Olga Kurasova

Optimal decisions in combining the SOM with nonlinear projection methods

Abstract Visual data mining is an efficient way to involve human in search for a optimal decision. This paper focuses on the optimization of the visual presentation of multidimensional data. A variety of methods for projection of multidimensional data on the plane have been developed. At present, a tendency of their joint use is observed. In this paper, two consequent combinations of the self-organizing map (SOM) with two other well-known nonlinear projection methods are examined theoretically and experimentally. These two methods are: Sammon’s mapping and multidimensional scaling (MDS). The investigations showed that the combinations (SOM_Sammon and SOM_MDS) have a similar efficiency. This grounds the possibility of application of the MDS with the SOM, because up to now in most researches SOM is applied together with Sammon’s mapping. The problems on the quality and accuracy of such combined visualization are discussed. Three criteria of different nature are selected for evaluation the efficiency of the combined mapping. The joint use of these criteria allows us to choose the best visualization result from some possible ones. Several different initialization ways for nonlinear mapping are examined, and a new one is suggested. A new approach to the SOM visualization is suggested. The obtained results allow us to make better decisions in optimizing the data visualization.

Heuristic approach for minimizing the projection error in the integrated mapping

Abstract In this paper, we have developed and examined a heuristic approach for minimizing the projection error in Sammon’s mapping applied in combination with the self-organizing map (SOM). As a final result, we need to visualize the neurons-winners of the SOM. The criterion of visualization quality is the projection error of Sammon’s mapping. Two combinations were considered: (1) a consecutive application of the SOM and Sammon’s mapping and (2) Sammon’s mapping taking into account the learning flow of the self-organizing neural network (integrated combination of the mapping methods). The goal is to obtain a lower projection error and its lower dependence on the so-called “magic factor” in Sammon’s mapping. Different modifications of Sammon’s mapping are examined experimentally and applied in the combination with the SOM. A parallel algorithm of the integrated combination has been proposed.

Strategies for Big Data Clustering

In the paper, an overview of methods and technologies used for big data clustering is presented. The clustering is one of the important data mining issue especially for big data analysis, where large volume data should be grouped. Here some clustering methods are described, great attention is paid to the k-means method and its modifications, because it still remains one of the popular methods and is implemented in innovative technologies for big data analysis. Neural network-based self-organizing maps and their extensions for big data clustering are reviewed, too. Some strategies for big data clustering are also presented and discussed. It is shown the data of which volume can be clustered in the well known data mining systems WEKA and KNIME and when new sophisticated technologies are needed.

Comparative Analysis of the Graphical Result Presentation in the SOM Software

In the paper, we analyze the software that realizes the self-organizing maps: SOM-PAK, SOM-TOOLBOX, Viscovery SOMine, Nenet, and two academic systems. Most of the software may be found in the Internet. These are freeware, shareware or demo. The self-organizing maps assist in data clustering and analyzing data similarities. The software differs one from another in the realization and visualization capabilities. The data on coastal dunes and their vegetation in Fin- land are used for the experimental comparison of the graphical result presentation of the software. Similarities of the systems and their differences, advantages and imperfections are exposed.

Investigation of human factors while solving multiple criteria optimization problems in computer network

Abstract The aim of this investigation is to analyze a class of multiple criteria optimization problems that are solved by human‐computer interaction, using a computer network. A multiple criteria problem is iterated by interactively selecting different weight coefficients of the criteria. Several parallel solution strategies for solving this optimization problem have been developed and analyzed. The experiments have shown the importance of human assistance in solving this multiple criteria problem. New experimental investigations have been carried out with a different number of computers and different strategies where the human factors are analyzed. We have investigated the time necessary for humans training to solve this multiple criteria optimization problem, the dependence of human factors on the strategy of parallel solution and on the number of computers in a computer network.

Visualization of Pareto Front Points when Solving Multi-objective Optimization Problems

In this paper, a new strategy of visualizing Pareto front points is proposed when solving multi-objective optimization problems. A problem of graphical representation of the Pareto front points arises when the number of objectives is larger than 2 or 3, because, in this case, the Pareto front points are multidimensional. We face the problem of multidimensional data visualization. The visualization strategy proposed is based on a combination of clustering and dimensionality reduction. Moreover, in the obtained projection of the Pareto front points onto a plane, the points are marked according to the Euclidean distance of multidimensional points, corresponding to the points visualized, from the ideal point. In the experimental investigation of the paper, neural gas is used for data clustering, and multidimensional scaling is applied to dimensionality reduction, as well as to visualizing multidimensional data. The strategy can be implemented in a decision support system and it would be useful for a decision maker, who needs to review and evaluate many points of the Pareto fronts, for example, obtained by genetic algorithms. DOI: http://dx.doi.org/10.5755/j01.itc.42.4.3209

The Problem of Visual Analysis of Multidimensional Medical Data

We consider the problem of visual analysis of the multidimensional medical data. A frequent problem in medicine is an assignment of a health state to one of the known classes (for example, healthy or sick persons). A particularity of medical data classification is the fact that the transit from the normal state to diseased one is often not so conspicuous. From the table of the parametric medical multidimensional data, it is difficult to notice which objects are similar, which ones are different, i.e., which class they belong to. Therefore it is necessary to classify the multidimensional data by various classification methods. However, classification errors arc inevitable and the results of classification in medicine must be as correct as possible. That is why it is advisable to use different types of data analysis methods, for example, in addition to visualize the multidimensional data (to project to a plane). A visual analysis allows us to estimate similarities and differences of objects, a partial assignment to one or another class in simple visual way. However, the shortcoming of this analysis is the fact that while projecting multidimensional data to a plane, a part of the information is inevitably lost. Thus, one of the agreeable methods is a combination of classification and visualization methods. This synthesis lets us to obtain a more objective conclusions on the analysed data. The results, obtained by the integrated method, proposed in this chapter, can help medics to preliminary diagnose successfully or have some doubt on the former diagnosis.

Influence of learning rates and neighboring functions on self-organizing maps

In the article, the influence of neighboring functions and learning rates on self-organizing maps (SOM) has been investigated. The target of a selforganizing map is data clustering and their graphical presentation. Bubble, Gaussian, and heuristic neighboring functions and four learning rates (linear, inverse-of-time, power series, and heuristics) have been analyzed here. The learning rate has been changed according to epochs and iterations. A comparative analysis has been made with three data sets: glass, wine, and zoo. The quantization error has been measured in order to estimate the SOM quality.

INTEGRATION OF THE SELF-ORGANIZING MAP AND NEURAL GAS WITH MULTIDIMENSIONAL SCALING

In the paper, two combinations (consecutive and integrated) of vector quantization methods (self-orga- nizing map and neural gas) and multidimensional scaling (MDS) have been investigated and compared. The vector quantization is used to reduce the number of dataset items. The dataset with a smaller number of items is analyzed by multidimensional scaling in order to reduce the number of features of data (dimensionality of space) and to map them onto the plane, i.e., to visualize. Some ways of the initialization (at random, on a line, by PCs and by variances) of two- dimensional vectors in MDS have been investigated. Two ways of assignment of two-dimensional vectors in the integ- rated combinations of MDS and vector quantization methods have been examined, too.

Combination of Vector Quantization and Visualization

In this paper, we present a comparative analysis of a combination of two vector quantization methods (self-organizing map and neural gas), based on a neural network and multidimensional scaling that is used for visualization of codebook vectors obtained by vector quantization methods. The dependence of computing time on the number of neurons, the ratio between the number of neuron-winners and that of all neurons, quantization and mapping qualities, and preserving of a data structure in the mapping image are investigated.