Multidimensional Data Visualization

It is often desirable to visualize a data set, the items of which are described by more than three features. Therefore, we have multidimensional data, and our goal is to make some visual insight into the data set analyzed. For human perception, the data must be represented in a low-dimensional space, usually of two or three dimensions. The goal of visualization methods is to represent the multidimensional data in a low-dimensional space so that certain properties (e.g. clusters, outliers) of the structure of the data set were preserved as faithfully as possible. Such a visualization of data is highly important in data mining because recent applications produce a large amount of data that require specific means for knowledge discovery. The dimensionality reduction or visualization methods are recent techniques to discover knowledge hidden in multidimensional data sets.

In this chapter, an analytical review of methods for multidimensional data visualization is presented. The methods based on direct visualization and projections are described. Some quantitative criteria of the visualization quality are also introduced.

The combination and integrated use of data visualization methods of a different nature are under a rapid development. The combination of different methods can be applied to make a data analysis, while minimizing the shortcomings of individual methods. This chapter is devoted to visualization methods based on an artificial neural network. The fundamentals of artificial neural networks that are essential for investigating their potential to visualize multidimensional data are presented below. A biological neuron is introduced here. The model of an artificial neuron is presented, too. Structures of one-layer and multilayer feed-forward neural networks are investigated. Learning algorithms are described. Some artificial neural networks, widely used for visualization of multidimensional data, are overviewed, such as a self-organizing map, neural gas, curvilinear component analysis, auto-associative neural network, and NeuroScale. Much attention is paid to two strategies of the combination of multidimensional scaling and artificial neural network. The first of them is based on the integration of a self-organizing map or neural gas with the multidimensional scaling. The second one is based on the minimization of Stress using a feed-forward neural network SAMANN. The possibility to train the artificial neural network by multidimensional scaling results is discussed, too.

This chapter is intended for applications of multidimensional data visualization. Some application examples and interpretations of the results are presented. These applications reveal the possibilities and advantages of the visual analysis. The applications can be grouped as follows: in social sciences, in medicine and pharmacology, and visual analysis of correlation matrices.