We propose Ordered Subspace Clustering (OSC) to segment data drawn from a sequentially ordered union of subspaces. Similar to Sparse Subspace Clustering (SSC) we formulate the problem as one of finding a sparse representation but include an additional penalty term to take care of sequential data. We test our method on data drawn from infrared hyper spectral, video and motion capture data. Experiments show that our method, OSC, outperforms the state of the art methods: Spatial Subspace Clustering (SpatSC), Low-Rank Representation (LRR) and SSC.
A method called spatial subspace clustering (SpatSC) is proposed for the hyperspectral data segmentation problem focusing on the hyperspectral data taken from a drill hole, which can be seen as one-dimensional image data compared with hyperspectral multispectral image data. Addressing this problem has several practical uses, such as improving interpretability of the data, and, especially, obtaining a better understanding of the mineralogy. SpatSC is a combination of subspace learning and the fused least absolute shrinkage and selection operator. As a result, it is able to produce spatially smooth clusters. From this point of view, it can be simply interpreted as a spatial information guided subspace learning algorithm. SpatSC has flexible structures that embrace the cases with and without library of pure spectra. It can be further extended, for example, using different error structures, such as including rank operator. We test this method on both simulated data and real-world hyperspectral data. SpatSC produces stable and continuous segments, which are more interpretable than those obtained from other state-of-the-art subspace learning algorithms.