Invertible mapping improves 2D visualization of complex data
NFMap: Topographic 2D Manifold Learning with Invertible Normalizing Flows
Machine Learning
Summary
Reducing complex data to two dimensions for visualization is tricky because some methods lose important details or are hard to interpret. The authors introduce NFMap, a technique that creates a reversible and clear 2D map of data while retaining important information. This method allows users to go back and forth between the 2D map and original data points, improving how new data can be visualized and understood. It also balances showing detailed neighborhood relationships and global distances better than previous methods.
What this means in practice
- •For chemical data analysts: Identify when new chemical data points do not fit the existing data distribution by projecting them onto the NFMap latent space.
- •For data visualization engineers: Create interactive 2D maps that allow users to explore high-dimensional data with reversible transformations between map and original data.
Authors
Héléna Alexandra Gaspar
Abstract
We present NFMap, a dimensionality reduction method for 2D visualisation that extends Generative Topographic Mapping (GTM) with a bijective normalizing flow. Like GTM, NFMap places a fixed mixture grid prior over a 2D latent map, giving a parametric embedding, an explicit likelihood, and the ability to project new points onto an existing map; the likelihood is an effective out-of-distribution signal on chemical datasets. Unlike GTM, whose latent-to-data mapping is an RBF network of bounded flexibility, NFMap's mapping is a normalizing flow, and is therefore fully invertible: any location on the map can be carried back to data space. To alleviate map crowding on large datasets, NFMap additionally supports heavy-tailed Student-t mixture components. NFMap maps data to a latent space of the same dimension, split into a 2-dimensional navigable map and an off-manifold residual. Because the flow is bijective and its objective penalises volume contraction, variance squeezed out of the residual must reappear in the navigable map. The residual scale is the main control between local neighbourhood fidelity and global distance fidelity; its effect depends on the dimensionality of the data and is coupled to the extent of the latent grid.