Non-Smooth Optimization over Stiefel Manifolds with Applications to Dimensionality Reduction and Graph Clustering
Abstract
This paper is concerned with the class of non-convex optimization problems with orthogonality constraints. We develop computationally efficient relaxations that transform non-convex orthogonality constrained problems into polynomial-time solvable surrogates. A novel penalization technique is used to enforce feasibility and derive certain conditions under which the constraints of the original non-convex problem are guaranteed to be satisfied. Moreover, we extend our approach to a feasibility-preserving sequential scheme that solves penalized relaxation to obtain near-globally optimal points. Experimental results on synthetic and real datasets demonstrate the effectiveness of the proposed approach on two practical applications in machine learning.
Cite
Text
Zohrizadeh et al. "Non-Smooth Optimization over Stiefel Manifolds with Applications to Dimensionality Reduction and Graph Clustering." International Joint Conference on Artificial Intelligence, 2019. doi:10.24963/IJCAI.2019/183Markdown
[Zohrizadeh et al. "Non-Smooth Optimization over Stiefel Manifolds with Applications to Dimensionality Reduction and Graph Clustering." International Joint Conference on Artificial Intelligence, 2019.](https://mlanthology.org/ijcai/2019/zohrizadeh2019ijcai-non/) doi:10.24963/IJCAI.2019/183BibTeX
@inproceedings{zohrizadeh2019ijcai-non,
title = {{Non-Smooth Optimization over Stiefel Manifolds with Applications to Dimensionality Reduction and Graph Clustering}},
author = {Zohrizadeh, Fariba and Kheirandishfard, Mohsen and Kamangar, Farhad and Madani, Ramtin},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2019},
pages = {1319-1326},
doi = {10.24963/IJCAI.2019/183},
url = {https://mlanthology.org/ijcai/2019/zohrizadeh2019ijcai-non/}
}