  An active learning algorithm for the classification of high-dimensional
images is proposed in which spatially-regularized nonlinear diffusion geometry
is used to characterize cluster cores. The proposed method samples from
estimated cluster cores in order to generate a small but potent set of training
labels which propagate to the remainder of the dataset via the underlying
diffusion process. By spatially regularizing the rich, high-dimensional
spectral information of the image to efficiently estimate the most significant
and influential points in the data, our approach avoids redundancy in the
training dataset. This allows it to produce high-accuracy labelings with a very
small number of training labels. The proposed algorithm admits an efficient
numerical implementation that scales essentially linearly in the number of data
points under a suitable data model and enjoys state-of-the-art performance on
real hyperspectral images.
