4 citations · 15 across the 18 of their papers we have counts for
24 papers
RhinoNet: Unsupervised Learning for Phenoscaping and Generation of High Dimensional Point Clouds
Siddharth Viswanath, Hiren Madhu, Eddie Cavallin +7
We present RhinoNet, a simplicial complex-based point cloud neural network, that creates a geometry-preserving embedding of high-dimensional point clouds. RhinoNet takes collection…
A Graph Laplacian Eigenvector-based Pre-training Method for Graph Neural Networks
Howard Dai, Nyambura Njenga, Hiren Madhu +4
The development of self-supervised graph pre-training methods is a crucial ingredient in recent efforts to design robust graph foundation models (GFMs). Structure-based pre-trainin…
HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Data
Siddharth Viswanath, Hiren Madhu, Dhananjay Bhaskar +7
In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Our wor…
Exploring the Manifold of Neural Networks Using Diffusion Geometry
Elliott Abel, Andrew J. Steindl, Selma Mazioud +12
Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of…
Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds
Xingzhi Sun, Danqi Liao, Kincaid MacDonald +7
Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it…
Assessing Neural Network Representations During Training Using Noise-Resilient Diffusion Spectral Entropy
Danqi Liao, Chen Liu, Benjamin W. Christensen +6
Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, i…
BLIS-Net: Classifying and Analyzing Signals on Graphs
Charles Xu, Laney Goldman, Valentina Guo +7
Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. However, much less work has been done on signal classif…
A Flow Artist for High-Dimensional Cellular Data
Kincaid MacDonald, Dhananjay Bhaskar, Guy Thampakkul +5
We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapsh…
Neural FIM for learning Fisher Information Metrics from point cloud data
Oluwadamilola Fasina, Guillaume Huguet, Alexander Tong +5
Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffus…
A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction
Guillaume Huguet, Alexander Tong, Edward De Brouwer +4
Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Su…
Diffusion Curvature for Estimating Local Curvature in High Dimensional Data
Dhananjay Bhaskar, Kincaid MacDonald, Oluwadamilola Fasina +4
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusi…
Geodesic nets on flat spheres
Ian Adelstein, Elijah Fromm, Rajiv Nelakanti +2
We consider geodesic nets (critical points of a length functional on the space of embedded graphs) on doubled polygons (topological 2-spheres endowed with a flat metric away from f…
Besse projective spaces with many diameters
Ian Adelstein, Franco Vargas Pallete
It is known that Blaschke manifolds (where injectivity radius equals diameter) are Besse manifolds (where all geodesics are closed). We show that Besse manifolds with sufficiently…
Oblivious points on translation surfaces
Ian Adelstein, Krish Desai, Anthony Ji +1
An oblivious point on a translation surface is a point with no closed geodesic passing through it. Nguyen, Pan, and Su (2017) showed that there are at most finitely many oblivious…
The length of the shortest closed geodesic on positively curved 2-spheres
Ian Adelstein, Franco Vargas Pallete
We show that the shortest closed geodesic on a 2-sphere with non-negative curvature has length bounded above by three times the diameter. We prove a new isoperimetric inequality fo…
Closed geodesics on doubled polygons
Ian Adelstein, Adam Fong
In this paper we study 1/k-geodesics, those closed geodesics that minimize on any subinterval of length , where is the length of the geodesic. We investigate the existence…
Minimizing closed geodesics on polygons and disks
Ian Adelstein, Arthur Azvolinsky, Joshua Hinman +1
In this paper we study 1/k geodesics, those closed geodesics that minimize on all subintervals of length , where is the length of the geodesic. We develop new techniques t…
Minimizing geodesic nets and critical points of distance
Ian M Adelstein
In this paper we establish a relationship between geodesic nets and critical points of the distance function. We bound the number of balanced points for certain minimizing geodesic…
Characterizing Round Spheres Using Half-Geodesics
Ian M Adelstein, Benjamin Schmidt
A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this note establishes th…
Leaf Space Isometries of Singular Riemannian Foliations and Their Spectral Properties
Ian M. Adelstein, M. R. Sandoval
In this paper, the authors consider leaf spaces of singular Riemannian foliations on compact manifolds and the associated -basic spectrum on , $sp…
Morse theory for the uniform energy
Ian Adelstein, Jonathan Epstein
In this paper we develop a Morse theory for the uniform energy. We use the one-sided directional derivative of the distance function to study the minimizing properties of variation…
The G-invariant spectrum and non-orbifold singularities
Ian M. Adelstein, Mary R. Sandoval
We consider the -invariant spectrum of the Laplacian on an orbit space where is a compact Riemannian manifold and acts by isometries. We generalize the Sunada-Pesc…
Existence and Non-existence of Half-Geodesics on
Ian Adelstein
In this paper we study half-geodesics, those closed geodesics that minimize on any subinterval of length . For each nonnegative integer , we construct Riemannian manifol…
Minimizing Closed Geodesics via Critical Points of the Uniform Energy
Ian Adelstein
In this paper we study 1/k-geodesics, those closed geodesics that minimize on any subinterval of length . We employ energy methods to provide a relationship between the 1/k…