Sparse discriminant learning with ℓ1-graph for hyperspectral remote-sensing image classification

Abstract

Graph-embedding (GE) algorithms have been widely used for dimensionality reduction (DR) of hyperspectral imagery (HSI), and k-nearest neighbour and ϵ-radius ball are usually used for graph construction in GE. However, the two approaches are sensitive to data noise and the optimum of k (or ϵ) is datum-dependent. In this paper, we propose a new supervised DR algorithm, called sparse discriminant learning (SDL), based on -graph for HSI classification. It constructs an inter- and an intra-manifold weight matrix that are computed from -graph, which is robust to data noise and the number of neighbours is adaptively selected to each sample. Then, the SDL algorithm seeks optimal projections with inter- and intra-manifold scatter, which can be formulated based on the modified sparse reconstruction weights. SDL not only reserves sparse reconstructive relations through -graph, but also enhances inter-manifold separability. Experiments on synthetic data and two real hyperspectral image data sets collected by AVIRIS and HDYICE sensors are performed to demonstrate the effectiveness of the SDL algorithm.