Search Results for author: Tingran Gao

Found 13 papers, 3 papers with code

Unsupervised Co-Learning on G-Manifolds Across Irreducible Representations

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.

Community Detection

Unsupervised Co-Learning on $\mathcal{G}$-Manifolds Across Irreducible Representations

1 code implementation6 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.

Community Detection

Representation Theoretic Patterns in Multi-Frequency Class Averaging for Three-Dimensional Cryo-Electron Microscopy

no code implementations31 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.

SelectNet: Learning to Sample from the Wild for Imbalanced Data Training

no code implementations23 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.

Fraud Detection

Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation

no code implementations2 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.

Stochastic Optimization

Semi-Riemannian Manifold Optimization

1 code implementation18 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

Wasserstein Soft Label Propagation on Hypergraphs: Algorithm and Generalization Error Bounds

no code implementations6 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.

SMAC: Simultaneous Mapping and Clustering Using Spectral Decompositions

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).


Curvature of Hypergraphs via Multi-Marginal Optimal Transport

no code implementations22 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.

Gaussian Process Landmarking on Manifolds

no code implementations9 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.

Experimental Design

Hypoelliptic Diffusion Maps I: Tangent Bundles

no code implementations17 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.

Dimensionality Reduction

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