Dhruv Kohli
*at SIAM MDS, Atlanta, 2024.
My research areas are geometric data analysis, manifold learning, spectral graph theory, optimization and optimal transport.
My PhD focuses on the following key questions:
- How to obtain low distortion low-dimensional local representations of high-dimensional data while accounting for the global geometry of the data manifold.
- How to integrate these local representations in an efficient and robust manner to produce a low-distortion global embedding.
- How does the distortion incurred in the low-dimensional embedding impacts the performance of the downstream tasks.
My advisors are Alex Cloninger and Gal Mishne.
Publications
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Robust estimation of boundary using doubly stochastic scaling of Gaussian kernel.
with Jesse He, Chester Holtz, Gal Mishne, Alex Cloninger
Preprint. [arXiv][Code]
-
RATS: Unsupervised manifold learning using low-distortion alignment of tangent spaces.
with Johannes S. Nieuwenhuis, Alex Cloninger, Gal Mishne, Devika Narain
Under review. [bioRxiv]
-
Tearing and Repulsion Enabled Registration of Point Clouds.
with Alex Cloninger, Gal Mishne
Submitted, 2024 [arXiv] [Code]
-
On a Generalization of Wasserstein Distance and the Beckmann Problem to Connection Graphs.
with Sawyer Robertson, Alex Cloninger, Gal Mishne
Revision under review. [arXiv]
-
Non-degenerate Rigid Alignment in a Patch Framework.
with Gal Mishne, Alex Cloninger
Revision under review. [arXiv]
-
LDLE: Low Distortion Local Eigenmaps.
with Alex Cloninger, Gal Mishne
Journal of Machine Learning Research, Volume 22, 2021. [arXiv] [Code]
-
Asymmetric expansion preserves hyperbolic convexity.
with Jeffrey Rabin
Journal of Geometry, Volume 111 Article 33, 2020. [arXiv]
-
Radial expansion preserves hyperbolic convexity and radial contraction preserves spherical convexity.
with Jeffrey Rabin
Journal of Geometry, Volume 110, Article 40, 2019. [arXiv]
-
Learning rotation invariance in deep hierarchies using circular symmetric filters.
with B. C. Das, V. Gopalakrishnan, K. N. Iyer.
2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, 2017, pp. 2846-2850.
Conferences and Presentations
| Oct 2024 | [Poster] | SIAM Conference on Mathematics of Data Science (SIAM MDS), Atlanta. |
| Sep 2024 | [Poster] | NSF visit, The Institute for Emerging CORE Methods in Data Science (EnCORE), UC San Diego. |
| Apr 2024 | Chaos, Computation, Analysis and Optimization (CaCAO), Scripps Institute of Oceanography, UC San Diego. | |
| Mar 2024 | [Talk] | Dagstuhl Seminar on Low-Dimensional Embeddings of High-Dimensional Data: Algorithms and Applications, Wadern, Germany. |
| Jul 2023 | Sampling Theory and Applications Conference (SAMPTA), Yale. | |
| Apr 2023 | [Talk] | Southern California Applied Mathematics Symposium (SOCAMS) at UC Irvine. |
| Mar 2023 | [Poster] | Computational and Systems Neuroscience (COSYNE), Montreal. |
| Oct 2022 | [Poster] | Fall Fourier Talks (FFT) at the Norbert Wiener Center, University of Maryland. |
| Mar 2021 | [Poster] | SoCal ML and NLP Symposium 2021 at UC San Diego. |
Teaching Assistant Experience
| DSC 205 | UCSD | Geoemtry of Data |
| Math 170A | UCSD | Numerical Linear Algebra |
| Math 170B | UCSD | Numerical Approximation and Nonlinear Equations |
| Math 183 | UCSD | Statistical Methods |
| Math 20E | UCSD | Vector Calculus |
| Math 11 | UCSD | Calculus Based Probability and Statistics. |
Links
Mindthegap: An opensource tracing software that converts bitmaps into vector graphics.
My winning solution for the Nvidia CUDA Coding Challenge India 2014.
Labmates, collaborators and friends (in lexicographic order): Jesse He, Samantha Chen, Sawyer Robertson, Sowmya Manojna, Tristan Brugere.