56,929 research outputs found
On landmark selection and sampling in high-dimensional data analysis
In recent years, the spectral analysis of appropriately defined kernel
matrices has emerged as a principled way to extract the low-dimensional
structure often prevalent in high-dimensional data. Here we provide an
introduction to spectral methods for linear and nonlinear dimension reduction,
emphasizing ways to overcome the computational limitations currently faced by
practitioners with massive datasets. In particular, a data subsampling or
landmark selection process is often employed to construct a kernel based on
partial information, followed by an approximate spectral analysis termed the
Nystrom extension. We provide a quantitative framework to analyse this
procedure, and use it to demonstrate algorithmic performance bounds on a range
of practical approaches designed to optimize the landmark selection process. We
compare the practical implications of these bounds by way of real-world
examples drawn from the field of computer vision, whereby low-dimensional
manifold structure is shown to emerge from high-dimensional video data streams.Comment: 18 pages, 6 figures, submitted for publicatio
Kinetic-Ion Simulations Addressing Whether Ion Trapping Inflates Stimulated Brillouin Backscattering Reflectivities
An investigation of the possible inflation of stimulated Brillouin
backscattering (SBS) due to ion kinetic effects is presented using
electromagnetic particle simulations and integrations of three-wave
coupled-mode equations with linear and nonlinear models of the nonlinear ion
physics. Electrostatic simulations of linear ion Landau damping in an ion
acoustic wave, nonlinear reduction of damping due to ion trapping, and
nonlinear frequency shifts due to ion trapping establish a baseline for
modeling the electromagnetic SBS simulations. Systematic scans of the laser
intensity have been undertaken with both one-dimensional particle simulations
and coupled-mode-equations integrations, and two values of the electron-to-ion
temperature ratio (to vary the linear ion Landau damping) are considered. Three
of the four intensity scans have evidence of SBS inflation as determined by
observing more reflectivity in the particle simulations than in the
corresponding three-wave mode-coupling integrations with a linear ion-wave
model, and the particle simulations show evidence of ion trapping.Comment: 56 pages, 20 figure
Multivariate side-band subtraction using probabilistic event weights
A common situation in experimental physics is to have a signal which can not
be separated from a non-interfering background through the use of any cut. In
this paper, we describe a procedure for determining, on an event-by-event
basis, a quality factor (-factor) that a given event originated from the
signal distribution. This procedure generalizes the "side-band" subtraction
method to higher dimensions without requiring the data to be divided into bins.
The -factors can then be used as event weights in subsequent analysis
procedures, allowing one to more directly access the true spectrum of the
signal.Comment: 17 pages, 9 figure
Exploring Zeptosecond Quantum Equilibration Dynamics: From Deep-Inelastic to Fusion-Fission Outcomes in Ni+Ni Reactions
Energy dissipative processes play a key role in how quantum many-body systems
dynamically evolve towards equilibrium. In closed quantum systems, such
processes are attributed to the transfer of energy from collective motion to
single-particle degrees of freedom; however, the quantum many-body dynamics of
this evolutionary process are poorly understood. To explore energy dissipative
phenomena and equilibration dynamics in one such system, an experimental
investigation of deep-inelastic and fusion-fission outcomes in the
Ni+Ni reaction has been carried out. Experimental outcomes have
been compared to theoretical predictions using Time Dependent Hartree Fock and
Time Dependent Random Phase Approximation approaches, which respectively
incorporate one-body energy dissipation and fluctuations. Excellent
quantitative agreement has been found between experiment and calculations,
indicating that microscopic models incorporating one-body dissipation and
fluctuations provide a potential tool for exploring dissipation in low-energy
heavy ion collisions.Comment: 11 pages, 9 figures, 1 table, including Supplemental Material -
Version accepted for publication in Physical Review Letter
Using generative models for handwritten digit recognition
We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B-splines with Gaussian ``ink generators'' spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. (1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. (2) During the process of explaining the image, generative models can perform recognition driven segmentation. (3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. (4) Unlike many other recognition schemes it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is it requires much more computation than more standard OCR techniques
On the relationship between Bayesian error bars and the input data density
We investigate the dependence of Bayesian error bars on the distribution of data in input space. For generalized linear regression models we derive an upper bound on the error bars which shows that, in the neighbourhood of the data points, the error bars are substantially reduced from their prior values. For regions of high data density we also show that the contribution to the output variance due to the uncertainty in the weights can exhibit an approximate inverse proportionality to the probability density. Empirical results support these conclusions
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