Exploring High-Dimensional Structure via Axis-Aligned Decomposition of Linear Projections
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Date
2018
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Publisher
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.
Description
@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}
}