Broadly I am interested in approximating large matrices. These methods, applicable and prevalent in literature, have become especially relevant in today’s world of million sized datasets and applications including but not limited to NLP. Specifically I am interested in designing approximations to matrices in sublinear time, i.e. algorithms that requires number of operations greater than the size of a dataset but lesser than the square of the size of a dataset. Applications include the study of quadratic forms and differential equations. On similar lines, a particular area of interest for me is Kernel approximation. A kernel is often a PSD matrix (and sometimes indefinte like reproducing Krien spaces) which stores inner product of data points in a dataset. These inner products can be in the input space but often is in a high dimensional space induced by a mapping function. Thus computations for big datsets are again non-trivial. Approximating them when such inducing functions are changing or the size of dataset growing is of interest to the community (like GDPR). My overarching research goal is to find solutions to these problems using techniques borrowed from linear algebra and functional analysis.
Prior to this I have dabbled unsuccessfully in computer vision, where I was working on detecting and recognizing texts in maps. I also worked on image synthesis in the kernel induced space during my masters.
- Sublinear Time Eigenvalue Approximation via Random Sampling
Rajarshi Bhattacharjee, Cameron Musco, Archan Ray
- Sublinear Time Approximation of Text Similarity Matrices
Archan Ray, Nicholas Monath, Andrew McCallum, and Cameron Musco
to appear in AAAI Conference on Artificial Intelligence (AAAI) 2022.
- Tight Coupling of Character, Word, and Place Recognition for End-to-End Text Recognition in Maps
Archan Ray, Aruni Roy Chowdhury, Yi Fung, Jerod Weinman, and Erik Learned-Miller
Technical Report, College of Information and Computer Sciences, University of Massachusetts, Amherst, MA, 2019.
- Historical map annotations for text detection and recognition
Archan Ray, Ziwen Chen, Ben Gafford, Nathan Gifford, Jagath Jai Kumar, Abyaya Lamsal, Liam Niehus-Staab, Jerod Weinman, and Erik Learned-Miller
Grinnell College, Technical Report, 2018.
- U-PC: Unsupervised planogram compliance
Archan Ray, Nishant Kumar, Avishek Shaw, and Dipti Prasad Mukherjee
European Conference on Computer Vision (ECCV), 2018.
- Estimation of image features representing facial emotions for emotion synthesis
M. Tech Dissertation Series, Indian Statistical Institute, Kolkata, 2015.
- System and method for object recognition based estimation of planogram compliance
Pranoy Hari, Shilpa Yadukumar Rao, Rajashree Ramakrishnan, Avishek Kumar Shaw, Archan Ray, Nishant Kumar, and Dipti Prasad Mukherjee
U.S. Patent 10,748,030, 2020.