## Neural and Statistical Methods for the Visualization of Multidimensional Data (2001)

Venue: | DISSERTATION, KATEDRA METOD KOMPUTEROWYCH UMK |

Citations: | 8 - 2 self |

### BibTeX

@TECHREPORT{Naud01neuraland,

author = {Antoine Naud},

title = {Neural and Statistical Methods for the Visualization of Multidimensional Data},

institution = {DISSERTATION, KATEDRA METOD KOMPUTEROWYCH UMK},

year = {2001}

}

### OpenURL

### Abstract

In many fields of engineering science we have to deal with multivariate numerical data. In order to choose the technique that is best suited to a given task, it is necessary to get an insight into the data and to "understand" them. Much information allowing the understanding of multivariate data, that is the description of its global structure, the presence and shape of clusters or outliers, can be gained through data visualization. Multivariate data visualization can be realized through a reduction of the data dimensionality, which is often performed by mathematical and statistical tools that are well known. Such tools are Principal Components Analysis or Multidimensional Scaling. Artificial neural networks have developed and found applications mainly in the last two decades, and they are now considered as a mature field of research. This thesis investigates the use of existing algorithms as applied to multivariate data visualization. First an overview of existing neural and statistical techniques applied to data visualization is presented. Then a comparison is made between two chosen algorithms from the point of view of multivariate data visualization. The chosen neural network algorithm is Kohonen's Self-Organizing Maps, and the statistical technique is Multidimensional Scaling. The advantages and drawbacks from the theoretical and practical viewpoints of both approaches are put into light. The preservation of data topology involved by those two mapping techniques is discussed. The multidimensional scaling method was analyzed in details, the importance of each parameter was determined, and the technique was implemented in metric and non-metric versions. Improvements to the algorithm were proposed in order to increase the performance of the mapping process. A graphic...