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.
Spatial Subspace Clustering (SpatSC) @cite_2 extended SSC by incorporating a sequential @math neighbour penalty where @math is a lower triangular matrix with @math on the diagonal and @math on the second lower diagonal: ]. Therefore @math . The aim of this formulation is to force consecutive columns of @math to be similar.
@cite_2
2296131993 2110726819 2152461258 2759684359
Given a data set from a union of multiple linear sub-spaces, a robust subspace clustering algorithm fits each group of data points with a low-dimensional subspace and then clusters these data even though they are grossly corrupted or sampled from the union of dependent sub-spaces. Under the framework of spectral clustering, recent works using sparse representation, low rank representation and their extensions achieve robust clustering results by formulating the errors (e.g., corruptions) into their objective functions so that the errors can be removed from the inputs. However, these approaches have suffered from the limitation that the structure of the errors should be known as the prior knowledge. In this paper, we present a new method of robust sub-space clustering by eliminating the effect of the errors from the projection space (representation) rather than from the input space. We firstly prove that l1-, l2-, and l∞ -norm-based linear projection spaces share the property of intra-subspace projection dominance, i.e., the coefficients over intra-subspace data points are larger than those over inter-subspace data points. Based on this property, we propose a robust and efficient sub-space clustering algorithm, called Thresholding Ridge Regression (TRR). TRR calculates the ∞2 -norm-based coefficients of a given data set and performs a hard thresholding operator; and then the coefficients are used to build a similarity graph for clustering. Experimental studies show that TRR outperforms the state-of-the-art methods with respect to clustering quality, robustness, and time-saving. 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. Subspace clustering refers to the task of nding a multi-subspace representation that best ts a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) (25) to cluster noisy data, and develops some novel theory demonstrating its correctness. In particular, the theory uses ideas from geometric functional analysis to show that the algorithm can accurately recover the underlying subspaces under minimal requirements on their orientation, and on the number of samples per subspace. Synthetic as well as real data experiments complement our theoretical study, illustrating our approach and demonstrating its eectiveness. In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data affinity matrix by simultaneously satisfying the sparsity principle of SSC and the nonlinearity given by neural networks. One of the appealing advantages brought by DSSC is: when original real-world data do not meet the class-specific linear subspace distribution assumption, DSSC can employ neural networks to make the assumption valid with its hierarchical nonlinear transformations. To the best of our knowledge, this is among the first deep learning based subspace clustering methods. Extensive experiments are conducted on four real-world datasets to show the proposed DSSC is significantly superior to 12 existing methods for subspace clustering.