7 citations · 8 across the 8 of their papers we have counts for
8 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…
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…
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…
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…
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…
LDLE: Low Distortion Local Eigenmaps
Dhruv Kohli, Alexander Cloninger, Gal Mishne
We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers t…
Radial expansion preserves hyperbolic convexity and radial contraction preserves spherical convexity
Dhruv Kohli, Jeffrey M. Rabin
On a flat plane, convexity of a set is preserved by both radial expansion and contraction of the set about any point inside it. Using the Poincaré disk model of hyperbolic geometry…
Asymmetric expansion preserves hyperbolic convexity
Dhruv Kohli, Jeffrey M. Rabin
In an earlier paper we showed that the radial expansion of a hyperbolic convex set in the Poincaré disk about any point inside it results in a hyperbolic convex set. In this work,…