LIBSVM is a library for Support Vector Machines (SVMs). We have been actively developing this package since the year 2000. The goal is to help users to easily apply SVM to their applications. LIBSVM has gained wide popularity in machine learning and many other areas. In this article, we present all implementation details of LIBSVM. Issues such as solving SVM optimization problems theoretical convergence multiclass classification probability estimates and parameter selection are discussed in detail.

The nu-support vector machine (nu-SVM) for classification proposed by Schölkopf, Smola, Williamson, and Bartlett (2000) has the advantage of using a parameter nu on controlling the number of support vectors. In this article, we investigate the relation between nu-SVM and C-SVM in detail. We show that in general they are two different problems with the same optimal solution set. Hence, we may expect that many numerical aspects of solving them are similar. However, compared to regular C-SVM, the formulation of nu-SVM is more complicated, so up to now there have been no effective methods for solving large-scale nu-SVM. We propose a decomposition method for nu-SVM that is competitive with existing methods for C-SVM. We also discuss the behavior of nu-SVM by some numerical experiments.

We discuss the relation between epsilon-support vector regression (epsilon-SVR) and nu-support vector regression (nu-SVR). In particular, we focus on properties that are different from those of C-support vector classification (C-SVC) and nu-support vector classification (nu-SVC). We then discuss some issues that do not occur in the case of classification: the possible range of epsilon and the scaling of target values. A practical decomposition method for nu-SVR is implemented, and computational experiments are conducted. We show some interesting numerical observations specific to regression.

A one-dimensional finite difference analysis describing the transient ther mal response of fiber-reinforced organic matrix composte plates subjected to intense surface heating is presented. The effects of fiber ablation, matrix decomposition, and radiation and convective heat losses are included in the formulation. Numerical results are in good agreement with mass loss and thermocouple mesurements obtained from laser irradiation tests on AS/3501-6 graphite epoxy coupons. A steady state analytic solution is also given which provides a reasonable estimate of the surface recession rate over much of the surface irradiation period.

An analytical procedure is presented for predicting the loss in integrity of composite structures subjected to simultaneous intense heating and applied mechanical loads. An in tegral part of the method is a nonlinear, two-dimensional, finite difference thermal analysis which considers the effects of surface ablation, re-irradiation losses, and temperature-dependent thermophysical properties. Another important feature of the structural survivability model is a flat-plate finite element code, based on the Mindlin theory, which is coupled to a maximum stress failure criterion. Predictions from the analysis methodology are compared with experimental results obtained on 24, 48, and 96 ply graphite epoxy tension specimens which were spot-irradiated at various intensity levels.