no code implementations • 9 Feb 2018 • 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 Gaussian process model.
no code implementations • 22 Mar 2018 • 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 random walk on the hypergraph.
no code implementations • 4 Jun 2016 • Rujie Yin, Tingran Gao, Yue M. Lu, Ingrid Daubechies
We propose an image representation scheme combining the local and nonlocal characterization of patches in an image.
no code implementations • 17 Mar 2015 • 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.
no code implementations • 6 Sep 2018 • Tingran Gao, Shahab Asoodeh, Yi Huang, James Evans
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 propagating "soft labels" (e. g. probability distributions, class membership scores) over hypergraphs, by means of optimal transportation.
no code implementations • ICML 2018 • Chandrajit Bajaj, Tingran Gao, Zihang He, Qi-Xing Huang, Zhenxiao Liang
We introduce a principled approach for simultaneous mapping and clustering (SMAC) for establishing consistent maps across heterogeneous object collections (e. g., 2D images or 3D shapes).
no code implementations • 2 Feb 2019 • Yuanyuan Feng, Tingran Gao, Lei LI, Jian-Guo Liu, Yulong Lu
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon.
no code implementations • 23 May 2019 • 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 significant challenge in machine learning.
no code implementations • 31 May 2019 • 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-dimensional cryo-electron microscopy (cryo-EM) by the similarity among their viewing directions.
1 code implementation • 6 Jun 2019 • 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 structures.
1 code implementation • NeurIPS 2019 • Yifeng Fan, Tingran Gao, Zhizhen Jane Zhao
We introduce a novel co-learning paradigm for manifolds naturally admitting an action of a transformation group $\mathcal{G}$, motivated by recent developments on learning a manifold from attached fibre bundle structures.
no code implementations • 25 Sep 2019 • Naganand Yadati, Tingran Gao, Shahab Asoodeh, Partha Talukdar, Anand Louis
In this paper, we explore GNNs for graph-based SSL of histograms.
1 code implementation • 18 Dec 2018 • 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.
Optimization and Control Numerical Analysis 90C30, 53C50, 53B30, 49M05, 49M15 F.2.1; G.1.6