3 papers
math.OC2025
Adaptive Stochastic Gradient Descents on Manifolds with an Application on Weighted Low-Rank Approximation
Peiqi Yang, Conglong Xu, Hao Wu
We prove a convergence theorem for stochastic gradient descents on manifolds with adaptive learning rate and apply it to the weighted low-rank approximation problem.
math.OC2025
Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds
Conglong Xu, Peiqi Yang, Hao Wu
We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we e…
math.AT2024
Decomposition of Persistent Homology and Spectral Sequences
Peiqi Yang, Yingfeng Hu, Hao Wu
We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent h…