Showing papers by "Andrei V. Kelarev published in 2011"

Robust artificial neural networks and outlier detection. Technical report

Abstract: Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks to contaminated data using least trimmed squares criterion. We introduce a penalized least trimmed squares criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression.

Optimization of matrix semirings for classification systems

Abstract: The max-plus algebra is well known and has useful applications in the investigation of discrete event systems and affine equations. Structural matrix rings have been considered by many authors too. This article introduces more general structural matrix semirings, which include all matrix semirings over the max-plus algebra. We investigate properties of ideals in this construction motivated by applications to the design of centroid-based classification systems, or classifiers, as well as multiple classifiers combining several initial classifiers. The first main theorem of this paper shows that structural matrix semirings possess convenient visible generating sets for ideals. Our second main theorem uses two special sets to determine the weights of all ideals and describe all matrix ideals with the largest possible weight, which are optimal for the design of classification systems. doi:10.1017/S0004972711002802

Establishing Reasoning Communities of Security Experts for Internet Commerce Security

Abstract: The highly sophisticated and rapidly evolving area of internet commerce security presents many novel challenges for the organization of discourse in reasoning communities. This chapter suggests appropriate reasoning methods and demonstrates how establishing reasoning communities of security experts and enabling productive group discourse among them can play a crucial role in successful resolution of problems concerning the implementation, integration, deployment and maintenance of flexible local security systems for defense against malware threats in internet security. Local security systems of this sort may combine several ready open source or commercial software packages behind a common frontend and may enhance and supplement their facilities with additional plug-ins. To illustrate the diverse character of challenges the reasoning communities in internet security are likely to be faced with, this chapter concentrates on defense against phishing attacks. This example was selected as it is one of the newest and most rapidly changing application domains for the principles of organizing reasoning communities. The major group discourse methods suggested for the reasoning communities of security DOI: 10.4018/978-1-60960-091-4.ch020

Optimization of classifiers for data mining based on combinatorial semigroups

Abstract: The aim of the present article is to obtain a theoretical result essential for applications of combinatorial semigroups for the design of multiple classification systems in data mining. We consider a novel construction of multiple classification systems, or classifiers, combining several binary classifiers. The construction is based on combinatorial Rees matrix semigroups without any restrictions on the sandwich-matrix. Our main theorem gives a complete description of all optimal classifiers in this novel construction.

Optimization and matrix constructions for classification of data

Abstract: Max-plus algebras and more general semirings have many useful applications and have been actively investigated. On the other hand, structural matrix rings are also well known and have been considered by many authors. The main theorem of this article completely describes all optimal ideals in the more general structural matrix semirings. Originally, our investigation of these ideals was motivated by applications in data mining for the design of centroid- based classication systems, as well as for the design of multiple classication systems combining several individual classiers.

A Grobner-Shirshov algorithm for applications in internet security

Abstract: The design of multiple classification and clustering systems for the detection of malware is an important problem in internet security. Grobner-Shirshov bases have been used recently by Dazeley et al. [15] to develop an algorithm for constructions with certain restrictions on the sandwich-matrices. We develop a new Grobner Shirshov algorithm which applies to a larger variety of constructions based on combinatorial Rees matrix semigroups without any restrictions on the sandwich matrices.