Takafumi Kanamori 1,4,*, Shuhei Fujiwara 2 and Akiko Takeda 3,4 1 Department of Computer Science and Mathematical Informatics, Nagoya University, Nagoya 464-8601, Japan 2 TOPGATE Co. Ltd., Bunkyo-ku, Tokyo 113-0033, Japan; [email protected] 3 Institute of Statistical Mathematics, Tokyo 190-8562, Japan; [email protected] 4 RIKEN Center for Advanced Intelligence Project, Tokyo 103-0027, J...

Let X be a metrizable compact convex subset of a locally convex space. Using Choquet's Theorem, wc determine the structure of the support point set of X when X has countably many extreme points. We also characterize the support points of certain families of analytic functions.

Floating-point arithmetic is often seen as untrustworthy. We show how manipulating precisions according to the following rules of thumb enhances the reliability of and removes surprises from calculations: • Store data narrowly, • compute intermediates widely, and • derive properties widely. Further, we describe a typing system for floating point that both supports and is supported by these rule...

The support vector machine (SVM) is one of the most successful learning methods for solving classification problems. Despite its popularity, SVM has a serious drawback, that is sensitivity to outliers in training samples. The penalty on misclassification is defined by a convex loss called the hinge loss, and the unboundedness of the convex loss causes the sensitivity to outliers. To deal with o...

Article history: Received 14 October 2011 Accepted 27 March 2012 Available online xxxx Communicated by D. Wagner

This paper explores the possibilities of point cloud reduction using  insensitive support vector regression (-SVR).  -SVR is a technique that can carry out the regression using different kernel functions (sigmoid, radial basis function, B-spline, spline, etc.) and it is suitable for detection of flat regions and regions with high curvature in scanned data. Using  -SVR the density of preserv...