Hyperspectral image classification is complicated by mixed pixels, spectral ambiguity, class imbalance, and limited annotations. Most current classifiers encode a pixel or patch as a deterministic vector and apply a linear or multilayer softmax head. Although effective for discrimination, this representation does not directly expose how mixed or uncertain a sample is. This paper presents \method, a classical density-matrix representation learning framework for hyperspectral images. The spectral bands are divided into groups and each group is mapped to a positive semi-definite, Hermitian, trace-normalized matrix state. A composable stack of spectral, spatial, and inter-group transitions then updates the states while repeatedly projecting them back to the valid state set. Instead of flattening the final features, \method\ aggregates the group states and compares them with learnable class-prototype density matrices through Uhlmann fidelity. The normalized eigenspectrum, von Neumann entropy, purity, and prototype fidelity provide sample-level diagnostics that are unavailable from a conventional vector head. On Indian Pines, ten runs yield an overall accuracy of 96.20±0.70%, an average accuracy of 95.57±1.29%, and a kappa coefficient of 95.66±0.80%. On WHU-Hi-LongKou, the best of ten runs reaches 97.52% overall accuracy. Classification maps and feature projections show that the transition stack produces compact and better separated class structures. The results support constrained matrix-state learning as a practical alternative to vector-only hyperspectral classification without requiring quantum hardware.
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.
Over the past decade, hyperspectral image (HSI) classification has drawn considerable interest due to HSIs' ability to effectively distinguish terrestrial objects by capturing detailed, continuous spectral information. The strong performance of recent deep learning techniques in tasks like image classification and semantic segmentation has led to their growing use in HSI classification, due to their ability to capture complex spatial and spectral features more effectively than traditional methods. This paper presents MixerCA, a novel lightweight model for HSI classification that leverages depthwise convolution and a self-attention mechanism. MixerCA integrates depth-wise convolutions, token and channel mixing, and coordinate attention into a unified structure to decouple spatial and channel interactions, maintain consistent resolution throughout the network, and directly process HSI patches. Extensive experiments on four hyperspectral benchmark datasets reveal MixerCA's clear advantages over several competing algorithms, including 2D-CNN, 3D-CNN, Tri-CNN, HybridSN, ViT, and Swin Transformer. The source code is publicly available at https://github.com/mqalkhatib/MixerCA.
Hyperspectral image classification demands spatially coherent predictions and precise boundary delineation. Yet prevailing superpixel-based methods face an inherent contradiction: clustering aggregates similar pixels into regions, but the subsequent classifier operates pixel-wise, undermining regional consistency. Consequently, existing approaches do not guarantee region-level, boundary-aligned classification. To address this limitation, we propose the Dual-stage Spectrum-Constrained Clustering-based Classifier (DSCC), an end-to-end framework that explicitly decouples clustering from classification by first grouping spectral similar and spatially proximate pixels into spectral supertokens and then performing token-level prediction. At its core, DSCC computes an image-level multi-criteria feature distance between pixels and centers, followed by a locality-aware assignment regularization, enabling the generation of boundary-preserving spectral supertokens. A density-isolation based center selection further yields representative, well-separated centers, reducing redundancy and improving robustness to scale variation. To accommodate mixed land-cover compositions within each token, we introduce a soft-label scheme that encodes class proportions and improves robustness for mixed-class tokens. DSCC attains a CF1 of 0.728 at 197.75 FPS on the WHU-OHS dataset, offering a superior accuracy-efficiency trade-off compared with state-of-the-art methods. Extensive experiments further validate the effectiveness and generality of the proposed dual-stage paradigm for hyperspectral image classification. The source code is available at https://github.com/laprf/DSCC.