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.
Rather than compute the sparsest representation of each data point individually, Low-Rank Representation (LRR) by Liu, Lin and Yu @cite_39 attempts to incorporate global structure of the data by computing the lowest-rank representation of the set of data points. Therefore the objective becomes This means that not only can the data points be decomposed as a linear combination of other points but the entire coefficient matrix should be low-rank. The aim of the rank penalty is to create a global grouping effect that reflects the underlying subspace structure of the data. In other words, data points belonging to the same subspace should have similar coefficient patterns.
@cite_39
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We propose low-rank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowest-rank representation among all the candidates that represent all vectors as the linear combination of the bases in a dictionary. Unlike the well-known sparse representation (SR), which computes the sparsest representation of each data vector individually, LRR aims at finding the lowest-rank representation of a collection of vectors jointly. LRR better captures the global structure of data, giving a more effective tool for robust subspace segmentation from corrupted data. Both theoretical and experimental results show that LRR is a promising tool for subspace segmentation.