The focus of my research is to develop, apply and analyze the mathematical tools needed to answer questions of applied mathematics and applied science.
Research Areas
- Data mining and high-dimensional data analysis
- Topic Modeling using Non-Negative Matrix Factorization
- Deep Learning
- Numerical Linear Algebra
- Laplacian Eigenfunctions of Diffusion Processes
- Digital signal and image processing
- Random Processes and Queueing Theory
Data mining or knowledge discovery is the process of analyzing and extracting meaningful information from enormous amounts of data to acquire knowledge by finding patterns, relationships and associations in data. There is a proliferation of data mining problems and mathematical applications, causing an ever growing need for new and rediscovered mathematics to analyze, understand and gain knowledge from data. My research in this field intersects many areas of applied math, statistics, computer science and applied science.
- Data - medical images, stock prices, social networks, gene sequences, Twitter tweets, text, objects in video, ...
- Previous Results - analyzed spectral methods using perturbation theory, analyzed noise from compressed sensing and matrix completion, studied new online extensions of diffusion maps and multislice networks, used PDEs for computer vision and imaging, applied non-negative matrix factorization for content based search and analyzed transitional probabilities of random walks and the spread of traits on mobile geometric graphs.
- Topic Modeling - ``Topic models are a suite of algorithms that uncover the hidden thematic structure in document collections. These algorithms help us develop new ways to search, browse and summarize large archives of texts. The structure uncovered by topic models can be used to explore an otherwise unorganized collection. '' - David Blei
- Cultural Analytics - Culture is a dynamic process that emerges from the interaction of individuals in groups. And Cultural Analytics is the science of data-driven evolving interaction of cultural artifacts and agents.
Publications
- J. Flenner and B. Hunter “Deep Topic Models”, submitted, 2016.
- E. Lai, D. Moyer, B. Yuan, E. Fox, B. Hunter, A.L. Bertozzi, J. Brantingham, “Topic Time Series Analysis of Microblogs” accepted in IMA Journal of Applied Mathematics, special issue, 2016. [preprint version]
- Y. van Gennip, B. Hunter, R. Ahn, P. Elliott, K. Luh, M. Halvorson, S. Reed, M. Valasik, j.
Wo, G. Tita, A.L. Bertozzi and P.J. Brantingham “Community detection using spectral
clustering on sparse geosocial data.” SIAM Journal on Applied Mathematics
(SIAP), 73(1), pp. 67-83, 2013. [journal version] [Arxiv version]
- B. Hunter, T. Strohmer, “Spectral Embeddings and Diffusion Maps Under Perturbation.”,
in review.
- Multislice Modularity Optimization in Community Detection and Image Segmentation, H. Hu, Y. van Gennip, B. Hunter, A.L. Bertozzi, M.A. Porter, IEEE International Conference on Data Mining (Brussels), ICDM'12, pp. 934-936, 2012. [pdf]
- Data mining compressed, incomplete and inaccurate high dimensional data
by Hunter, advised by T. Strohmer, UC Davis PhD Dissertation, 2011. [pdf]
- Performance analysis of spectral clustering compressed, incomplete and inaccurate measurements by Hunter and T. Strohmer, in review. [pdf]
- Compressive spectral clustering - error analysis by B. Hunter and T. Strohmer, Manifold Learning and Its Applications: Papers from the AAAI Fall Symposium, (FS-10-06) 2010. [pdf]
- Gambler's Ruin with Catastrophes and Windfalls by B. Hunter, A.C. Krinik, N. Nguyen, J. Switkes and H. von Bremmen, Journal of Statistical Theory and Practice, Vol. 2, No. 2, page 199-219, 2008. [pdf]
- Approaches to Gambler's Ruin with Catastrophes by B. Hunter, A.C. Krinik, N. Nguyen, J. Switkes and H. von Bremmen, Journal of Combinatorics, Information & System Sciences. [pdf]
- Gambler's Ruin and the Three State Markov Process by B. Hunter, advised by A.C. Krinik, Cal Poly Pomona Master's Thesis, 2005. [pdf]
Research Experience
- Visiting Research Fellow for Cultural Analytics, Inst. for Pure & Applied Mathematics, UCLA, April 2016 - June 2016.
- I organized a Data Mining workshop on Graph Algorithms for Imaging and Networks (GAIN2015) at the 2015 IEEE International Conference on Data Mining (ICDM2015). For more information check out GAIN2015.
- Adjunct Assistant Professor, Mathematics Department, , June 2011 - June 2014.
- Postdoctoral Scholar with Andrea Bertozzi , Applied Mathematics, , June 2011 - June 2014.
- Graduate Student Researcher for Thomas Strohmer, UC Davis, June 2008 - June 2011
- Research Fellow for Mathematics of Knowledge and Search Engines, Inst. for Pure & Applied Mathematics, UCLA, Sept 2007 - Dec 2007
The focus of my research is to develop, apply and analyze the mathematical tools needed to answer questions of applied mathematics and applied science.