László Aszalós

Rough Clustering Generated by Correlation Clustering

Correlation clustering relies on a relation of similarity and the generated cost function. If the similarity relation is a tolerance relation, then not only one optimal partition may exist: an object can be approximated from lower and upper side with the help of clusters containing the given object and belonging to different partitions. In practical cases there is no way to take into consideration all optimal partitions. The authors give an algorithm which produces near optimal partitions and can be used in practical cases to avoid the combinatorial explosion. From the practical point of view it is very important, that the system of sets appearing as lower or upper approximations of objects can be taken as a system of base sets of general partial approximation spaces.

Payment Approval for PayWord

In case of micropayment schemes, all costs that appear during functioning should be minimized. This includes cost of disputes and charge backs that result in penalties for the vendor. We extend the PayWord micropayment scheme with payment approval to minimize disputes, charge backs or to avoid attacks that ruin the reputation of the vendor. Payment approval is achieved by employing a MAC function per a purchase, that does not increase time complexity significantly. A formal evaluation in applied π and a proof that our scheme fulfills secure payment authorization, payment approval and secrecy of payment information are also given.

Rough Classification Based on Correlation Clustering

In this article we propose a two-step classification method. At the first step it constructs a tolerance relation from the data, and at second step it uses correlation clustering to construct the base sets, which are used at the classification of the objects. Besides the exposition of the theoretical background we also show this method in action: we present the details of the classification of the well-known iris data set. Moreover we frame some open question due this kind of classification.

Correlation clustering by contraction

We suggest an effective method for solving the problem of correlation clustering. This method is based on an extension of a partial tolerance relation to clusters. We present several implementation of this method using different data structures, and we show a method to speed up the execution by a quasi-parallelism.

Similarity Based Rough Sets

Pawlak’s indiscernibility relation (which is an equivalence relation) represents a limit of our knowledge embedded in an information system. In many cases covering approximation spaces rely on tolerance relations instead of equivalence relations. In real practice (for example in data mining) tolerance relations may be generated from the properties of objects. A given tolerance relation represents similarity between objects, but the usage of similarity is very special: it emphasizes the similarity to a given object and not the similarity of objects ‘in general’. The authors show that this usage has some problematic consequences. The main goal of the paper is to show that if one uses the method of correlation clustering then there is a way to construct a general (partial) approximation space with disjoint base sets relying on the similarity of objects generated by their properties. At the end a software describing a real life problem is presented.

Correlation Clustering by Contraction, a More Effective Method

In this article we propose two effective methods to produce a near optimal solution for the problem of correlation clustering. We study their properties at different circumstances, and show that the inner structure generated by a tolerance relation has effect on the accuracy of the methods. Finally, we show that there is no royal road to the sequence of clusterings.

Correlation clustering: divide and conquer.

The correlation clustering is an NP-hard problem, hence its solving methods do not scale well. The contraction method and its improvement enable us to construct a divide and conquer algorithm, which could help us to clustering bigger sets. In this article we present the contraction method and compare the effectiveness of this new new and our old methods.

A logic for semi-public communication in multi-agent systems

In this paper we investigate a modal logic of knowing, saying and asking to reason about agents in a system of communicating agents. We suppose that communication is reliable and semi-public: an agents utterances are communicated to all the adjacent agents. The knowledge is divided between agents hence they need to put questions in order to collect the desired information.

Similarity Based Rough Sets with Annotation

In the authors’ previous research the possible usage of the correlation clustering in rough set theory was investigated. Correlation clustering relies on a tolerance relation. Its result is a partition. From the similarity point of view singleton clusters have no information. A system of base sets can be generated from the partition, and if the singleton clusters are left out, then it is a partial approximation space. This way the approximation space focuses on the similarity (the tolerance relation) itself and it is different from the covering type approximation space relying on the tolerance relation. In this paper the authors examine how the partiality can be decreased by inserting the members of some singletons into an arbitrary base set and how this annotation affects the approximations. The authors provide software that can execute this process and also helps to select the destination base set and it can also handle missing data with the help of the annotation.

Distance-constrained grid colouring

Abstract Distance-constrained colouring is a mathematical model of the frequency assignment problem. This colouring can be treated as an optimization problem so we can use the toolbar of the optimization to solve concrete problems. In this paper, we show performance of distance-constrained grid colouring for two methods which are good in map colouring.