Implicit Multidimensional Projection of Local Subspaces

Rongzheng Bian, Yumeng Xue, Liang Zhou, Jian Zhang, Baoquan Chen, Daniel Weiskopf, Yunhai Wang

External link (DOI)
View presentation:2020-10-30T16:15:00ZGMT-0600Change your timezone on the schedule page
2020-10-30T16:15:00Z
Exemplar figure
The face dataset is projected to 2D using nonlinear MDS. (a) Traditional visualization just shows the projected data points; here, no obvious correlation can be seen. (b) With our new implicit local subspace projection method, global trends and local structures (i.e., local linear subspaces around data points in the original high-dimensional space) are visualized through the orientation and shape of glyphs that replace the dots in the 2D plot. Now, two groups of glyphs associated with right- and left-facing faces are clearly separated (near the bottom), and some more of the interesting local patterns are identified in the zoom-ins. (c) Two trends that cross at the center of the plot are highlighted in green in the image view (also in (b), transparent dashed lines in green); such crossing would not be visible without the orientation encoding in our new glyphs.
Fast forward

Direct link to video on YouTube: https://youtu.be/QZsMyOMHJmY

Keywords

High-dimensional data visualization, dimensionality reduction, local linear subspaces, user interaction

Abstract

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data points. Existing methods focus on the projection of multidimensional data points, and the neighborhood information is ignored. Our method is able to analyze the shape and directional information of the local subspace to gain more insights into the global structure of the data through the perception of local structures. Local subspaces are fitted by multidimensional ellipses that are spanned by basis vectors. An accurate and efficient vector transformation method is proposed based on analytical differentiation of multidimensional projections formulated as implicit functions. The results are visualized as glyphs and analyzed using a full set of specifically-designed interactions supported in our efficient web-based visualization tool. The usefulness of our method is demonstrated using various multi- and high-dimensional benchmark datasets. Our implicit differentiation vector transformation is evaluated through numerical comparisons; the overall method is evaluated through exploration examples and use cases.