Latent Space Sparse Subspace Clustering

Abstract

We propose a novel algorithm called Latent Space Sparse Subspace Clustering for simultaneous dimensionality reduction and clustering of data lying in a union of subspaces. Specifically, we describe a method that learns the projection of data and finds the sparse coefficients in the low-dimensional latent space. Cluster labels are then assigned by applying spectral clustering to a similarity matrix built from these sparse coefficients. An efficient optimization method is proposed and its non-linear extensions based on the kernel methods are presented. One of the main advantages of our method is that it is computationally efficient as the sparse coefficients are found in the low-dimensional latent space. Various experiments show that the proposed method performs better than the competitive state-of-theart subspace clustering methods.

Robust Subspace Clustering With Complex Noise

“…We compare SCHQ with state-of-the-art subspace clustering methods, e.g., Local Subspace Analysis (LSA) [44], Spectral curvature clustering (SCC) [45], LRR [9], block-diagonal LRR (BD-LRR) [12], LSR [11], Low-Rank Subspace Clustering (LRSC) [46], SSC [7], Latent Space SSC (LS3C) [19] and Sparse Additive Subspace Clustering (SASC) [47]. We denote the semi-supervised extension of SCHQ to deal with link constraints as S-SCHQ.…”

“…Bayesian method [14], quadratic programming [15], least squares regression [11], [16], manifold regularization [17] and Markov random walks [18] were also used respectively to improve clustering accuracy. In addition, Patel et al [19] proposed a latent space sparse subspace clustering method to simultaneously reduce dimension and segment data. Dictionary learning methods [16], [20] were adopted to learn a clean dictionary for subspace clustering.…”

Latent Space Sparse and Low-Rank Subspace Clustering

“…Statistical [12] and algebraic [13], [14] approaches have also been proposed in the literature for subspace clustering. In particular, sparse representation and low-rank approximation-based methods for subspace clustering [15], [16], [11], [17], [18], [19], [20], [21], [22], [23], [24] have gained a lot of traction in recent years. These methods find a sparse or low-rank representation of the data and build a similarity graph whose weights depend on the sparse or lowrank coefficient matrix for segmenting the data.…”

Unbiased Sparse Subspace Clustering by Selective Pursuit

“…Since the subspace model is often motivated by some underlying physical model, for instance each rigidly moving body induces a 4-dimensional subspace in motion segmentation, over-segmenting the data can be difficult to correct. On the other hand, because most algorithms of this class (Elhamifar and Vidal 2013;Patel, Nguyen, and Vidal 2013;Li and Vidal 2015;Liu, Lin, and Yu 2010) require the number of clusters to be known in advance, cluster centers will be incorrect which causes the labelling to be wrong. It is therefore more desirable to address the original problem in the first place.…”

“…An extension of SSC jointly estimates the parameters of a global subspace which includes all the data (Patel, Nguyen, and Vidal 2013). In a recent work, both steps of sparse optimization and spectral clustering were combined into a single, iterative algorithm (Li and Vidal 2015).…”