Name
Title | ||
|---|---|---|
A Linearly Convergent Method for Non-Smooth Non-Convex Optimization on the Grassmannian with Applications to Robust Subspace and Dictionary Learning |
Abstract | ||
|---|---|---|
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 (RRC) with respect to some point in the Grassmannian, then a projected Riemannian subgradient method with appropriate initialization and geometrically diminishing step size converges at a linear rate to that point. We show that for both the robust subspace learning method Dual Principal Component Pursuit (DPCP) and the Orthogonal Dictionary Learning (ODL) problem, the RRC is satisfied with respect to appropriate points of interest, namely the subspace orthogonal to the sought subspace for DPCP and the orthonor-mal dictionary atoms for ODL. Consequently, we obtain in a unified framework significant improvements for the convergence theory of both methods. |
Year | Venue | Keywords |
|---|---|---|
2019 | NeurIPS | dictionary learning |
Field | DocType | Citations |
Mathematical optimization,Non convex optimization,Dictionary learning,Algebra,Subspace topology,Computer science,Grassmannian | Conference | 1 |
PageRank | References | Authors |
0.34 | 0 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhihui Zhu | 1 | 1 | 0.34 |
| Tianyu Ding | 2 | 2 | 2.04 |
| Daniel P. Robinson | 3 | 261 | 21.51 |
| Manolis C. Tsakiris | 4 | 50 | 9.79 |
| rene victor valqui vidal | 5 | 5331 | 260.14 |