Low rank sequential subspace clustering

Sequential data are ubiquitous in data analysis. For example hyperspectral data taken from a drill hole in geology, high throughput X-ray diffraction measurements in materials research and EEG brain wave signals in neuroscience. The common feature of sequential data is that they are all acquired subject to one external variable such as location, time or temperature. The data evolve along the direction of that variable through several patterns and the “neighboring” data are very likely to share similar features. The purpose of the segmentation for sequential data is then to identify those sequentially continuous segments/patterns. We approach this problem by adopting the subspace clustering method and propose a novel algorithm called low rank sequential subspace clustering (LRSSC), inspired by another method called spatial subspace clustering (SpatSC). SpatSC finds the subspaces by data self-reconstruction with a sparsity constraint on reconstruction weights and promotes the spatial smoothness of the weights by fusion, the essential part in the fused LASSO. However, the subspace identification capability is limited due to the indeterminacy of the sparse regression in finding suitable samples to linearly reconstruct a given sample. This confuses the graph cut algorithm that produces the final clustering results on the weights. To overcome this drawback, we propose to use the low rank penalty instead of sparsity in learning phase to separate subspaces. This improves the subspace identification as well as the robustness to noise. To demonstrate its effectiveness, we test LRSSC on both simulated and real world data compared with SpatSC and other methods. The proposed algorithm is superior to others when noise level is very high.