Search Results for author:
Found 13 papers, 3 papers with code
Unsupervised Co-Learning on G-Manifolds Across Irreducible Representations
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.
Graph Neural Networks for Soft Semi-Supervised Learning on Hypergraphs
In this paper, we explore GNNs for graph-based SSL of histograms.
Unsupervised Co-Learning on $\mathcal{G}$-Manifolds Across Irreducible Representations
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.
Representation Theoretic Patterns in Multi-Frequency Class Averaging for Three-Dimensional Cryo-Electron Microscopy
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
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.
Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon.
Semi-Riemannian Manifold Optimization
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
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
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
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
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.
A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets
We propose an image representation scheme combining the local and nonlocal characterization of patches in an image.
Hypoelliptic Diffusion Maps I: Tangent Bundles
We introduce the concept of Hypoelliptic Diffusion Maps (HDM), a framework generalizing Diffusion Maps in the context of manifold learning and dimensionality reduction.
