4,886 research outputs found
Training Support Vector Machines Using Frank-Wolfe Optimization Methods
Training a Support Vector Machine (SVM) requires the solution of a quadratic
programming problem (QP) whose computational complexity becomes prohibitively
expensive for large scale datasets. Traditional optimization methods cannot be
directly applied in these cases, mainly due to memory restrictions.
By adopting a slightly different objective function and under mild conditions
on the kernel used within the model, efficient algorithms to train SVMs have
been devised under the name of Core Vector Machines (CVMs). This framework
exploits the equivalence of the resulting learning problem with the task of
building a Minimal Enclosing Ball (MEB) problem in a feature space, where data
is implicitly embedded by a kernel function.
In this paper, we improve on the CVM approach by proposing two novel methods
to build SVMs based on the Frank-Wolfe algorithm, recently revisited as a fast
method to approximate the solution of a MEB problem. In contrast to CVMs, our
algorithms do not require to compute the solutions of a sequence of
increasingly complex QPs and are defined by using only analytic optimization
steps. Experiments on a large collection of datasets show that our methods
scale better than CVMs in most cases, sometimes at the price of a slightly
lower accuracy. As CVMs, the proposed methods can be easily extended to machine
learning problems other than binary classification. However, effective
classifiers are also obtained using kernels which do not satisfy the condition
required by CVMs and can thus be used for a wider set of problems
Reduced basis method for source mask optimization
Image modeling and simulation are critical to extending the limits of leading
edge lithography technologies used for IC making. Simultaneous source mask
optimization (SMO) has become an important objective in the field of
computational lithography. SMO is considered essential to extending immersion
lithography beyond the 45nm node. However, SMO is computationally extremely
challenging and time-consuming. The key challenges are due to run time vs.
accuracy tradeoffs of the imaging models used for the computational
lithography. We present a new technique to be incorporated in the SMO flow.
This new approach is based on the reduced basis method (RBM) applied to the
simulation of light transmission through the lithography masks. It provides a
rigorous approximation to the exact lithographical problem, based on fully
vectorial Maxwell's equations. Using the reduced basis method, the optimization
process is divided into an offline and an online steps. In the offline step, a
RBM model with variable geometrical parameters is built self-adaptively and
using a Finite Element (FEM) based solver. In the online step, the RBM model
can be solved very fast for arbitrary illumination and geometrical parameters,
such as dimensions of OPC features, line widths, etc. This approach
dramatically reduces computational costs of the optimization procedure while
providing accuracy superior to the approaches involving simplified mask models.
RBM furthermore provides rigorous error estimators, which assure the quality
and reliability of the reduced basis solutions. We apply the reduced basis
method to a 3D SMO example. We quantify performance, computational costs and
accuracy of our method.Comment: BACUS Photomask Technology 201
Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training
We consider the convex quadratic linearly constrained problem
with bounded variables and with huge and dense Hessian matrix that arises
in many applications such as the training problem of bias support vector machines.
We propose a decomposition algorithmic scheme suitable to parallel implementations
and we prove global convergence under suitable conditions. Focusing
on support vector machines training, we outline how these assumptions
can be satisfied in practice and we suggest various specific implementations.
Extensions of the theoretical results to general linearly constrained problem
are provided. We included numerical results on support vector machines with
the aim of showing the viability and the effectiveness of the proposed scheme
Thermodynamic analysis of the Quantum Critical behavior of Ce-lattice compounds
A systematic analysis of low temperature magnetic phase diagrams of Ce
compounds is performed in order to recognize the thermodynamic conditions to be
fulfilled by those systems to reach a quantum critical regime and,
alternatively, to identify other kinds of low temperature behaviors. Based on
specific heat () and entropy () results, three different types of
phase diagrams are recognized: i) with the entropy involved into the ordered
phase () decreasing proportionally to the ordering temperature
(), ii) those showing a transference of degrees of freedom from the
ordered phase to a non-magnetic component, with their jump
() vanishing at finite temperature, and iii) those ending in a
critical point at finite temperature because their do not decrease
with producing an entropy accumulation at low temperature.
Only those systems belonging to the first case, i.e. with as
, can be regarded as candidates for quantum critical behavior.
Their magnetic phase boundaries deviate from the classical negative curvature
below \,K, denouncing frequent misleading extrapolations down to
T=0. Different characteristic concentrations are recognized and analyzed for
Ce-ligand alloyed systems. Particularly, a pre-critical region is identified,
where the nature of the magnetic transition undergoes significant
modifications, with its discontinuity strongly
affected by magnetic field and showing an increasing remnant entropy at . Physical constraints arising from the third law at are discussed
and recognized from experimental results
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