8 citations · 32 across the 13 of their papers we have counts for
14 papers
Unsupervised Co-Learning on -Manifolds Across Irreducible Representations
Yifeng Fan, Tingran Gao, Zhizhen Zhao
We introduce a novel co-learning paradigm for manifolds naturally equipped with a group action, motivated by recent developments on learning a manifold from attached fibre bundle s…
Representation Theoretic Patterns in Multi-Frequency Class Averaging for Three-Dimensional Cryo-Electron Microscopy
Yifeng Fan, Tingran Gao, Zhizhen Zhao
We develop in this paper a novel intrinsic classification algorithm -- multi-frequency class averaging (MFCA) -- for classifying noisy projection images obtained from three-dimensi…
SelectNet: Learning to Sample from the Wild for Imbalanced Data Training
Yunru Liu, Tingran Gao, Haizhao Yang
Supervised learning from training data with imbalanced class sizes, a commonly encountered scenario in real applications such as anomaly/fraud detection, has long been considered a…
Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
Yuanyuan Feng, Tingran Gao, Lei Li +2
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the back…
Multi-Frequency Phase Synchronization
Tingran Gao, Zhizhen Zhao
We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimiz…
Semi-Riemannian Manifold Optimization
Tingran Gao, Lek-Heng Lim, Ke Ye
We introduce in this paper a manifold optimization framework that utilizes semi-Riemannian structures on the underlying smooth manifolds. Unlike in Riemannian geometry, where each…
Wasserstein Soft Label Propagation on Hypergraphs: Algorithm and Generalization Error Bounds
Tingran Gao, Shahab Asoodeh, Yi Huang +1
Inspired by recent interests of developing machine learning and data mining algorithms on hypergraphs, we investigate in this paper the semi-supervised learning algorithm of propag…
Gaussian Process Landmarking for Three-Dimensional Geometric Morphometrics
Tingran Gao, Shahar Z. Kovalsky, Doug M. Boyer +1
We demonstrate applications of the Gaussian process-based landmarking algorithm proposed in [T. Gao, S.Z. Kovalsky, and I. Daubechies, SIAM Journal on Mathematics of Data Science (…
Curvature of Hypergraphs via Multi-Marginal Optimal Transport
Shahab Asoodeh, Tingran Gao, James Evans
We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined…
Gaussian Process Landmarking on Manifolds
Tingran Gao, Shahar Z. Kovalsky, Ingrid Daubechies
As a means of improving analysis of biological shapes, we propose an algorithm for sampling a Riemannian manifold by sequentially selecting points with maximum uncertainty under a…
The Geometry of Synchronization Problems and Learning Group Actions
Tingran Gao, Jacek Brodzki, Sayan Mukherjee
We develop a geometric framework that characterizes the synchronization problem --- the problem of consistently registering or aligning a collection of objects. The theory we formu…
A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets
Rujie Yin, Tingran Gao, Yue M. Lu +1
We propose an image representation scheme combining the local and nonlocal characterization of patches in an image. Our representation scheme can be shown to be equivalent to a tig…
The Diffusion Geometry of Fibre Bundles: Horizontal Diffusion Maps
Tingran Gao
Kernel-based non-linear dimensionality reduction methods, such as Local Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores, w…
Hypoelliptic Diffusion Maps I: Tangent Bundles
Tingran Gao
We introduce the concept of Hypoelliptic Diffusion Maps (HDM), a framework generalizing Diffusion Maps in the context of manifold learning and dimensionality reduction. Standard no…