aiqbench analysis
NFMap introduces a bijective normalizing flow extension to Generative Topographic Mapping, offering full invertibility and explicit likelihoods for 2D visualization of high-dimensional data like chemical datasets. By splitting the latent space into a navigable map and an off-manifold residual, it provides a robust out-of-distribution signal while managing large dataset crowding through Student-t mixture components. This method advances dimensionality reduction techniques by ensuring that variance constraints are strictly maintained between local fidelity and global distance preservation.
NFMap: Topographic 2D Manifold Learning with Invertible Normalizing Flows
arXiv:2610.16750v1 Announce Type: new 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.
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.
20 pages, 10 figures. Code: this https URL
Machine Learning (cs.LG)
arXiv:2610.16750 [cs.LG]
(or arXiv:2610.16750v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.16750 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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