Research Interests
- Machine Learning
- Reinforcement Learning
- Dimension Reduction techniques and their Application
- Coding Theory
- Distributed Data Storage
- Parallel Computing
- Graph Theory
- Mathematics and Music
Doctoral Research
- Dimension Reduction Techniques via Johnson Lindenstrauss Transformations
Publications
- Michael Burr, Shuhong Gao, Fiona Knoll. “On the Lower Bounds of Johnson-Lindenstrauss Transformation.” Journal of Machine Learning, 2018.
- Lin You, Fiona Knoll, Yue Mao, Shuhong Gao. “Practical Johnson-Lindenstrauss Transforms via Algebraic Geometry Codes.” 2017 International Conference on Control, Artificial Intelligence, Robotics and Optimization, 2017.
- Shuhong Gao, Fiona Knoll, Felice Mangianello, Gretchen Matthews. "Codes for distributed storage from 3-regular graphs.” Discrete Applied Mathematics, 2016.
- S. Hedetniemi, F. Knoll, R. Laskar. “Split Domination, Independence, and Irredundance in Graphs.” Congressus Numerantium, 2016.
- A. Grady, F. Knoll, R. Laskar, D.J. Lipman. “Cycle Domination, Independence, and Irredundance in Graphs.” Congressus Numerantium, 224:159-174, 2015.
- A. Grady, F. Knoll, D. J. Lipman. “Clique Independence, Domination, and Irredundance in Graphs.” Congressus Numerantium, 223:193-198, 2015.
Conference Presentations
AMS Meeting at Ohio State March 2018
Joint Mathematics Meetings January 2017
2016 Fall Central Sectional Meeting October 2016
Southeastern International Conference on Combinatorics, Graph Theory, and Computing March 2016
Joint Mathematics Meetings January 2016
Association for Women in Mathematics Research Symposium April 2015
Southeastern International Conference on Combinatorics, Graph Theory, and Computing March 2015
Invited Presentation: Error-Correcting Codes Applied to Parallel Computation.
Presented research on the bounds of Johnson-Lindenstrauss transformations.
Presented research on Johnson-Lindenstrauss transformations via Algebraic Geometry codes.
Presented research on the graph theory concepts of split irredundance and split independence.
Presented research on Johnson-Lindenstrauss transformations via Algebraic Geometry codes.
Presented a poster on Johnson-Lindenstrauss projection of high dimensional data.
Presented research on an abstraction of domination chains, specifically domination chains concerning cycle independence graphs.