Abstract. Feature selection is an important combinatorial optimisation problem in the context of supervised pattern classification. This paper presents four novel continuous feature selection approaches directly minimising the classifier performance. In particular, we include linear and nonlinear Support Vector Machine classifiers. The key ideas of our approaches are additional regularisation and embedded nonlinear feature selection. To solve our optimisation problems, we apply difference of convex functions programming which is a general framework for non-convex continuous optimisation. Experiments with artificial data and with various real-world problems including organ classification in computed tomography scans demonstrate that our methods accomplish the desired feature selection and classification performance simultaneously.

Several alternatives to manage large XML document collections exist, ranging from file systems over relational or other database systems to specifically tailored XML repositories. In this paper we give a tour of Natix, a database management system designed from scratch for storing and processing XML data. Contrary to the common belief that management of XML data is just another application for traditional databases like relational systems, we illustrate how almost every component in a database system is affected in terms of adequacy and performance. We show how to design and optimize areas such as storage, transaction management comprising recovery and multiuser synchronization as well as query processing for XML.

Splines play an important role as solutions of various interpolation and approximation problems that minimize special functionals in some smoothness spaces. In this paper, we show in a strictly discrete setting that splines of degree m−1 solve also a minimization problem with quadratic data term and m-th order total variation (TV) regularization term. In contrast to problems with quadratic regularization terms involving m-th order derivatives, the spline knots are not known in advance but depend on the input data and the regularization parameter λ. More precisely, the spline knots are determined by the contact points of the m-th discrete antiderivative of the solution with the tube of width 2λ around the m-th discrete antiderivative of the input data. We point out that the dual formulation of our minimization problem can be considered as support vector regression problem in the discrete counterpart of the Sobolev space W m 2,0 . From this point of view, the solution of our minimization problem has a sparse representation in terms of discrete fundamental splines.

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We examine Kingsbury's dual-tree complex wavelet transform in the frequency domain, where it can be formulated for standard wavelet filters without special filter design and apply the method to the classification of signals.The obtained transforms achieve low shift sensitivity and better directionality compared to the real discrete wavelet transform while retaining the perfect reconstruction property.