11,487 research outputs found
Representation Learning: A Review and New Perspectives
The success of machine learning algorithms generally depends on data
representation, and we hypothesize that this is because different
representations can entangle and hide more or less the different explanatory
factors of variation behind the data. Although specific domain knowledge can be
used to help design representations, learning with generic priors can also be
used, and the quest for AI is motivating the design of more powerful
representation-learning algorithms implementing such priors. This paper reviews
recent work in the area of unsupervised feature learning and deep learning,
covering advances in probabilistic models, auto-encoders, manifold learning,
and deep networks. This motivates longer-term unanswered questions about the
appropriate objectives for learning good representations, for computing
representations (i.e., inference), and the geometrical connections between
representation learning, density estimation and manifold learning
Proton imaging of stochastic magnetic fields
Recent laser-plasma experiments report the existence of dynamically
significant magnetic fields, whose statistical characterisation is essential
for understanding the physical processes these experiments are attempting to
investigate. In this paper, we show how a proton imaging diagnostic can be used
to determine a range of relevant magnetic field statistics, including the
magnetic-energy spectrum. To achieve this goal, we explore the properties of an
analytic relation between a stochastic magnetic field and the image-flux
distribution created upon imaging that field. We conclude that features of the
beam's final image-flux distribution often display a universal character
determined by a single, field-scale dependent parameter - the contrast
parameter - which quantifies the relative size of the correlation length of the
stochastic field, proton displacements due to magnetic deflections, and the
image magnification. For stochastic magnetic fields, we establish the existence
of four contrast regimes - linear, nonlinear injective, caustic and diffusive -
under which proton-flux images relate to their parent fields in a qualitatively
distinct manner. As a consequence, it is demonstrated that in the linear or
nonlinear injective regimes, the path-integrated magnetic field experienced by
the beam can be extracted uniquely, as can the magnetic-energy spectrum under a
further statistical assumption of isotropy. This is no longer the case in the
caustic or diffusive regimes. We also discuss complications to the
contrast-regime characterisation arising for inhomogeneous, multi-scale
stochastic fields, as well as limitations currently placed by experimental
capabilities on extracting magnetic field statistics. The results presented in
this paper provide a comprehensive description of proton images of stochastic
magnetic fields, with applications for improved analysis of given proton-flux
images.Comment: Main paper pp. 1-29; appendices pp. 30-84. 24 figures, 2 table
Disparity and Optical Flow Partitioning Using Extended Potts Priors
This paper addresses the problems of disparity and optical flow partitioning
based on the brightness invariance assumption. We investigate new variational
approaches to these problems with Potts priors and possibly box constraints.
For the optical flow partitioning, our model includes vector-valued data and an
adapted Potts regularizer. Using the notation of asymptotically level stable
functions we prove the existence of global minimizers of our functionals. We
propose a modified alternating direction method of minimizers. This iterative
algorithm requires the computation of global minimizers of classical univariate
Potts problems which can be done efficiently by dynamic programming. We prove
that the algorithm converges both for the constrained and unconstrained
problems. Numerical examples demonstrate the very good performance of our
partitioning method
A semidiscrete version of the Citti-Petitot-Sarti model as a plausible model for anthropomorphic image reconstruction and pattern recognition
In his beautiful book [66], Jean Petitot proposes a sub-Riemannian model for
the primary visual cortex of mammals. This model is neurophysiologically
justified. Further developments of this theory lead to efficient algorithms for
image reconstruction, based upon the consideration of an associated
hypoelliptic diffusion. The sub-Riemannian model of Petitot and Citti-Sarti (or
certain of its improvements) is a left-invariant structure over the group
of rototranslations of the plane. Here, we propose a semi-discrete
version of this theory, leading to a left-invariant structure over the group
, restricting to a finite number of rotations. This apparently very
simple group is in fact quite atypical: it is maximally almost periodic, which
leads to much simpler harmonic analysis compared to Based upon this
semi-discrete model, we improve on previous image-reconstruction algorithms and
we develop a pattern-recognition theory that leads also to very efficient
algorithms in practice.Comment: 123 pages, revised versio
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