6 accepted papers
State-of-the-art subspace clustering methods are based on convex formulations whose theoretical guarantees require the subspaces to be low-dimensional. Dual Principal Component Pursuit (DPCP) is a non-convex method that is specifically designed for learning high-dimensional subspaces, such as hyperp…
Minimizing a non-smooth function over the Grassmannian appears in many applications in machine learning. In this paper we show that if the objective satisfies a certain Riemannian regularity condition with respect to some point in the Grassmannian, then a Riemannian subgradient method with appropri…
A recent line of research termed "unlabeled sensing" and "shuffled linear regression" has been exploring under great generality the recovery of signals from subsampled and permuted measurements; a challenging problem in diverse fields of data science and machine learning. In this paper we introduce…
Dual Principal Component Pursuit (DPCP) is a recently proposed non-convex optimization based method for learning subspaces of high relative dimension from noiseless datasets contaminated by as many outliers as the square of the number of inliers. Experimentally, DPCP has proved to be robust to noise…
Recent methods for learning a linear subspace from data corrupted by outliers are based on convex L1 and nuclear norm optimization and require the dimension of the subspace and the number of outliers to be sufficiently small [27]. In sharp contrast, the recently proposed Dual Principal Component Pur…
Sparse Subspace Clustering (SSC) is a popular unsupervised machine learning method for clustering data lying close to an unknown union of low-dimensional linear subspaces; a problem with numerous applications in pattern recognition and computer vision. Even though the behavior of SSC for complete da…