Classification algorithms are used in numerous applications everyday, from assigning letter grades to student student’s scores, to computerized letter recognition in mail processing. Discretization consists of applying a set of rules to reduce the number of discrete intervals from which an attribute is assigned. Discretization is generally applied to datasets whose numerical range consists of c...

Abstract Density-based topology optimization and node-based shape are often used sequentially to generate production-ready designs. In this work, we address the challenge couple density-based into a single problem by using an embedding domain discretization technique. our approach, variable is explicitly represented boundary of embedded body. Furthermore, in form structured mesh allows us intro...

The transport and continuum equations exhibit a number of conservation laws. For example, scalar multiplication is conserved by the transport equation, while positivity of probabilities is conserved by the continuum equation. Certain discretization techniques, such as particle based methods, conserve these properties, but converge slower than spectral discretization methods on smooth data. Stan...

We consider an eddy current problem in time-domain relying on impedance boundary conditions on the surface of the conductor(s). We pursue its full discretization comprising (i) a finite element Galerkin discretization by means of lowest order edge elements in space, and (ii) temporal discretization based on Runge-Kutta convolution quadrature (CQ) for the resulting Volterra integral equation in ...

A concept of fuzzy discretization of feature space for a rough set theoretic classifier is explained. Fuzzy discretization is characterised by membership value, group number and affinity corresponding to an attribute value, unlike crisp discretization which is characterised only by the group number. The merit of this approach over both crisp discretization in terms of classification accuracy, i...

Steplength thresholds for invariance preserving of three types of discretization methods on a polyhedron are considered. For Taylor approximation type discretization methods we prove that a valid steplength threshold can be obtained by finding the first positive zeros of a finite number of polynomial functions. Further, a simple and efficient algorithm is proposed to numerically compute the ste...