Exploring High-Dimensional Structure via Axis-Aligned Decomposition of Linear Projections

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Date
2018
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The Eurographics Association and John Wiley & Sons Ltd.
Abstract
Two-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively, to axis-aligned projections, which are easy to interpret but are limited to bivariate relationships. Linear project can be considered as a compromise between complexity and interpretability, as they allow explicit axes labels, yet provide significantly more degrees of freedom compared to axis-aligned projections. Nevertheless, interpreting the axes directions, which are often linear combinations of many non-trivial components, remains difficult. To address this problem we introduce a structure aware decomposition of (multiple) linear projections into sparse sets of axis-aligned projections, which jointly capture all information of the original linear ones. In particular, we use tools from Dempster-Shafer theory to formally define how relevant a given axis-aligned project is to explain the neighborhood relations displayed in some linear projection. Furthermore, we introduce a new approach to discover a diverse set of high quality linear projections and show that in practice the information of k linear projections is often jointly encoded in ~ k axis-aligned plots. We have integrated these ideas into an interactive visualization system that allows users to jointly browse both linear projections and their axis-aligned representatives. Using a number of case studies we show how the resulting plots lead to more intuitive visualizations and new insights.
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@article{
10.1111:cgf.13416
, journal = {Computer Graphics Forum}, title = {{
Exploring High-Dimensional Structure via Axis-Aligned Decomposition of Linear Projections
}}, author = {
Thiagarajan, Jayaraman J.
and
Liu, Shusen
and
Ramamurthy, Karthikeyan Natesan
and
Bremer, Peer-Timo
}, year = {
2018
}, publisher = {
The Eurographics Association and John Wiley & Sons Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.13416
} }
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