The Grassmannian of affine subspaces
文献类型：期刊论文
| 作者 | Lim, Lek-Heng2; Wong, Ken Sze-Wai1; Ye, Ke3 |
| 刊名 | FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
 |
| 出版日期 | 2020-05-27 |
| 页码 | 38 |
| 关键词 | Affine Grassmannian Affine subspaces Schubert calculus homotopy and (co)homology Probability densities Distances and metrics Multivariate data analysis |
| ISSN号 | 1615-3375 |
| DOI | 10.1007/s10208-020-09459-8 |
| 英文摘要 | The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being 0-dimensional affine subspaces, and the usual Grassmannian, linear subspaces being special cases of affine subspaces. We show that, like the Grassmannian, the affine Grassmannian has rich geometrical and topological properties: It has the structure of a homogeneous space, a differential manifold, an algebraic variety, a vector bundle, a classifying space, among many more structures; furthermore, it affords an analogue of Schubert calculus and its (co)homology and homotopy groups may be readily determined. On the other hand, like the Euclidean space, the affine Grassmannian serves as a concrete computational platform on which various distances, metrics, probability densities may be explicitly defined and computed via numerical linear algebra. Moreover, many standard problems in machine learning and statistics-linear regression, errors-in-variables regression, principal components analysis, support vector machines, or more generally any problem that seeks linear relations among variables that either best represent them or separate them into components-may be naturally formulated as problems on the affine Grassmannian. |
| 资助项目 | DARPA[D15AP00109] ; DARPA[NSFIIS 1546413] ; DARPA[DMS1209136] ; NSFC[11801548] ; NSFC[11688101] ; National Key R&D Program of China[2018YFA0306702] ; DARPA Director's Fellowship ; Eckhardt Faculty Fund ; Hundred Talents Program of the Chinese Academy of Sciences ; Recruitment Program of Global Experts of China |
| WOS研究方向 | Computer Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000535870100001 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51523]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Lim, Lek-Heng |
| 作者单位 | 1.Univ Chicago, Dept Stat, Chicago, IL 60637 USA 2.Univ Chicago, Dept Stat, Computat & Appl Math Initiat, Chicago, IL 60637 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Lim, Lek-Heng,Wong, Ken Sze-Wai,Ye, Ke. The Grassmannian of affine subspaces[J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS,2020:38. |
| APA | Lim, Lek-Heng,Wong, Ken Sze-Wai,&Ye, Ke.(2020).The Grassmannian of affine subspaces.FOUNDATIONS OF COMPUTATIONAL MATHEMATICS,38. |
| MLA | Lim, Lek-Heng,et al."The Grassmannian of affine subspaces".FOUNDATIONS OF COMPUTATIONAL MATHEMATICS (2020):38. |
入库方式： OAI收割
来源：数学与系统科学研究院
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