Attribute-based Explanation of Non-Linear Embeddings of High-Dimensional Data

The embedding (MDS, top right) shows a non-linear projection of the 4D latent feature space as computed by machine learning for 240 chemical compounds [26]. Color-based augmentation helps relate structures in the embedded point cloud to input attributes (bottom, continuous variables) and domain knowledge (top, categorical variables). Our new approach enabled domain scientists detect previously unrecognizable patterns and outliers in their data.

Abstract-Embeddings of high-dimensional data are widely used to explore data, to verify analysis results, and to communicate information. Their explanation, in particular with respect to the input attributes, is often difficult. With linear projects like PCA the axes can still be annotated meaningfully. With non-linear projections this is no longer possible and alternative strategies such as attribute-based color coding are required. In this paper, we review existing augmentation techniques and discuss their limitations. We present the Non-Linear Embeddings Surveyor (NoLiES) that combines a novel augmentation strategy for projected data (rangesets) with interactive analysis in a small multiples setting. Rangesets use a set-based visualization approach for binned attribute values that enable the user to quickly observe structure and detect outliers. We detail the link between algebraic topology and rangesets and demonstrate the utility of NoLiES in case studies with various challenges (complex attribute value distribution, many attributes, many data points) and a real-world application to understand latent features of matrix completion in thermodynamics.