Visualizing Spaces of Structures

Designing tools to visualize the world of high-dimensional structures — 4D and far beyond.

Structures hold the key to important tasks like factorizations, clusterings, and learning. These structures can be lines, planes, subspaces, algebraic varieties, and more.

Understanding the relationships between these structures — such as similarities or distances — is a critical step toward advancing our knowledge of these tasks, and visualization serves as a fundamental tool in this endeavor.

Visualizing the massive space containing these high-dimensional structures can be challenging, because it requires projecting onto the restrictive 2D or 3D world that we as humans can visualize.

We are developing tools to visualize these massive spaces with as little loss of information as possible, so that our visualizations represent these high-dimensional worlds as accurately as possible.

Our tools have already proved instrumental for our analysis and understanding of several clustering and learning methods, and we anticipate their impact will only grow.