Collaborative representation-based semisupervised feature extraction of hyperspectral images using attraction points

Feature extraction (FE) is an important preprocessing step for classification of high-dimensional data. However, when the number of labeled training samples is small, less discriminant information induces some FE methods that use statistical moments, for example, linear discriminant analysis, even fail to work. We present a collaborative representation (CR)-based semisupervised FE method using attraction points (CRSUAP). By CR, CRSUAP defines a membership matrix that contains the correlation between multiple samples. Then, a nonmembership matrix is designed to enrich the discriminant information and further enhance the separability of classes. To avoid estimating statistical moments, an attraction point is selected from each class to calculate the projection matrix, avoiding matrix singularity problem. The experimental results on three real hyperspectral images demonstrate that CRSUAP has better performance than other related FE methods in a small labeled sample size situation.