Visual exploration of high-dimensional data using dimensionality reduction

Abstract

Intuitively analyzing multidimensional data for exploratory purposes is challenging. Multidimensional data visualization is used to tackle this challenge. In the field of multidimensional data visualization, dimensionality reduction (DR) provides a lower-embedding of the original high-dimensional data so that the data are more accessible by visualization. Furthermore, DR is the preferred method to find visual clusters of points that represent the clusters in the original data. However, finding visually well-separated clusters using conventional DR methods is challenging, as there are numerous DR methods applicable to a wide range of data sets. Therefore, this thesis focuses on using a preconditioning step of DR by sharpening the multidimensional data in the high-dimensional space prior to dimensionality reduction so that clusters are also separated better in the lower-dimensional embedding. We improve this sharpened DR method in terms of dimensional scalability, computational scalability, ease-of-use, and stability. The method is also applicable to any real-valued multidimensional data set allowing applications in various fields. We show applications in various labeled data sets and an unlabeled astronomical data set. We further analyze the resulting clusters from sharpened DR for this astronomical data set to conclude that the clusters are associated with different sub-components of the Milky Way. In summary, we argue that this work is an important step towards finding interesting and meaningful visual clusters for the exploratory analysis of high-dimensional data in various fields.