21,518 research outputs found
Representing complex data using localized principal components with application to astronomical data
Often the relation between the variables constituting a multivariate data
space might be characterized by one or more of the terms: ``nonlinear'',
``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or,
more general, ``complex''. In these cases, simple principal component analysis
(PCA) as a tool for dimension reduction can fail badly. Of the many alternative
approaches proposed so far, local approximations of PCA are among the most
promising. This paper will give a short review of localized versions of PCA,
focusing on local principal curves and local partitioning algorithms.
Furthermore we discuss projections other than the local principal components.
When performing local dimension reduction for regression or classification
problems it is important to focus not only on the manifold structure of the
covariates, but also on the response variable(s). Local principal components
only achieve the former, whereas localized regression approaches concentrate on
the latter. Local projection directions derived from the partial least squares
(PLS) algorithm offer an interesting trade-off between these two objectives. We
apply these methods to several real data sets. In particular, we consider
simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and
Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds),
Lecture Notes in Computational Science and Engineering, Springer, 2007, pp.
180--204,
http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-
A control algorithm for autonomous optimization of extracellular recordings
This paper develops a control algorithm that can autonomously position an electrode so as to find and then maintain an optimal extracellular recording position. The algorithm was developed and tested in a two-neuron computational model representative of the cells found in cerebral cortex. The algorithm is based on a stochastic optimization of a suitably defined signal quality metric and is shown capable of finding the optimal recording position along representative sampling directions, as well as maintaining the optimal signal quality in the face of modeled tissue movements. The application of the algorithm to acute neurophysiological recording experiments and its potential implications to chronic recording electrode arrays are discussed
Inferring the photometric and size evolution of galaxies from image simulations
Current constraints on models of galaxy evolution rely on morphometric
catalogs extracted from multi-band photometric surveys. However, these catalogs
are altered by selection effects that are difficult to model, that correlate in
non trivial ways, and that can lead to contradictory predictions if not taken
into account carefully. To address this issue, we have developed a new approach
combining parametric Bayesian indirect likelihood (pBIL) techniques and
empirical modeling with realistic image simulations that reproduce a large
fraction of these selection effects. This allows us to perform a direct
comparison between observed and simulated images and to infer robust
constraints on model parameters. We use a semi-empirical forward model to
generate a distribution of mock galaxies from a set of physical parameters.
These galaxies are passed through an image simulator reproducing the
instrumental characteristics of any survey and are then extracted in the same
way as the observed data. The discrepancy between the simulated and observed
data is quantified, and minimized with a custom sampling process based on
adaptive Monte Carlo Markov Chain methods. Using synthetic data matching most
of the properties of a CFHTLS Deep field, we demonstrate the robustness and
internal consistency of our approach by inferring the parameters governing the
size and luminosity functions and their evolutions for different realistic
populations of galaxies. We also compare the results of our approach with those
obtained from the classical spectral energy distribution fitting and
photometric redshift approach.Our pipeline infers efficiently the luminosity
and size distribution and evolution parameters with a very limited number of
observables (3 photometric bands). When compared to SED fitting based on the
same set of observables, our method yields results that are more accurate and
free from systematic biases.Comment: 24 pages, 12 figures, accepted for publication in A&
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