Topics: visualization, dimensionality reduction, (trajectory) patterns
Supervision: Andreas Hinterreiter, Marc Streit
Contact: email@example.com, firstname.lastname@example.org
Type: BSc Thesis, MSc Thesis, BSc Practicum, MSc Practicum
Many real-world problems can be viewed as sequences of high-dimensional states. As an example, each color configuration of Rubik’s cube can be encoded in a vector, and solving the cube can be viewed as transitioning from one high-dimensional vector to the next. In order to better understand patterns of these paths through high-dimensional state spaces, the states can be projected to 2D using non-linear dimensionality reduction techniques such as t-SNE or UMAP. The paths can then be visualized as trajectories in the embedded space.
We developed an interactive visualization prototype to explore such groups of projected paths (see image and link above). We already obtained some interesting findings for different application areas, but we would like to further expand our prototype in two directions:
- Automatic detection of high- and low-dimensional patterns of points and trajectories
The visualization system should be able to autonomously detect interesting patterns for both points and paths. It should be able to determine whether these patterns in the low-dimensional states actually relate to the “true” high-dimensional data.
- Automatic and effective visualization of the detected patterns
The visualization system should automatically highlight the detected patterns and visualize them in an effective way. This will likely include novel visual encodings for similarity of high-dimensional states. It is of particular interest how suitable similarity encodings compare between different application areas.
The work will combine traditional data analysis techniques (e.g., dimensionality reduction and clustering techniques), conceptual visualization research (novel similarity encodings), and implementation of the developed techniques in the form of a web application.