88,443 research outputs found
An Exponential Lower Bound on the Complexity of Regularization Paths
For a variety of regularized optimization problems in machine learning,
algorithms computing the entire solution path have been developed recently.
Most of these methods are quadratic programs that are parameterized by a single
parameter, as for example the Support Vector Machine (SVM). Solution path
algorithms do not only compute the solution for one particular value of the
regularization parameter but the entire path of solutions, making the selection
of an optimal parameter much easier.
It has been assumed that these piecewise linear solution paths have only
linear complexity, i.e. linearly many bends. We prove that for the support
vector machine this complexity can be exponential in the number of training
points in the worst case. More strongly, we construct a single instance of n
input points in d dimensions for an SVM such that at least \Theta(2^{n/2}) =
\Theta(2^d) many distinct subsets of support vectors occur as the
regularization parameter changes.Comment: Journal version, 28 Pages, 5 Figure
Performance and optimization of support vector machines in high-energy physics classification problems
In this paper we promote the use of Support Vector Machines (SVM) as a
machine learning tool for searches in high-energy physics. As an example for a
new- physics search we discuss the popular case of Supersymmetry at the Large
Hadron Collider. We demonstrate that the SVM is a valuable tool and show that
an automated discovery- significance based optimization of the SVM
hyper-parameters is a highly efficient way to prepare an SVM for such
applications. A new C++ LIBSVM interface called SVM-HINT is developed and
available on Github.Comment: 20 pages, 6 figure
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
Accelerated Particle Swarm Optimization and Support Vector Machine for Business Optimization and Applications
Business optimization is becoming increasingly important because all business
activities aim to maximize the profit and performance of products and services,
under limited resources and appropriate constraints. Recent developments in
support vector machine and metaheuristics show many advantages of these
techniques. In particular, particle swarm optimization is now widely used in
solving tough optimization problems. In this paper, we use a combination of a
recently developed Accelerated PSO and a nonlinear support vector machine to
form a framework for solving business optimization problems. We first apply the
proposed APSO-SVM to production optimization, and then use it for income
prediction and project scheduling. We also carry out some parametric studies
and discuss the advantages of the proposed metaheuristic SVM.Comment: 12 page
Support Vector Machines in High Energy Physics
This lecture will introduce the Support Vector algorithms for classification
and regression. They are an application of the so called kernel trick, which
allows the extension of a certain class of linear algorithms to the non linear
case. The kernel trick will be introduced and in the context of structural risk
minimization, large margin algorithms for classification and regression will be
presented. Current applications in high energy physics will be discussed.Comment: 11 pages, 12 figures. Part of the proceedings of the Track
'Computational Intelligence for HEP Data Analysis' at iCSC 200
Binarized support vector machines
The widely used Support Vector Machine (SVM) method has shown to yield very good results in
Supervised Classification problems. Other methods such as Classification Trees have become
more popular among practitioners than SVM thanks to their interpretability, which is an important
issue in Data Mining.
In this work, we propose an SVM-based method that automatically detects the most important
predictor variables, and the role they play in the classifier. In particular, the proposed method is
able to detect those values and intervals which are critical for the classification. The method
involves the optimization of a Linear Programming problem, with a large number of decision
variables. The numerical experience reported shows that a rather direct use of the standard
Column-Generation strategy leads to a classification method which, in terms of classification
ability, is competitive against the standard linear SVM and Classification Trees. Moreover, the
proposed method is robust, i.e., it is stable in the presence of outliers and invariant to change of
scale or measurement units of the predictor variables.
When the complexity of the classifier is an important issue, a wrapper feature selection method is
applied, yielding simpler, still competitive, classifiers
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