Robust Subspace Segmentation with Block-Diagonal Prior

Abstract

The subspace segmentation problem is addressed in this paper by effectively constructing an exactly block-diagonal sample affinity matrix. The block-diagonal structure is heavily desired for accurate sample clustering but is rather difficult to obtain. Most current state-of-the-art subspace segmentation methods (such as SSC [4] and LRR [12]) resort to alternative structural priors (such as sparseness and low-rankness) to construct the affinity matrix. In this work, we directly pursue the block-diagonal structure by proposing a graph Laplacian constraint based formulation, and then develop an efficient stochastic subgradient algorithm for optimization. Moreover, two new subspace segmentation methods, the block-diagonal SSC and LRR, are devised in this work. To the best of our knowledge, this is the first research attempt to explicitly pursue such a block-diagonal structure. Extensive experiments on face clustering, motion segmentation and graph construction for semi-supervised learning clearly demonstrate the superiority of our novelly proposed subspace segmentation methods.

Multiple subspaces separation in case of camera motion

“…We compare our method to some previous subspace segmentation methods including RANSAC [10], GPCA [18], LSA [29], ALC [21], SSC [5], SCC [2], MSL [23], LLMC [11], LBF [30], LRR [17], LRR-H [17], LRSC [7], RPCA methods from RPCA 1 [1], RPCA 2,1 [28], and [22], SR [4], and SLBF [30], BDLRR [9], and the most recent work S 3 C [15].…”

Robust unsupervised subspace learning for visual representation

“…The authors also theoretically proved that Least Squares Regression (LSR) can generate a better block-diagonal graph when the underlying subspaces are orthogonal or subspaces are independent if data are sufficient. Targeting the block-diagonal property, Feng et al directly pursued a block-diagonal structure by incorporating a graph Laplacian constraint based formulation [20]. Hu et al designed smooth representation model, which integrated the grouping effect into the learned representation and demonstrated the manifold structure within the data is critical in subspace clustering problem [21].…”

“…In this experiment, the first 10 subjects data are generated as [3,93], with the only pre-precessing of resizing the images to 32 ⇥ 32 pixels [3,5]. All the algorithms are run on the same prepossessed data.…”

“…• BD-LRR [93] 6 . There is one major parameter in their model, which we fine tune in the range of [1,10] with a step of 0.1, and report the best result.…”

“…• BD-SSC [93]. Similar to BD-LRR, we fine tune the parameter in their model, which we fine tune in the range of [100,2000] with a step of 10, covering the default one, i.e.…”