Gaussian manifold metric learning for hyperspectral image dimensionality reduction and classification

Abstract

Dimensionality reduction techniques can remove redundant information from hyperspectral images (HSIs) and improve discriminability. However, due to the inherent nonlinear characteristics of HSI, there may be non-Euclidean structures in the data and its topological properties may make it suboptimal to recover the low-dimensional manifolds by means of a linear projection. As a result, linear projection from highdimensional space to low-dimensional discriminative space is not always effective. To better explore the intrinsic geometric structure of HSI, we propose a Gaussian manifold metric learning (GMML) method, which performs explicit and nonlinear dimensionality reduction for HSI. It models pixel neighborhoods as Gaussian distributions to combine spatial and spectral information. In GMML, samples are mapped as elements on the Gaussian manifold consisting of Gaussian distributions to retain the intrinsic characteristics of data. By treating the inner product of the tangent space on the manifold as a kernel function, our method performs metric learning in the tangent space. Therefore, the proposed GMML method makes intra-class samples more compact and inter-class samples more separated while preserving the geometric structure information inherent in the data. Experiments on six real hyperspectral datasets validate the effectiveness of the proposed GMML algorithm to extract discriminating features compared to several related methods.