Visualizing High-Dimensional Structures by Dimension Ordering and Filtering using Subspace Analysis

High-dimensional data visualization is receiving increasing interest because of the growing abundance of high-dimensional datasets. To understand such datasets, visualization of the structures present in the data, such as clusters, can be an invaluable tool. Structures may be present in the full high-dimensional space, as well as in its subspaces. Two widely used methods to visualize high-dimensional data are the scatter plot matrix (SPM) and the parallel coordinate plot (PCP). SPM allows a quick overview of the structures present in pairwise combinations of dimensions. On the other hand, PCP has the potential to visualize not only bi-dimensional structures but also higher dimensional ones. A problem with SPM is that it suffers from crowding and clutter which makes interpretation hard. Approaches to reduce clutter are available in the literature, based on changing the order of the dimensions. However, usually this reordering has a high computational complexity. For effective visualization of high-dimensional structures, also PCP requires a proper ordering of the dimensions.

In this paper, we propose methods for reordering dimensions in PCP in such a way that high-dimensional structures (if present) become easier to perceive. We also present a method for dimension reordering in SPM which yields results that are comparable to those of existing approaches, but at a much lower computational cost. Our approach is based on finding relevant subspaces for clustering using a quality criterion and cluster information. The quality computation and cluster detection are done in image space, using connected morphological operators. We demonstrate the potential of our approach for synthetic and astronomical datasets, and show that our method compares favorably with a number of existing approaches.