V2EX low-rank

Low-rank

释义 Definition

low-rank(形容词,常用于数学/机器学习/线性代数语境):指秩较低的(如矩阵、近似、结构),意味着可用较少的独立成分/维度来表示,常用于降维、压缩、去噪、推荐系统等。也可引申为“结构简单、内在维度小”的。

发音 Pronunciation (IPA)

/lo rk/

例句 Examples

A low-rank matrix can be stored using much less memory.
低秩矩阵可以用更少的内存来存储。

By assuming the data has a low-rank structure, the algorithm can recover missing entries with high accuracy.
通过假设数据具有低秩结构,该算法可以高精度地恢复缺失项。

词源 Etymology

low 来自古英语 lāh(“不高的、低的”),“rank”在此并非“军衔”,而是数学中的“”(来自法语 rang,有“等级/排列”之意)。在现代数学与工程语境中,rank(秩)表示线性独立信息的“数量”,因此 low-rank 就是“秩较低、信息维度较少”。

相关词 Related Words

文学作品 Literary Works

  • The Princeton Companion to Mathematics(常在矩阵分解、线性代数相关条目中讨论“低秩/低秩近似”等概念)
  • Numerical Linear Algebra(Lloyd N. Trefethen & David Bau III;涉及 low-rank approximation、SVD 等核心主题)
  • Matrix Computations(Gene H. Golub & Charles F. Van Loan;广泛出现 low-rank updates/approximations 等表述)
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