1 citations · 3 across the 11 of their papers we have counts for
12 papers
Kempe factorizations for rational curves on
Yifan Li, Zijia Li, Ke Ye
We study constructive Kempe factorizations for rational curves on . Motivated by motion-polynomial factorization and rational matrix curves on real…
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…
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…
Euclidean distance degree in manifold optimization
Zehua Lai, Lek-Heng Lim, Ke Ye
We determine the Euclidean distance degrees of the three most common manifolds arising in manifold optimization: flag, Grassmann, and Stiefel manifolds. For the Grassmannian, we wi…
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…
Rational Curves on Real Classical Groups
Zijia Li, Ke Ye
This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classic…
Simple matrix models for the flag, Grassmann, and Stiefel manifolds
Lek-Heng Lim, Ke Ye
We derive three families of orthogonally-equivariant matrix submanifold models for the Grassmann, flag, and Stiefel manifolds respectively. These families are exhaustive -- every o…
Minimal equivariant embeddings of the Grassmannian and flag manifold
Lek-Heng Lim, Ke Ye
We show that the flag manifold , with Grassmannian the special case , has an -equivariant e…
Grassmannian optimization is NP-hard
Zehua Lai, Lek-Heng Lim, Ke Ye
We show that unconstrained quadratic optimization over a Grassmannian is NP-hard. Our results cover all scenarios: (i) when and are both allowed to…
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 ap…