Visualizing High-Dimensional Temporal Data Using Direction-Aware t-SNE

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.

Explainable Point-Based Document Visualizations

Two-dimensional data maps can visually reveal information about the relations between data instances. Popular techniques to construct data maps are t-SNE and UMAP. The resulting point-based visualizations, though, provide information only through their interpretation. We here consider a set of abstracts from the articles on longevity to argue for using keyword extraction methods to label clusters of documents in the map. Among the considered approaches, the best results were obtained by recently proposed YAKE!. Surprisingly, a classical TF-IDF term ranking outperformed graph and embedding-based techniques.

Data Fusion by Matrix Factorization

For most problems in science and engineering we can obtain data sets that describe the observed system from various perspectives and record the behavior of its individual components. Heterogeneous data sets can be collectively mined by data fusion. Fusion can focus on a specific target relation and exploit directly associated data together with contextual data and data about system's constraints. In the paper we describe a data fusion approach with penalized matrix tri-factorization (DFMF) that simultaneously factorizes data matrices to reveal hidden associations. The approach can directly consider any data that can be expressed in a matrix, including those from feature-based representations, ontologies, associations and networks. We demonstrate the utility of DFMF for gene function prediction task with eleven different data sources and for prediction of pharmacologic actions by fusing six data sources. Our data fusion algorithm compares favorably to alternative data integration approaches and achieves higher accuracy than can be obtained from any single data source alone.