Av Kelarev

Cayley graphs as classifiers for data mining: The influence of asymmetries

The endomorphism monoids of graphs have been actively investigated. They are convenient tools expressing asymmetries of the graphs. One of the most important classes of graphs considered in this framework is that of Cayley graphs. Our paper proposes a new method of using Cayley graphs for classification of data. We give a survey of recent results devoted to the Cayley graphs also involving their endomorphism monoids.

On transitive Cayley graphs of groups and semigroups

We investigate Cayley graphs of semigroups and show that they sometimes enjoy properties analogous to those of the Cayley graphs of groups.

Power graphs: A survey

This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also included.

Consensus clustering and supervised classification for profiling phishing emails in internet commerce security

This article investigates internet commerce security applications of a novel combined method, which uses unsupervised consensus clustering algorithms in combination with supervised classification methods. First, a variety of independent clustering algorithms are applied to a randomized sample of data. Second, several consensus functions and sophisticated algorithms are used to combine these independent clusterings into one final consensus clustering. Third, the consensus clustering of the randomized sample is used as a training set to train several fast supervised classification algorithms. Finally, these fast classification algorithms are used to classify the whole large data set. One of the advantages of this approach is in its ability to facilitate the inclusion of contributions from domain experts in order to adjust the training set created by consensus clustering. We apply this approach to profiling phishing emails selected from a very large data set supplied by the industry partners of the Centre for Informatics and Applied Optimization. Our experiments compare the performance of several classification algorithms incorporated in this scheme.

Constructing Stochastic Mixture Policies for Episodic Multiobjective Reinforcement Learning Tasks

Multiobjective reinforcement learning algorithms extend reinforcement learning techniques to problems with multiple conflicting objectives. This paper discusses the advantages gained from applying stochastic policies to multiobjective tasks and examines a particular form of stochastic policy known as a mixture policy. Two methods are proposed for deriving mixture policies for episodic multiobjective tasks from deterministic base policies found via scalarised reinforcement learning. It is shown that these approaches are an efficient means of identifying solutions which offer a superior match to the users preferences than can be achieved by methods based strictly on deterministic policies.

Clustering algorithms for ITS sequence data with alignment metrics

The article describes two new clustering algorithms for DNA nucleotide sequences, summarizes the results of experimental analysis of performance of these algorithms for an ITS-sequence data set, and compares the results with known biologically significant clusters of this data set. It is shown that both algorithms are efficient and can be used in practice.

A new model for classifying DNA code inspired by neural networks and FSA

This paper introduces a new model of classifiers CL(V,E,l,r) designed for classifying DNA sequences and combining the flexibility of neural networks and the generality of finite state automata. Our careful and thorough verification demonstrates that the classifiers CL(V,E,l,r) are general enough and will be capable of solving all classification tasks for any given DNA dataset. We develop a minimisation algorithm for these classifiers and include several open questions which could benefit from contributions of various researchers throughout the world.

Abelian Groups, Rings and Modules

Generalizing results of Higman and Houghton on varieties generated by wreath products of finite cycles, we prove that the (direct or cartesian) wreath product of arbitrary abelian groups A and B generates the product variety var (A) · var (B) if and only if one of the groups A and B is not of finite exponent, or if A and B are of finite exponents m and n respectively and for all primes p dividing both m and n, the factors B[p]/B[p] are infinite, where B[s] = 〈b ∈ B| b = 1〉 and where p is the highest power of p dividing n.

COMBINATORIAL PROPERTIES AND HOMOMORPHISMS OF SEMIGROUPS

A complete description of ultrarepetitive semigroups is given. As an application of this result all semigroups S are described such that the class of permutational semigroups is S-closed, i.e., closed under taking preimages of certain homomorphisms onto S.

Application of Rank Correlation, Clustering and Classification in Information Security

This article is devoted to experimental investigation of a novel application of a clustering technique introduced by the authors recently in order to use robust and stable consensus functions in information security, where it is often necessary to process large data sets and monitor outcomes in real time, as it is required, for example, for intrusion detection. Here we concentrate on a particular case of application to profiling of phishing websites. First, we apply several independent clustering algorithms to a randomized sample of data to obtain independent initial clusterings. Silhouette index is used to determine the number of clusters. Second, rank correlation is used to select a subset of features for dimensionality reduction. We investigate the effectiveness of the Pearson Linear Correlation Coefficient, the Spearman Rank Correlation Coefficient and the Goodman--Kruskal Correlation Coefficient in this application. Third, we use a consensus function to combine independent initial clusterings into one consensus clustering. Fourth, we train fast supervised classification algorithms on the resulting consensus clustering in order to enable them to process the whole large data set as well as new data. The precision and recall of classifiers at the final stage of this scheme are critical for the effectiveness of the whole procedure. We investigated various combinations of several correlation coefficients, consensus functions, and a variety of supervised classification algorithms.