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Abstract—A new approach to support vector machine (SVM) classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other. Each plane is generated such that it is closest to one of the two data sets and as far as possible from the other data set. Each of the two nonparallel proximal planes is obtained by a single MATLAB command as the eigenvector corresponding to a smallest eigenvalue of a generalized eigenvalue problem. Classification by proximity to two distinct nonlinear surfaces generated by a nonlinear kernel also leads to two simple generalized eigenvalue problems. The effectiveness of the proposed method is demonstrated by tests on simple examples as well as on a number of public data sets. These examples show the advantages of the proposed approach in both computation time and test set correctness. Index Terms—Support vector machines, proximal classification, generalized eigenvalues. 1

Logistic regression with ℓ1 regularization has been proposed as a promising method for feature selection in classification problems. In this paper we describe an efficient interior-point method for solving large-scale ℓ1-regularized logistic regression problems. Small problems with up to a thousand or so features and examples can be solved in seconds on a PC; medium sized problems, with tens of thousands of features and examples, can be solved in tens of seconds (assuming some sparsity in the data). A variation on the basic method, that uses a preconditioned conjugate gradient method to compute the search step, can solve very large problems, with a million features and examples (e.g., the 20 Newsgroups data set), in a few minutes, on a PC. Using warm-start techniques, a good approximation of the entire regularization path can be computed much more efficiently than by solving a family of problems independently.

AbstractÐWe present a novel technique for texture mapping on arbitrary surfaces with minimal distortions by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces made it possible to compute a geodesic distance map from a given surface point in O…n lg n † operations, where n is the number of triangles that represent the surface. We use this method to design a surface flattening approach based on multidimensional scaling �MDS). MDS is a family of methods that map a set of points into a finite dimensional flat �Euclidean) domain, where the only given data is the corresponding distances between every pair of points. The MDS mapping yields minimal changes of the distances between the corresponding points. We then solve an ªinverseº problem and map a flat texture patch onto the curved surface while preserving the structure of the texture. Index TermsÐTexture mapping, multidimensional scaling, fast marching method, Geodesic distance, Euclidean distance. æ 1

in signal and image processing, including image denoising, coding, and super-resolution. # 2001 Academic Press 1. INTRODUCTION Stochastic models of natural images underlie a variety of applications in image processing and low-level computer vision, including image coding, denoising and 1 MW supported by NSERC 1967 fellowship; AW and MW by AFOSR Grant F49620-98-1-0349 and ONR Grant N00014-91-J-1004. Address correspondence to MW. 2 ES supported by NSF Career Grant MIP-9796040 and an Alfred P. Sloan fellowship. 89 1063-5203/01 $35.00 Copyright # 2001 by Academic Press All rights of reproduction in any form reserved. 90 WAINWRIGHT, SIMONCELLI, AND WILLSKY restoration, interpolation and synthesis. Accordingly, the past decade has witnessed an increasing amount of research devoted to developing stochastic models of images (e.g., [19, 38, 45, 48, 55]). Simultaneously, wavel

Realistic behavior of deformable objects is essential for many applications such as simulation for surgical training. Existing techniques of deformable modeling for real time simulation have either used approximate methods that are not physically accurate or linear methods that do not produce reasonable global behavior. Nonlinear finite element methods (FEM) are globally accurate, but conventional FEM is not real time. In this paper, we apply nonlinear FEM using mass lumping to produce a diagonal mass matrix that allows real time computation. Adaptive meshing is necessary to provide sufficient detail where required while minimizing unnecessary computation. We propose a scheme for mesh adaptation based on an extension of the progressive mesh concept, which we call dynamic progressive meshes. 1.

We present the main algorithmic features in the software package SuperLU DIST, a distributedmemory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with a focus on scalability issues, and demonstrate the software’s parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication patterns, which lets us exploit techniques used in parallel sparse Cholesky algorithms to better parallelize both LU decomposition and triangular solution on large-scale distributed machines.

Overlay network monitoring enables distributed Internet applications to detect and recover from path outages and periods of degraded performance within seconds. For an overlay network with n end hosts, existing systems either require O(n²) measurements, and thus lack scalability, or can only estimate the latency but not congestion or failures. Our earlier extended abstract [1] briefly proposes an algebraic approach that selectively monitors k linearly independent paths that can fully describe all the O(n²) paths. The loss rates and latency of these k paths can be used to estimate the loss rates and latency of all other paths. Our scheme only assumes knowledge of the underlying IP topology, with links dynamically varying between lossy and normal. In this

In this paper we review studies of the growth of the Internet and technologies that are useful for information search and retrieval on the Web. We present data on the Internet from several different sources, e.g., current as well as projected number of users, hosts, and Web sites. Although numerical figures vary, overall trends cited

This paper summarizes the BLAS Technical Forum Standard, a speci- #cation of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms and commonly known as the BLAS. The complete standard can be found in #1#, and on the BLAS Technical Forum webpage #http:##www.netlib.org#blas#blast-forum##