4,745 research outputs found
Bivariate hierarchical Hermite spline quasi--interpolation
Spline quasi-interpolation (QI) is a general and powerful approach for the
construction of low cost and accurate approximations of a given function. In
order to provide an efficient adaptive approximation scheme in the bivariate
setting, we consider quasi-interpolation in hierarchical spline spaces. In
particular, we study and experiment the features of the hierarchical extension
of the tensor-product formulation of the Hermite BS quasi-interpolation scheme.
The convergence properties of this hierarchical operator, suitably defined in
terms of truncated hierarchical B-spline bases, are analyzed. A selection of
numerical examples is presented to compare the performances of the hierarchical
and tensor-product versions of the scheme
Nonparametric Transient Classification using Adaptive Wavelets
Classifying transients based on multi band light curves is a challenging but
crucial problem in the era of GAIA and LSST since the sheer volume of
transients will make spectroscopic classification unfeasible. Here we present a
nonparametric classifier that uses the transient's light curve measurements to
predict its class given training data. It implements two novel components: the
first is the use of the BAGIDIS wavelet methodology - a characterization of
functional data using hierarchical wavelet coefficients. The second novelty is
the introduction of a ranked probability classifier on the wavelet coefficients
that handles both the heteroscedasticity of the data in addition to the
potential non-representativity of the training set. The ranked classifier is
simple and quick to implement while a major advantage of the BAGIDIS wavelets
is that they are translation invariant, hence they do not need the light curves
to be aligned to extract features. Further, BAGIDIS is nonparametric so it can
be used for blind searches for new objects. We demonstrate the effectiveness of
our ranked wavelet classifier against the well-tested Supernova Photometric
Classification Challenge dataset in which the challenge is to correctly
classify light curves as Type Ia or non-Ia supernovae. We train our ranked
probability classifier on the spectroscopically-confirmed subsample (which is
not representative) and show that it gives good results for all supernova with
observed light curve timespans greater than 100 days (roughly 55% of the
dataset). For such data, we obtain a Ia efficiency of 80.5% and a purity of
82.4% yielding a highly competitive score of 0.49 whilst implementing a truly
"model-blind" approach to supernova classification. Consequently this approach
may be particularly suitable for the classification of astronomical transients
in the era of large synoptic sky surveys.Comment: 14 pages, 8 figures. Published in MNRA
Support vector machine for functional data classification
In many applications, input data are sampled functions taking their values in
infinite dimensional spaces rather than standard vectors. This fact has complex
consequences on data analysis algorithms that motivate modifications of them.
In fact most of the traditional data analysis tools for regression,
classification and clustering have been adapted to functional inputs under the
general name of functional Data Analysis (FDA). In this paper, we investigate
the use of Support Vector Machines (SVMs) for functional data analysis and we
focus on the problem of curves discrimination. SVMs are large margin classifier
tools based on implicit non linear mappings of the considered data into high
dimensional spaces thanks to kernels. We show how to define simple kernels that
take into account the unctional nature of the data and lead to consistent
classification. Experiments conducted on real world data emphasize the benefit
of taking into account some functional aspects of the problems.Comment: 13 page
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