Large scale hyperspectral data segmentation by random spatial subspace clustering

A novel method called spatial subspace clustering (SpatSC)for 1D hyperspectral data segmentation problem, e.g. hyperspectraldata taken from a drill hole, exploring spatial informationhas been proposed in [1]. The purpose of this exerciseis to improve interpretability of the hyperspectral data.The spatial subspace clustering has two major components inits formulation, i.e. data self reconstruction and fused lasso.The first component is mainly to separate different subspaceswhere data lie on or close to, while the second is to exploitthe spatial smoothness based on the observation of stratificationof rocks. It produces interpretable and consistent clustersby utilizing the spatial information. However, the implementationof SpatSC requires an optimization of N2 variables,where N is the number of samples in the data set. WhenN is large, for example, tens of thousands for a typical drillhole data set, the algorithm is no longer suitable for personalcomputers. To alleviate the computational intensity, we proposeto run SpatSC on a randomly chosen calibration set fromcrude spatial clustering, which is only a small proportion ofthe whole data set. The final clustering result is then propagatedcombining the crude spatial clustering and SpatSC resultson calibration set. By doing so, the computation cost isreduced by an order of two magnitude compare to the originalSpatSC. We applied this random spatial subspace clusteringalgorithm on real thermal infrared drill hole data set to showits effectiveness.