James M. Murphy

Sam L. Polk, James M. Murphy

Clustering algorithms partition a dataset into groups of similar points. The primary contribution of this article is the Multiscale Spatially-Regularized Diffusion Learning (M-SRDL) clustering algorithm, which uses spatially-regularized diffusion distances to efficiently and accurately learn multiple scales of latent structure in hyperspectral images. The M-SRDL clustering algorithm extracts clusterings at many scales from a hyperspectral image and outputs these clusterings' variation of information-barycenter as an exemplar for all underlying cluster structure. We show that incorporating spatial regularization into a multiscale clustering framework results in smoother and more coherent clusters when applied to hyperspectral data, yielding more accurate clustering labels.

James M. Murphy

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.