Fuzzy Signature-Based Discriminative Subspace Projection for Hyperspectral Data Classification

Mixed pixels in the hyperspectral image (HSI) are often misclassified under a strict clustering assumption. In this paper, we relax the assumption and assign a fuzzy signature for each pixel in HSI, whose element indicates the probability it belongs to some class. A fuzzy signature-based discriminative subspace projection (FS-DSP) approach is then developed for simultaneous dimensionality reduction and classification of HSI. In FS-DSP, a signature Laplacian regularizer is derived from both labeled and unlabeled pixels to pull the neighbors with similar fuzzy signatures together. A discriminant term is constructed to further pull different classes away and push the same classes toward after the projection. The two terms are combined to define a subspace projection optimization problem, and an alternating direction method of multipliers (ADMM) algorithm is employed to iteratively calculate fuzzy signatures. Effectiveness of FS-DSP is evaluated by five datasets, and the results show that it exhibits state-of-the-art performance as to the numerical guidelines, such as overall accuracy (OA), average accuracy (AA), and Kappa coefficients (KC), when there are only very few labeled pixels.