6,169 research outputs found
A computational framework for sound segregation in music signals
Tese de doutoramento. Engenharia Electrotécnica e de Computadores. Faculdade de Engenharia. Universidade do Porto. 200
The geometry of kernelized spectral clustering
Clustering of data sets is a standard problem in many areas of science and
engineering. The method of spectral clustering is based on embedding the data
set using a kernel function, and using the top eigenvectors of the normalized
Laplacian to recover the connected components. We study the performance of
spectral clustering in recovering the latent labels of i.i.d. samples from a
finite mixture of nonparametric distributions. The difficulty of this label
recovery problem depends on the overlap between mixture components and how
easily a mixture component is divided into two nonoverlapping components. When
the overlap is small compared to the indivisibility of the mixture components,
the principal eigenspace of the population-level normalized Laplacian operator
is approximately spanned by the square-root kernelized component densities. In
the finite sample setting, and under the same assumption, embedded samples from
different components are approximately orthogonal with high probability when
the sample size is large. As a corollary we control the fraction of samples
mislabeled by spectral clustering under finite mixtures with nonparametric
components.Comment: Published at http://dx.doi.org/10.1214/14-AOS1283 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Estimating Local Function Complexity via Mixture of Gaussian Processes
Real world data often exhibit inhomogeneity, e.g., the noise level, the
sampling distribution or the complexity of the target function may change over
the input space. In this paper, we try to isolate local function complexity in
a practical, robust way. This is achieved by first estimating the locally
optimal kernel bandwidth as a functional relationship. Specifically, we propose
Spatially Adaptive Bandwidth Estimation in Regression (SABER), which employs
the mixture of experts consisting of multinomial kernel logistic regression as
a gate and Gaussian process regression models as experts. Using the locally
optimal kernel bandwidths, we deduce an estimate to the local function
complexity by drawing parallels to the theory of locally linear smoothing. We
demonstrate the usefulness of local function complexity for model
interpretation and active learning in quantum chemistry experiments and fluid
dynamics simulations.Comment: 19 pages, 16 figure
Computer simulation of liquid crystals
A review is presented of molecular and mesoscopic computer simulations of liquid crystalline systems. Molecular simulation approaches applied to such systems are described and the key findings for bulk phase behaviour are reported. Following this, recently developed lattice Boltzmann (LB) approaches to the mesoscale modelling of nemato-dynamics are reviewed. The article concludes with a discussion of possible areas for future development in this field.</p
Analytical QCD and multiparticle production
We review the perturbative approach to multiparticle production in hard
collision processes. It is investigated to what extent parton level analytical
calculations at low momentum cut-off can reproduce experimental data on the
hadronic final state. Systematic results are available for various observables
with the next-to-leading logarithmic accuracy (the so-called modified leading
logarithmic approximation - MLLA). We introduce the analytical formalism and
then discuss recent applications concerning multiplicities, inclusive spectra,
correlations and angular flows in multi-jet events. In various cases the
perturbative picture is surprisingly successful, even for very soft particle
production.Comment: 97 pages, LaTeX, 22 figures, uses sprocl.sty (included
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