论文标题
同时强大的子空间恢复和箭袋表示的半稳定性
Simultaneous robust subspace recovery and semi-stability of quiver representations
论文作者
论文摘要
我们考虑在给定的$ m $ m $ $ tuple中同时找到较低维的子空间结构的问题，这些结构可能会损坏，高维数据集所有相同的大小。我们将此问题称为同时强大的子空间恢复（SRSR），并为其提供了一种颤抖的理论方法。我们表明，SRSR是一个更普遍的问题的特殊情况，即有效地确定颤抖的代表是否是半稳定的（在几何不变理论的意义上），并且如果不是，以至于没有找到以最佳方式证明该代表性不是半稳定的。在本文中，我们表明SRSR和更一般的箭量半稳定性问题可以有效解决。
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.
