带权重或缺失数据的低秩矩阵逼近是NP难的
Low-Rank Matrix Approximation with Weights or Missing Data is NP-hard
AI总结：
本文通过从最大边双团问题归约，证明带权重或缺失数据的低秩矩阵逼近（包括秩一逼近）是NP难的。
摘要：
加权低秩逼近（WLRA）是一种用于数据分析的降维技术，已成功应用于多个领域，例如协同过滤中的推荐系统设计或计算机视觉中的运动恢复结构。本文研究了WLRA的计算复杂度，并证明即使寻求秩一逼近，找到近似解也是NP难的。我们的证明基于从最大边双团问题的归约，适用于严格正权重以及二元权重（后者对应于缺失数据的低秩矩阵逼近）。
英文摘要：
Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data analysis, has been successfully used in several applications, such as in collaborative filtering to design recommender systems or in computer vision to recover structure from motion. In this paper, we study the computational complexity of WLRA and prove that it is NP-hard to find an approximate solution, even when a rank-one approximation is sought. Our proofs are based on a reduction from the maximum-edge biclique problem, and apply to strictly positive weights as well as binary weights (the latter corresponding to low-rank matrix approximation with missing data).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
