Semisupervised Dual-Geometric Subspace Projection for Dimensionality Reduction of Hyperspectral Image Data

Exploring the geometric prior in the dimensionality reduction (DR) of hyperspectral image data (HID) is an important issue because it can overcome the possible overclassification of spectrally homogeneous areas in the HID classification. In this paper, the local geometric similarity of hyperspectral vectors is explored in both the manifold domain and image domain, and a semisupervised dual-geometric subspace projection (DGSP) approach is proposed for the DR of HID, by utilizing both labeled and unlabeled samples. First, the geometric information in the manifold domain is captured by a sparse coding-based geometric graph, and then, a local-consistency-constrained geometric matrix is defined to reveal the geometric structure in the image domain. Second, unlabeled samples are used to refine the geometric structure by defining a pairwise similarity matrix. Third, three scatter matrices are then derived from these similarity matrices to find the optimal subspace projection that captures the most important properties of the subspaces with respect to classification. Some experiments are taken on the airborne visible infrared imaging spectrometer (AVIRIS) HID to prove the efficiency of the proposed method.