, our approach
reduces the dimensionality of the original problem by orders of magnitude and
yields up to two orders of magnitude in computational savings
Likelihood contrasts: a machine learning algorithm for binary classification of longitudinal data
Machine learning methods have gained increased popularity in biomedical research during the recent years. However, very few of them support the analysis of longitudinal data, where several samples are collected from an individual over time. Additionally, most of the available longitudinal machine learning methods assume that the measurements are aligned in time, which is often not the case in real data. Here, we introduce a robust longitudinal machine learning method, named likelihood contrasts (LC), which supports study designs with unaligned time points. Our LC method is a binary classifier, which uses linear mixed models for modelling and log-likelihood for decision making. To demonstrate the benefits of our approach, we compared it with existing methods in four simulated and three real data sets. In each simulated data set, LC was the most accurate method, while the real data sets further supported the robust performance of the method. LC is also computationally efficient and easy to use.</p
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