Jiří Dvorský

Hash Functions Based on Large Quasigroups

In this article we discuss a simple hash function based upon properties of a well-known combinatorial design called quasigroups. The quasigroups are equivalent to the more familiar Latin squares and one of their most important properties is that all possible element of certain quasigroup occurs with equal probability. Actual implementations are based on look-up table implementation of the quasigroup, which is unusable for large quasigroups. In contrast, presneted hash function can be easily implemented. It allows us to compute hash function without storing large amount of data (look-up table). The hash function computation is illustrated by experiments summarized in the last section of this paper.

Growing Neural Gas – A Parallel Approach

The paper deals with the high dimensional data clustering problem. One possible way to cluster this kind of data is based on Artificial Neural Networks (ANN) such as SOM or Growing Neural Gas (GNG). The learning phase of the ANN, which is time-consuming especially for large high-dimensional datasets, is the main drawback of this approach to data clustering. The parallel modification, Growing Neural Gas, and its implementation on the HPC cluster is presented in the paper. Some experimental results are also presented.

On Wind Power Station Production Prediction

The paper deals with results following from the research of prediction of wind power plant production. The model was developed at VsB – Technical university of Ostrava and it is based on knowledge of weather forecast and power curve of predicted wind power plant. To improve accuracy of prediction several correction mechanisms are adopted. In conclusion, the paper describes comparison of predicted values and measured values.

Genetic algorithms evolving quasigroups with good pseudorandom properties

Quasigroups are a well-known combinatorial design equivalent to more familiar Latin squares. Because all possible elements of a quasigroup occur with equal probability, it makes it an interesting tool for the application in computer security and for production of pseudorandom sequences. Prior implementations of quasigroups were based on look-up table of the quasigroup, on system of distinct representatives etc. Such representations are infeasible for large quasigroups. In contrast, presented analytic quasigroup can be implemented easily. It allows the generation of pseudorandom sequences without storing large amount of data (look-up table). The concept of isotopy enables consideration of many quasigroups and genetic algorithms allow efficient search for good ones.

Effective clustering algorithm for high-dimensional sparse data based on SOM

With increasing opportunities for analyzing large data sources, we have noticed a lack of effective processing in datamining tasks working with large sparse datasets of high dimensions. This work focuses on this issue and on effective clustering using models of artificial intelligence. The authors of this article propose an effective clustering algorithm to exploit the features of neural networks, and especially Self Organizing Maps (SOM), for the reduction of data dimensionality. The issue of computational complexity is resolved by using a parallelization of the standard SOM algorithm. The authors have focused on the acceleration of the presented algorithm using a version suitable for data collections with a certain level of sparsity. Effective acceleration is achieved by improving the winning neuron finding phase and the weight actualization phase. The output presented here demonstrates sufficient acceleration of the standard SOM algorithm while preserving the appropriate accuracy.

Parallel Hybrid SOM Learning on High Dimensional Sparse Data

Self organizing maps (also called Kohonen maps) are known for their capability of projecting high-dimensional space into lower dimensions. There are commonly discussed problems like rapidly increased computational complexity or specific similarity representation in the high-dimensional space. In the paper there is proposed the effective clustering algorithm based on self organizing map with the main purpose to reduce high dimension of the input dataset. The problem of computational complexity is solved using parallelization; the speed of proposed algorithm is accelerated using the algorithm version suitable for data collections with certain level of sparsity.

Self Organizing Maps with Delay Actualization

The paper deals with the Self Organizing Maps (SOM). The SOM is a standard tool for clustering and visualization of high-dimensional data. The learning phase of SOM is time-consuming especially for large datasets. There are two main bottleneck in the learning phase of SOM: finding of a winner of competitive learning process and updating of neurons’ weights. The paper is focused on the second problem. There are two extremal update strategies. Using the first strategy, all necessary updates are done immediately after processing one input vector. The other extremal choice is used in Batch SOM – updates are processed at the end of whole epoch. In this paper we study update strategies between these two extremal strategies. Learning of the SOM with delay updates are proposed in the paper. Proposed strategies are also experimentally evaluated.

OPTIMAL PATH PROBLEM WITH POSSIBILISTIC WEIGHTS

The selection of optimal path is one of the classic problems in graph theory. Its utilization have various practical uses ranging from the transportation, civil engineering and other applications. Rarely those applications take into account the uncertainty of the weights of the graph. However this uncertainty can have high impact on the results. Several studies offer solution by implementing the fuzzy arithmetic for calculation of the optimal path but even in those cases neither of those studies proposed complete solution to the problem of ranking of the fuzzy numbers. In the study the ranking system based on the Theory of Possibility is used. The biggest advantage of this approach is that it very well addresses the indistinguishability of fuzzy numbers. Lengths of the paths are compared based on the possibility and the necessity of being smaller than the alternative. The algorithm offers the user more information than only the optimal path, instead the list of possible solutions is calculated and the alternatives can be ranked using the possibility and the necessity to identify the possibly best variant.

Comparison of Crisp, Fuzzy and Possibilistic Threshold in Spatial Queries

Decision making is one of the most important application areas of geoinformatics. Such support is mainly oriented on the identification of locations that fulfil certain criterion. The contribution presents the suitability of various approaches of spatial query using different types of Fuzzy thresolds. Presented methods are based on the classical logic (Crisp queries), Fuzzy logic (Fuzzy queries) and Possibility theory (Possibilistic Queries). All presented approaches are applied in the case study. Use these findings may contribute to the better understanding of the nature of the methods used and can help to obtain more accurate results, which have a determining influence on subsequent decision-making process.

Querying on Fuzzy Surfaces with Vague Queries

The aim of the study is to present utilization of Possibility theory to evaluate soft spatial queries on Fuzzy Surfaces. Fuzzy Surfaces are constructed from incomplete datasets or from data that contain uncertainty that is not of statistical nature. Soft spatial queries are common in geography because a lot of classes that should be found in the data have naturally vague definitions or are defined by expert opinion in term of interval rather than exact threshold. Soft thresholds and Surfaces with uncertainty can be expressed with use of Fuzzy Numbers. To evaluate their exceedance or ranking the procedures from Possibility theory are utilized. The whole concept is shown on a Case study.