Spatial-Spectral Dimensionality Reduction of Hyperspectral Imagery with Partial Knowledge of Class Labels

Laplacian Eigenmaps (LE) and Schroedinger Eigenmaps (SE) are effective dimensionality reduction algorithms that are capable of integrating both the spatial and spectral information inherent in a hyperspectral image. In this paper, we consider how to extend LEand SE-based spatial-spectral dimensionality reduction algorithms to situations where partial knowledge of class labels exists, for example, when a subset of pixels has been manually labeled by an expert user. This partial knowledge is incorporated through the use of cluster potentials, turning each underlying algorithm into an instance of SE. Using publicly available data, we show that incorporating this partial knowledge improves the performance of subsequent classification algorithms.