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In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Laboratories [3, 6, 8, 24]. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. The main idea behind the technique is to separate the classes with a surface that maximizes the margin between them. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle [23]. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Since Structural Risk Minimization is an inductive principle that aims at minimizing a bound on the generalization error of a model, rather than minimizing the Mean Square Error over the data set (as Empirical Risk Minimization methods do), training a SVM to obtain the maximum margin classi er requires a different objective function. This objective function is then optimized by solving a large-scale quadratic programming problem with linear and box constraints. The problem is considered challenging, because the quadratic form is completely dense, so the memory

In this paper we discuss the use of non-stationary penalty functions to solve general nonlinear programming problems (NP ) using real-valued GAs. The non-stationary penalty is a function of the generation number; as the number of generations increases so does the penalty. Therefore, as the penalty increases it puts more and more selective pressure on the GA to find a feasible solution. The ideas presented in this paper come from two basic areas: calculus-based nonlinear programming and simulated annealing. The non-stationary penalty methods are tested on four NP test cases and the effectiveness of these methods are reported.. 1 Introduction Constrained function optimization is an extremely important tool used in almost every facet of engineering, operations research, mathematics, and etc. Constrained optimization can be represented as a nonlinear programming problem. The general nonlinear programming problem is defined as follows: (NP ) minimize f(X) subject to (nonlinear and linear)...

Abstract. The decomposition method is currently one of the major methods for solving support vector machines. An important issue of this method is the selection of working sets. In this paper through the design of decomposition methods for bound-constrained SVM formulations we demonstrate that the working set selection is not a trivial task. Then from the experimental analysis we propose a simple selection of the working set which leads to faster convergences for difficult cases. Numerical experiments on different types of problems are conducted to demonstrate the viability of the proposed method.

2 Everything Old Is New Again: A Fresh Look at Historical

In the area of automatic parallelization of programs, analyzing and transforming loop nests with parametric affine loop bounds requires fundamental mathematical results. The most common geometrical model of iteration spaces, called the polytope model, is based on mathematics dealing with convex and discrete geometry, linear programming, combinatorics and geometry of numbers. In this paper, we present automatic methods for computing the parametric vertices and the Ehrhart polynomial, i.e. a parametric expression of the number of integer points, of a polytope defined by a set of parametric linear constraints. These methods have many applications in analysis and transformations of nested loop programs. The paper is illustrated with exact symbolic array dataflow analysis, estimation of execution time, and with the computation of the maximum available parallelism of given loop nests.

A fundamental task in data analysis is understanding the differences between several con-trasting groups. These groups can represent different classes of objects, such as male or female students, or the same group over time, e.g. freshman students in 1993 through 1998. We present the problem of mining contrast sets: conjunctions of attributes and values that differ meaningfully in their distribution across groups. We provide a search algorithm for mining contrast sets with pruning rules that drastically reduce the computational complexity. Once the contrast sets are found, we post-process the results to present a subset that are surprising to the user given what we have already shown. We explicitly control the probability of Type I error (false positives) and guarantee a maximum error rate for the entire analysis by using Bonferroni corrections.

Active contour and surface models, also known as deformable models, are powerful image segmentation techniques. Geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior, parameterization independence, and ease of implementation. However, a long claimed advantage of geometric deformable models—the ability to automatically handle topology changes—turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved. In this paper, we present a new class of geometric deformable models designed using a novel topology-preserving level set method, which achieves topology preservation by applying the simple point concept from digital topology. These new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces. Moreover, since the topology-preserving constraint is enforced efficiently through local computations, the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models. Several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm.

This paper introduces an approach to performance animation that employs video cameras and a small set of retro-reflective markers to create a low-cost, easy-to-use system that might someday be practical for home use. The low-dimensional control signals from the user's performance are supplemented by a database of pre-recorded human motion. At run time, the system automatically learns a series of local models from a set of motion capture examples that are a close match to the marker locations captured by the cameras. These local models are then used to reconstruct the motion of the user as a full-body animation. We demonstrate the power of this approach with real-time control of six different behaviors using two video cameras and a small set of retro-reflective markers. We compare the resulting animation to animation from commercial motion capture equipment with a full set of markers.