Julia Neumann

Anatomy of a native XML base management system

Abstract. Several alternatives to manage large XML document collections exist, ranging from file systems over relational or other database systems to specifically tailored XML base management systems. 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 multi-user synchronization - as well as query processing for XML.

Combined SVM-Based Feature Selection and Classification

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.

Dual-tree complex wavelet transform in the frequency domain and an application to signal classification

We examine Kingsburys 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.

Splines in Higher Order TV Regularization

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 W2,0m. From this point of view, the solution of our minimization problem has a sparse representation in terms of discrete fundamental splines.

Natix: A Technology Overview

Several alternatives to manage large XML document collections exist, ranging from file systems over relational or other database systems to specifically tailored XML base management systems. In this paper we review 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 indicate how almost every component in a database system is affected in terms of adequacy and performance. We show what kind of problems have to be tackled when designing and optimizing areas such as storage, transaction management comprising recovery and multi-user synchronization as well as query processing for XML.

Relations between higher order TV regularization and support vector regression

We study the connection between higher order total variation (TV) regularization and support vector regression (SVR) with spline kernels in a one-dimensional discrete setting. We prove that the contact problem arising in the tube formulation of the TV minimization problem is equivalent to the SVR problem. Since the SVR problem can be solved by standard quadratic programming methods this provides us with an algorithm for the solution of the contact problem even for higher order derivatives. Our numerical experiments illustrate the approach for various orders of derivatives and show its close relation to corresponding nonlinear diffusion and diffusion–reaction equations.

SVM-Based Feature Selection by Direct Objective Minimisation

We propose various novel embedded approaches for (simultaneous) feature selection and classification within a general optimisation framework. In particular, we include linear and nonlinear SVMs. We apply difference of convex functions programming to solve our problems and present results for artificial and real-world data.

Efficient wavelet adaptation for hybrid wavelet-large margin classifiers

Hybrid wavelet-large margin classifiers have recently proven to solve difficult signal classification problems in cases where solely using a large margin classifier like, e.g., the Support Vector Machine may fail. In this paper, we evaluate several criteria rating feature sets obtained from various orthogonal filter banks for the classification by a Support Vector Machine. Appropriate criteria may then be used for adapting the wavelet filter with respect to the subsequent support vector classification. Our results show that criteria which are computationally more efficient than the radius-margin Support Vector Machine error bound are sufficient for our filter adaptation and, hence, feature selection. Further, we propose an adaptive search algorithm that, once the criterion is fixed, efficiently finds the optimal wavelet filter. As an interesting byproduct we prove a theorem which allows the computation of the radius of a set of vectors by a standard Support Vector Machine.

Feasible Adaptation Criteria for Hybrid Wavelet : Large Margin Classifiers

In the context of signal classification, this paper assembles and compares criteria to easily judge the discrimination quality of a set of feature vectors. The quality measures are based on the assumption that a Support Vector Machine is used for the final classification. Thus, the ultimate criterion is a large margin separating the two classes. We apply the criteria to control the feature extraction process for signal classification. Adaptive features related to the shape of the signals are extracted by wavelet filtering followed by a nonlinear map. To be able to test many features, the criteria are easily computable while still reliably predicting the classification performance. We also present a novel approach for computing the radius of a set of points in feature space. The radius, in relation to the margin, forms the most commonly used error bound for Support Vector Machines. For isotropic kernels, the problem of radius computation can be reduced to a common Support Vector Machine classification problem.