Spatially Constrained Semisupervised Local Angular Discriminant Analysis for Hyperspectral Images

Dimensionality reduction is an important preprocessing step for hyperspectral image analysis. Hyperspectral images contain the reflectances measured at a very large number of wavelengths. Due to the over-dimensionality and potential redundancy of information, extraction of features which are meaningful for the purpose of classification becomes a step of prime importance. This is especially true when we have computational constraints (both in terms of time and memory) or a small number of samples available for training the classifier. For most applications, the number of labeled training samples for hyperspectral images is usually small, though the number of unlabeled samples are abundantly available. In this paper, we propose a semisupervised feature extraction algorithm which minimizes the angular similarity between the spectrally similar spatial neighbors and maximizes the angular separation between the pixels belonging to different classes in the projected lower dimensional subspace by utilizing unlabeled samples. We propose a method to incorporate the spatial information from the neighborhood pixels to generate a spatial-spectral dimension reduction algorithm for a semisupervised dimension reduction approach and show that it outperforms the present state-of-the-art feature extraction approaches. In general our approach for incorporating the spatial information can be applied to other supervised and unsupervised feature extraction methods.