A Supervised Geometry-Aware Mapping Approach for Classification of Hyperspectral Images

The multi-path scattering of light within a pixel [1], bidirectional reflectance distribution [2], and the heterogeneity of sub-pixel constituents [3] are the major concerns in the hyperspectral (HS) data classification. These nonlinearity properties naturally place the HS data on a non-euclidean space. Handling these high dimensional redundant data in a non-euclidean space is one of the major bottlenecks in HS data analysis. Typically, HS classification consists of dimensionality reduction (DR) and subsequent classification operation. The popular DR methods such as principal component analysis (PCA) [4] and linear discriminant analysis (LDA) [5] are linear and operate on Euclidean structures. These linear DR methods skip the curved nonlinear structures of the HS data. On the other hand, manifold learning helps in recovering compact, meaningful low dimensional structures from those complex high dimensional data from a non-euclidean space. The manifold learning methods consider the real world high dimensional data to be generated with a few degrees of freedom [6]. This leads to the projection of the data into lower dimensional space while preserving their underlying geometrical structure [7].