5 papers
Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization
Dhruv Kohli, Sawyer J. Robertson, Gal Mishne +1
Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis. The standard approach, Local Principal Component Analysis (LPCA), struggles in…
Robust boundary detection and density estimation using doubly stochastic scaling of the Gaussian kernel
Dhruv Kohli, Jesse He, Chester Holtz +2
This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the pre…
Low-dimensional embeddings of high-dimensional data
Cyril de Bodt, Alex Diaz-Papkovich, Michael Bleher +18
Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working…
Non-degenerate Rigid Alignment in a Patch Framework
Dhruv Kohli, Gal Mishne, Alexander Cloninger
Given a set of overlapping local views (patches) of a dataset, we consider the problem of finding a rigid alignment of the views that minimizes a -norm based alignment error. In…
On a Generalization of Wasserstein Distance and the Beckmann Problem to Connection Graphs
Sawyer Robertson, Dhruv Kohli, Gal Mishne +1
We propose a model of optimal parallel transport between vector fields on a connection graph, which consists of a weighted graph along with a map from its edges to an orthogonal gr…