Algorithm for the detection of outliers based on the theory of rough sets

Outliers are objects that show abnormal behavior with respect to their context or that have unexpected values in some of their parameters. In decision-making processes, information quality is of the utmost importance. In specific applications, an outlying data element may represent an important deviation in a production process or a damaged sensor. Therefore, the ability to detect these elements could make the difference between making a correct and an incorrect decision. This task is complicated by the large sizes of typical databases. Due to their importance in search processes in large volumes of data, researchers pay special attention to the development of efficient outlier detection techniques. This article presents a computationally efficient algorithm for the detection of outliers in large volumes of information. This proposal is based on an extension of the mathematical framework upon which the basic theory of detection of outliers, founded on Rough Set Theory, has been constructed. From this starting point, current problems are analyzed; a detection method is proposed, along with a computational algorithm that allows the performance of outlier detection tasks with an almost-linear complexity. To illustrate its viability, the results of the application of the outlier-detection algorithm to the concrete example of a large database are presented.

Lower semicontinuity of the feasible set mapping of linear systems relative to their domains

This paper deals with stability properties of the feasible set of linear inequality systems having a finite number of variables and an arbitrary number of constraints. Several types of perturbations preserving consistency are considered, affecting respectively, all of the data, the left-hand side data, or the right-hand side coefficients.

On the existence of fractal strings whose set of dimensions of fractality is not perfect

In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.

Improving some thermodynamic consistency tests for VLE data evaluation

Thermodynamics Conference 2013 (Statistical Mechanics and Thermodynamics Group of the Royal Society of Chemistry), The University of Manchester, 3-6 September 2013.

Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Discontinuity Set Extractor

Disponible en Github: https://github.com/adririquelme/DSE

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.