Visualizing High-Dimensional Temporal Data Using Direction-Aware t-SNE
Pavlin G. Poličar Blaž Zupan
Many real-world data sets contain a temporal component or involve transitions
from state to state. For exploratory data analysis, we can represent these
high-dimensional data sets in two-dimensional maps, using embeddings of the
data objects under exploration and representing their temporal relationships
with directed edges. Most existing dimensionality reduction techniques, such as
t-SNE and UMAP, do not take into account the temporal or relational nature of
the data when constructing the embeddings, resulting in temporally cluttered
visualizations that obscure potentially interesting patterns. To address this
problem, we propose two complementary, direction-aware loss terms in the
optimization function of t-SNE that emphasize the temporal aspects of the data,
guiding the optimization and the resulting embedding to reveal temporal
patterns that might otherwise go unnoticed. The Directional Coherence Loss
(DCL) encourages nearby arrows connecting two adjacent time series points to
point in the same direction, while the Edge Length Loss (ELL) penalizes arrows
- which effectively represent time gaps in the visualized embedding - based on
their length. Both loss terms are differentiable and can be easily incorporated
into existing dimensionality reduction techniques. By promoting local
directionality of the directed edges, our procedure produces more temporally
meaningful and less cluttered visualizations. We demonstrate the effectiveness
of our approach on a toy dataset and two real-world datasets.