Research Group on Artificial Intelligence
SEMINARS - 2003/04. I.
Role of inclusion functions in interval global optimization
12 Sept, 2003
In this talk a short overview on the interval arithmetic (IA) and the branch-and-bound type global optimization algorithms based on IA is given. The mathematical descriptions and the computer oriented realizations are introduced. In the main part of the talk a new inclusion function (called kite) is presented. The one dimensional case and a possible (componentwise) multidimensional extension is discussed. In both cases the numerical investigations are presented. As future work the Lennard-Jones atom cluster problem is introduced. Here my tasks would be: optimization with validated methods and a theoretical oriented problem (minimal inter-particle distance in the optimal structure).
Sept 19, 2003
Revision of projective DNF formulae
Oct 10, 2003
Projection learning, introduced by Valiant, aims to learn a target concept by learning some of the concept's projections to a class of smaller domains, and by combining these projections. A natural special case of this framework is when the projection domains are subcubes of a fixed dimension, and the restrictions of the target to these domains are conjunctions.
We extend Valiant's result on attribute-efficient learning of projective DNFs to the related case of efficient revision. We show why the plain revision version of the original algorithm loses its efficiency when noise is added to the model, and how to overcome this problem.
Global optimization -- reliable computations
Oct 17, 2003
After a short introduction to my previous research work I will focus on my recent results in the development of a new verified optimization method for the problem of finding the densest packing of non-overlapping equal circles within a square. In order to provide reliable numerical results, the developed algorithm is based on interval analysis. As one of the most efficient parts of the algorithm, an interval-based version of a previous elimination procedure is introduced. This method represents the remaining areas still of interest as polygons fully calculated in a reliable way. The most promising strategy of finding globally optimal circle packing configurations is currently the partitioning of the original problem into subproblems. Still as a result of the highly increasing number of subproblems, earlier computer-aided methods were not able to solve problem instances where the number of circles was greater than 27. The present method provides a carefully developed technique resolving this difficulty by eliminating large groups of subproblems together. As a demonstration of the capabilities of the new algorithm the problems of packing 28, 29, and 30 circles were solved within very tight tolerance values.
(Further details of my research works are available at www.inf.u-szeged.hu/~markot.)
An overview of the OASIS system - its structure and some problems to be solved
Oct 26, 2003
Our lecture presents the current structure of the OASIS speech recognizer, starting from the phoneme classification task, up to the language model. In the second part of the presentation we discuss those components of the system that require further improvement, and so are possible further research directions.
Classification by a hyperplane
Nov 7, 2003
In machine learning the classification approach may be linear or nonlinear, but it seems that by using the so-called kernel idea, linear methods can be readily generalized to the nonlinear ones. The key idea was originally presented by Aizermann and it was successfully renewed in the context of the ubiquitous Support Vector Machines (SVM). The roots of SV methods can be traced back to the need for the determination of the optimal parameters of a separating hyperplane, which can be formulated both in input space or in kernel induced feature spaces. While the former is a linear method, the latter results in a nonlinear counterpart. Optimality can vary from method to method and SVM is just one of several possible approaches.
In this lecture a new family of hyperplane classifiers is presented, that make use of various contrast functions for different optimality aspects. However, in contrast to SVM - where a contrained quadratic optimization is used - the method leads to the unconstrained minimization of convex functions when a convex penalty function is applied to non-separated samples.
The main consequence of the lecture is that in numerous cases our algorithms proved to be the more beneficial to the classification task out of the methods examined.
Kernel-Based Feature Extraction
Nov 21, 2003
Kernel-based nonlinear feature extraction and classification algorithms are a popular new research direction in machine learning. We first give a concise overview of the nonlinear feature extraction methods such as kernel principal component analysis (KPCA), kernel independent component analysis (KICA), kernel linear discriminant analysis (KLDA) and kernel springy discriminant analysis (KSDA). The overview deals with all the methods in a unified framework, regardless of whether they are unsupervised or supervised. The effect of the transformations on a subsequent classification is tested in combination with numerous learning algorithms. We found in most cases that the transformations have a beneficial effect on the classification performance. Furthermore, the nonlinear supervised algorithms yielded the best results.
Solving a Huff-like competitive location and design model for profit maximization in the plane
A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximise the profit obtained for the chain. Several types of constraints and costs are considered.
Two solution methods are developed and tested. The first is a repeated local optimisation heuristic, extending earlier proposals to the supplementary design question and the presence of locational constraints. The second is an exact global optimisation technique based on reliable computing using interval analysis, incorporating several novel features.