论文标题
与零近似近似值的精确溶液
Exact solutions in low-rank approximation with zeros
论文作者
论文摘要
与零的低排名近似旨在找到一个固定等级的矩阵和固定零模式，以最大程度地减少欧几里得距离与给定数据矩阵的距离。我们使用代数工具研究了此优化问题的关键点。特别是，我们描述了临界点满足的特殊线性，仿射和决定性关系。我们还研究了关键点的数量以及该数字与非负矩阵分解问题的复杂性有关。
Low-rank approximation with zeros aims to find a matrix of fixed rank and with a fixed zero pattern that minimizes the Euclidean distance to a given data matrix. We study the critical points of this optimization problem using algebraic tools. In particular, we describe special linear, affine, and determinantal relations satisfied by the critical points. We also investigate the number of critical points and how this number is related to the complexity of nonnegative matrix factorization problem.
