Immersive visualization of the quality of dimensionality reduction

Dimensionality reduction is the most widely used approach for extracting the most informative low-dimensional features from highdimensional ones. During the last two decades, different techniques (linear and nonlinear) have been proposed by researchers in various fields. However, the main question is now how well a specific technique does this job. In this paper, we introduce a qualitative method to assess the quality of dimensionality reduction. In contrast to numerical assessment, we focus here on visual assessment. We visualize the Minimum Spanning Tree (MST) of neighborhood graphs of data before and after dimensionality reduction in an immersive 3D virtual environment. We employe a mixture of linear and nonlinear dimension reduction techniques to apply to both synthetic and real datasets. The visualization depicts the quality of each technique in term of preserving distances and neighborhoods. The results show that a specific dimension reduction technique exhibits different performance in dealing with different datasets.