Invex Regularizers Meet Subspace-Based Feature Extraction for Hyperspectral Image Classification

The pursuit of global optimality has confined feature extraction in hyperspectral imaging to convex formulations, despite the known effectiveness of non-convex models. However, the adoption of non-convex models remains limited due to the lack of optimization guarantees. This letter bridges this gap by introducing a novel invex-regularized framework for subspace-based feature extraction. Invexity, a generalization of convexity, enables us to incorporate non-convex penalties that promote spatial piecewise smoothness and noise resilience while retaining global optimality guarantees. Our formulation is an ℓ2-norm minimization problem regularized by a penalty that combines the ℓ2-norm with an invex function. Extensive experiments on urban hyperspectral datasets for image classification demonstrate that the proposed invex-based method achieves outstanding classification accuracy, outperforming state-of-the-art methods.