Simultaneous robust subspace recovery and semi-stability of quiver representations
Abstract
We consider the problem of simultaneously finding lower-dimensional subspace structures in a given $m$-tuple of possibly corrupted, high-dimensional data sets all of the same size. We refer to this problem as simultaneous robust subspace recovery (SRSR) and provide a quiver invariant theoretic approach to it. We show that SRSR is a particular case of the more general problem of effectively deciding whether a quiver representation is semi-stable (in the sense of Geometric Invariant Theory) and, in case it is not, finding a subrepresentation certifying in an optimal way that the representation is not semi-stable. In this paper, we show that SRSR and the more general quiver semi-stability problem can be solved effectively.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2020
- DOI:
- 10.48550/arXiv.2003.02962
- arXiv:
- arXiv:2003.02962
- Bibcode:
- 2020arXiv200302962C
- Keywords:
-
- Mathematics - Representation Theory;
- Computer Science - Computational Complexity;
- Computer Science - Data Structures and Algorithms;
- 16G20;
- 13A50;
- 14L24
- E-Print:
- Journal of Algebra, Volume 577, 1 July 2021, Pages 210-236