Entropy

Hyperspectral image (HSI) classification is hampered by the high cost of pixel-level annotation, which leaves supervised deep networks exposed to the high-dimensional small-sample problem. Semi-supervised learning (SSL) can exploit the abundant unlabeled pixels, but SSL frameworks designed for natural images do not directly account for the spectral continuity, the coupled spatial–spectral structure and the pronounced class imbalance of HSIs. Taking the weak-to-strong consistency framework UniMatch as a starting point, this paper proposes SEUM, a semi-supervised HSI classification network with three targeted modifications. First, a multi-branch parallel convolution block with squeeze-and-excitation recalibration replaces the single-path encoder so that spatial detail, spectral mixing and salient responses are captured at several scales. Second, a dual-head classifier separates supervised classification from pseudo-label generation, and feature-level dropout is combined with input-level strong augmentation to enlarge the consistency constraint. Third, an adaptive class-aware threshold lowers the confidence requirement for under-represented classes according to their instantaneous learning state, which counteracts the self-reinforcing bias of a fixed threshold. On the Pavia University, Houston 2013 and Kennedy Space Center benchmarks with 10% labeled samples, SEUM reaches overall accuracies of 96.67%, 92.81% and 95.99%, respectively, improving on UniMatch by 0.48–2.20 percentage points and on ten supervised and semi-supervised competitors, with the largest gains on spectrally confusable and texture-rich classes, and it shows consistent improvements in average accuracy, which reflect more balanced pseudo-label utilization across the class distribution. Ablation, pseudo-label quality, label-budget and sensitivity analyses confirm that the encoder, the dual head and the adaptive threshold contribute complementary and stable improvements.

The Maxwellian distribution is rarely observed in space plasmas, as it represents the limiting case of zero correlations among particles. Nevertheless, it is often adopted as a reference example due to its simplicity, serving as a preliminary step before extending the method to kappa distributions, which more accurately capture the thermodynamics of correlated space plasma particles. In this paper, we employ the angular distribution associated with a drifting Maxwellian distribution to derive practical measures of angular spread and quantify their implications for solar-wind instrumentation. We then apply the resulting framework to OMNI observations near 1 AU to determine statistical requirements on instrument field of view and angular resolution. As an application, we illustrate how the angular spread can be used to determine the required field-of-view and angular resolution needed for a bulk solar wind monitor instrument near Earth.

Generalized cross-entropy regression can be formulated as either a constrained primal optimization problem over probability distributions or a dual optimization problem over Lagrange multipliers. Although the two formulations are theoretically equivalent under the conditions considered, their performance depends on the optimization strategy. This study compares two primal and 10 dual routines targeting the generalized maximum entropy (GME) estimator to inform practical optimizer selection. The optimization formulations use the weighted generalized cross-entropy framework, which includes generalized cross-entropy and GME as particular cases. The Portland cement benchmark and 1000 simulated datasets varying sample size, predictor conditioning, and signal-to-noise ratio assess the routines under GME. We compare elapsed time and coefficient-recovery mean squared error (MSE), alongside interface-reported termination, common feasibility checks, and a separate dual-multiplier moment-residual diagnostic. The results reveal substantial differences in computational efficiency but smaller differences in coefficient-estimation accuracy among most routines. dual.lbfgsb3c has the lowest median time, while dual.BFGS combines competitive time and coefficient recovery and was selected as GCEstim’s default. Coefficient recovery and reported termination should be considered alongside numerical residuals. The comparison reflects a practical use case in which users do not tune each optimizer separately, yet relative performance at matched numerical accuracy remains to be established.