7 papers
Linear representations of manifolds
Rongbiao Thomas Wang, Lek-Heng Lim, Ke Ye
A finite-dimensional linear representation of a group or an algebra may be regarded as a map into a space of matrices, endowing abstract elements with coordinates, and encoding alg…
Atlas Gaussian processes on restricted domains and point clouds
Mu Niu, Yue Zhang, Ke Ye +3
In real-world applications, data often reside in restricted domains with unknown boundaries, or as high-dimensional point clouds lying on a lower-dimensional, nontrivial, unknown m…
Special orthogonal, special unitary, and symplectic groups as products of Grassmannians
Lek-Heng Lim, Xiang Lu, Ke Ye
We describe a curious structure of the special orthogonal, special unitary, and symplectic groups that has not been observed, namely, they can be expressed as matrix products of th…
Simple matrix expressions for the curvatures of Grassmannian
Zehua Lai, Lek-Heng Lim, Ke Ye
We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q =…
Degree of the Grassmannian as an affine variety
Lek-Heng Lim, Ke Ye
The degree of the Grassmannian with respect to the Plücker embedding is well-known. However, the Plücker embedding, while ubiquitous in pure mathematics, is almost never used in…
Commutative algebra-enhanced topological data analysis
Chuanshen Hu, Yu Wang, Kelin Xia +2
Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space…