Rule learning has the major advantage of understandability by human experts when performing knowledge discovery within the biomedical domain. Many rule learning algorithms require discrete data in order to learn the IF-THEN rule sets. This requirement makes the selection of a discretization technique an important step in rule learning. We compare the performance of one standard technique, Fayya...

In this paper, we will consider an hp-finite elements discretization of a highly indefinite Helmholtz problem by some dG formulation which is based on the ultra-weak variational formulation by Cessenat and Deprés. We will introduce an a posteriori error estimator and derive reliability and efficiency estimates which are explicit with respect to the wavenumber and the discretization parameters h...

This study analyzes the effect of discretization on classification of datasets including continuous valued features. Six datasets from UCI which containing continuous valued features are discretized with entropy-based discretization method. The performance improvement between the dataset with original features and the dataset with discretized features is compared with k-nearest neighbors, Naive...

An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is shown to converge quadratically to the value function for the original problem. This is done by using that the value functions solve similar Hamilton-Jacobi equ...

The development of an effective and efficient method for discretization of continuous variables is an important problem to be solved in developing generally applicable methods for data mining. In Ho and Scott 1997, we describe a new technique for discretization of continuous variables based on zeta, a measure of strength of association between nominal variables. The old zeta method partitions a...

We present a vertex-centered finite volume method for the fully coupled, fully implicit discretization of two-phase flow in fractured porous media. Fractures are discretely modeled as lower dimensional elements. The method works on unstructured, locally refined grids and on parallel computers with distributed memory. An implicit time discretization is employed and the nonlinear systems of equat...

In this paper, we describe an efficient method for 3D image segmentation. The method uses a PDE model – the so called generalized subjective surface equation which is an equation of advection-diffusion type. The main goal is to develop an efficient and stable numerical method for solving this problem. The numerical solution is based on semi-implicit time discretization and flux-based level set ...

Abstact. Bioinformatics and data mining require data analysis schemes. Many methods of analysis, such as those focusing on entropy, have been developed and assume that the input data has discrete values. Therefore, when using continuous data, discretization needs to be performed before analysis can begin. Many discretization algorithms have been proposed, and these discretize a given dataset at...

This work focuses on the extension of the recently introduced Spectral Difference Method to viscous flow. The spectral difference method is a conservative pseudo-spectral scheme based on a local collocation on unstructured elements. Recently results for scalar transport equations and the Euler equations have been presented. For the extension to viscous flow several techniques are investigated, ...

In this paper, space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convectionreaction equation without control constraints is studied. Time discretization is performed by discontinuous Galerkin method with piecewise constant and linear polynomials, while symmetric interior penalty Galerkin with upwinding is used for spa...