Currently, various hardware and software companies are developing augmented reality devices, most prominently Microsoft with its Hololens. Besides gaming, such devices can be used for serious pervasive applications, like interactive mobile simulations to support engineers in the field. Interactive simulations have high demands on resources, which the mobile device alone is unable to satisfy. Therefore, we propose a framework to support mobile simulations by distributing the computation between mobile device and a remote server. For the computation of parameter-dependent solutions of the simulation, we use the reduced basis method, which allows to drastically reduce the computation time and energy consumption. We present three approaches for the distributed execution of the reduced basis method between mobile device and server. Evaluations show that we can speed-up the numerical computation to over 131 times while using 73 times less energy compared to offloading everything to a server.

Kernel methods are a class of well established and successful algorithms for pattern analysis thanks to their mathematical elegance and good performance. Numerous nonlinear extensions of pattern recognition techniques have been proposed so far based on the so-called kernel trick. The objective of this paper is twofold. First, we derive an additional kernel tool that is still missing, namely kernel quadratic discriminant (KQD). We discuss different formulations of KQD based on the regularized kernel Mahalanobis distance in both complete and class-related subspaces. Secondly, we propose suitable extensions of kernel linear and quadratic discriminants to indefinite kernels. We provide classifiers that are applicable to kernels defined by any symmetric similarity measure. This is important in practice because problem-suited proximity measures often violate the requirement of positive definiteness. As in the traditional case, KQD can be advantageous for data with unequal class spreads in the kernel-induced spaces, which cannot be well separated by a linear discriminant. We illustrate this on artificial and real data for both positive definite and indefinite kernels.

Indefinite kernels arise in practice, e.g. from problem-specific kernel construction. Therefore, it is necessary to understand the behavior and suitability of classifiers in the corresponding indefinite inner product spaces. In this paper we address the Indefinite Kernel Fisher Discriminant (IKFD). First, we give the geometric interpretation of the Fisher Discriminant in indefinite inner product spaces. We show that IKFD is closely related to the well-known formulation of the traditional Kernel Fisher Discriminant derived for positive definite kernels. Practical implications are that IKFD can be directly applied to indefinite kernels without manipulation of the kernel matrix. Experiments demonstrate the geometrically intuitive classification and enable comparisons to other indefinite kernel classifiers.

Kernel methods are becoming increasingly popular for various kinds of machine learning tasks, the most famous being the support vector machine (SVM) for classification. The SVM is well understood when using conditionally positive definite (cpd) kernel functions. However, in practice, non-cpd kernels arise and demand application in SVMs. The procedure of "plugging" these indefinite kernels in SVMs often yields good empirical classification results. However, they are hard to interpret due to missing geometrical and theoretical understanding. In this paper, we provide a step toward the comprehension of SVM classifiers in these situations. We give a geometric interpretation of SVMs with indefinite kernel functions. We show that such SVMs are optimal hyperplane classifiers not by margin maximization, but by minimization of distances between convex hulls in pseudo-Euclidean spaces. By this, we obtain a sound framework and motivation for indefinite SVMs. This interpretation is the basis for further theoretical analysis, e.g., investigating uniqueness, and for the derivation of practical guidelines like characterizing the suitability of indefinite SVMs.