Interpreting High-Dimensional Projections With Capacity

Dimensionality reduction (DR) algorithms are diverse and widely used for analyzing high-dimensional data. Various metrics and tools have been proposed to evaluate and interpret the DR results. However, most metrics and methods fail to be well generalized to measure any DR results from the perspective of original distribution fidelity or lack interactive exploration of DR results. There is still a need for more intuitive and quantitative analysis to interactively explore high-dimensional data and improve interpretability. We propose a metric and a generalized algorithm-agnostic approach based on the concept of capacity to evaluate and analyze the DR results. Based on our approach, we develop a visual analytic system HiLow for exploring high-dimensional data and projections. We also propose a mixed-initiative recommendation algorithm that assists users in interactively DR results manipulation. Users can compare the differences in data distribution after the interaction through HiLow. Furthermore, we propose a novel visualization design focusing on quantitative analysis of differences between high and low-dimensional data distributions. Finally, through user study and case studies, we validate the effectiveness of our approach and system in enhancing the interpretability of projections and analyzing the distribution of high and low-dimensional data.