Visualizing Manifold Evolution with IRIS

Manifold Learning algorithms, such as t-SNE and UMAP, are widely used to elucidate structure in high-dimensional data, yet cannot incorporate temporal information. Though variants like Dynamic t-SNE and Aligned UMAP can jointly optimize discrete time slices, they require each item to be tracked across these slices, precluding their use for event-stream data, like news items, papers in citation networks, or cellular-level gene expression. Here, we present IRIS, a new Manifold Learning algorithm that reveals the evolving structure of high-dimensional data, even when each item only has a single observation. The core advance of IRIS is to reparameterize a Cartesian objective through the complex plane, defining radius a monotonic function of time and angle as the optimized variable. This creates an intuitive polar structure in which the manifold grows outward from the origin. Using synthetic data with known topology, we show that IRIS excels at recovering time-dependent branching, outperforming a range of baselines. Then, for real data of multiple modalities, we demonstrate that IRIS reveals temporal structure that existing algorithms cannot, while keeping classes more contiguous. IRIS unlocks temporal Manifold Learning for event-stream data, allowing exploration of population-level phenomena—like the appearance, disappearance, splitting, or merging of submanifolds—in a single, unified layout, and with no requirement to track items across discrete time slices.