Dhruv Kohli
My research areas are geometric data analysis, manifold learning, spectral graph theory 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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On a Generalization of Wasserstein Distance and the Beckmann Problem to Connection Graphs.
with Sawyer Robertson, Alex Cloninger, Gal Mishne
Submitted. [arXiv]
-
Non-degenerate Rigid Alignment in a Patch Framework.
with Alex Cloninger, Gal Mishne
Submitted. [arXiv]
-
LDLE: Low Distortion Local Eigenmaps.
with Gal Mishne, Alex Cloninger
Journal of Machine Learning Research, Volume 22, 2021. [arXiv] [Code]
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Asymmetric expansion preserves hyperbolic convexity.
with Jeffrey Rabin
Journal of Geometry, Volume 111 Article 33, 2020. [arXiv]
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Radial expansion preserves hyperbolic convexity and radial contraction preserves spherical convexity.
with Jeffrey Rabin
Journal of Geometry, Volume 110, Article 40, 2019. [arXiv]
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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.
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.