Semi-supervised learning (SSL) on graphs is critical in applications where labeled data are scarce and costly, yet existing graph-based methods often degrade under extreme label sparsity or class imbalance, yielding trivial or unstable solutions. We introduce \textbf{CombCut}, the first exact combinatorial optimization framework for multi-class graph-based semi-supervised learning that operates directly on binary one-hot assignments, without any convex relaxation or heuristic volume constraints. By employing a minorization–maximization (MM) scheme, CombCut transforms each step into a structured linear assignment problem solved efficiently via network-flow algorithms. Total unimodularity guarantees integral iterates, and our theoretical analysis establishes both monotonic ascent of the true discrete objective and convergence of every limit point to a Karush–Kuhn–Tucker (KKT) stationary solution of the original combinatorial problem. Our approach requires no hyperparameter tuning and scales near-linearly in the number of vertices. Empirical evaluation on MNIST, Fashion-MNIST, and CIFAR-10 with as few as 1–5 labels per class shows that CombCut excels in worst-case labeling scenarios, significantly outperforming state-of-the-art graph-SSL baselines and yielding more stable and accurate label propagation under severe supervision constraints.

In recent years, the synthetic aperture radar tomography (TomoSAR) technique is becoming an increasingly hot research topic in the three-dimensional (3D) reconstruction of the structure of urban buildings. The robustness of the many advanced non-parametric spectral estimation methods in use is based on a high number of observations. This letter aims to evaluate the ability of the five non-parametric estimator techniques, including propagator, generalized maximum entropy (GME), minimum norm (MN), singular value decomposition (SVD), and capon in the separation of scattering contributions with a small number of SAR images. The performance comparison of the employed algorithms is carried out on the simulated and real datasets. The study results show that the novel high-resolution propagator and generalized maximum entropy estimators, respectively, based on the partitioning and extrapolation of the covariance matrix, can discriminate the number of scatterers in one azimuth-range resolution and satisfactorily prevent the appearance of undesirable sidelobes. The experimental results on real SAR images acquired by the TerraSAR-X satellite show the proposed propagator spectral estimation can significantly improve the 3D building reconstruction in the urban environment. Also, the estimated height of the scatters using the propagator technique is similar to the data obtained from ground observations.