Seeded Laplacian in Sparse Subspace for Hyperspectral Image Classification

Sparse Representation (SR) has received an increasing amount of interest in recent years. It aims to find the sparsest representation of each data capturing high-level semantics among the linear combinations of the base sets in a given dictionary. In order to further improve the classification performance, the joint SR that incorporates interpixel correlation information of neighborhoods has been proposed for image pixel classification. However, joint SR method yields high computational cost. To improve the performance and computation efficiency of SR and joint SR, we propose a seeded Laplacian based on sparse representation (SeedLSR) framework for hyperspectral image classification, where a hypergraph Laplacian explicitly takes into account the local manifold structure of the hyperspectral pixel in a spatial-type weighted graph. Given the training data in a dictionary, SeedLSR algorithm firstly finds the sparse representation of hyperspectral pixels, which is used to define the spectral-type affinity matrix of an undirected graph. Then, using the training data as user-defined seeds, the final classification can be obtained by solving the combination of spectral and spatial hypergraph Laplacian quadratic problem. To assess the efficiency of the proposed SeedLSR method, experiments were performed on the scene data under daylight illumination. Compared with SR algorithm, the classification results vary smoothly along the geodesics of the data manifold.