Fermat Active Laplace Learning for Semi-Supervised Hyperspectral Image Classification
2026-08-03 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors developed two methods to help computers better classify hyperspectral images by choosing which pixels to label next in a smart way. Their first method, FALL, uses a special way to measure distances between data points called Fermat distances and then spreads label information across the data. The second method, A-FALL, is a faster version that uses selected landmark points to handle big images more efficiently. Both methods use these distance calculations to understand the shape and density of the data, which helps improve labeling accuracy. They tested these methods on real datasets and showed that FALL works well and A-FALL can handle large images quickly.
Hyperspectral image classificationActive learningFermat distanceHarmonic label propagationPoisson Reweighted Laplace LearningAffinity matrixUncertainty acquisition functionMultidimensional scalingFarthest-point samplingCross-validation
Authors
Vutichart Buranasiri, James M. Murphy
Abstract
Two active learning algorithms for hyperspectral image (HSI) classification are proposed that combine density-aware Fermat distances with Poisson-reweighted harmonic label propagation. Our methods actively query points using an uncertainty-based acquisition function, extending Poisson ReWeighted Laplace Learning (PWLL). Our first algorithm, Fermat Active Laplace Learning (FALL), builds an affinity matrix using Fermat distances between all data points. Then, PWLL is run with a diagonal perturbation using the minimum-norm acquisition function. In contrast, Approximate FALL (A-FALL) computes Fermat distances between each data point and landmark pixels selected via farthest-point sampling and constructs the affinity matrix using landmark multidimensional scaling. After several query rounds, A-FALL selects the Fermat exponent $p$ using a leave-one-out cross-validation variant. FALL and A-FALL leverage Fermat distances and subsequent harmonic label propagation to provide a density-aware estimation of the data manifold, improving labeling accuracy. Experiments on Salinas A and Pavia show the effectiveness of FALL and the scalability of A-FALL to large HSI scenes.