PhD Advising

If you’re interested in working with me, please email me to schedule a 30-minute meeting. During this meeting, please be prepared to discuss the following.

• Your background and previous research experience
• Your future research plans and goals
• Why you think working with me would be a good fit for your future research plans and goals
• Which of my papers you’ve read, and what research directions you’d be interested in exploring
• Potential papers for your small starter project (see below for details)

Small Starter Project

The deliverable for your small starter project (due in 4 to 6 weeks) is a PDF report typeset in LaTeX that is between 10 and 13 pages long. It should include the following.

1. A review of the selected paper summarizing key results in the context of current literature. (4 to 5 pages) Also be prepared to explain key results and to rederive their proofs.
2. An investigation of a research question (or questions) that you explored in the paper. (4 to 5 pages)
3. A detailed description of a potential research project that you would like to work on based on an idea from the paper. (2 to 3 pages)

Below are examples of papers on topics that I’m currently intersted in advising. I am particularly interested in projects involving randomized numerical linear algebra and stochastic iterative methods and their applications. I am also interested in applications, particularly those in healthcare, health policy, public policy, and text-based data. If you have papers in these areas that you are interested in, please don’t hesitate to discuss them with me.

• Ye, Fei, Zhiping Shi, and Zhongzhi Shi. “A comparative study of PCA, LDA and Kernel LDA for image classification.” In 2009 international symposium on ubiquitous virtual reality, pp. 51-54. IEEE, 2009.
• Yang, Jian, Zhong Jin, Jing-yu Yang, David Zhang, and Alejandro F. Frangi. “Essence of kernel Fisher discriminant: KPCA plus LDA.” Pattern Recognition 37, no. 10 (2004): 2097-2100.
• Cai, Deng, Xiaofei He, and Jiawei Han. “Efficient kernel discriminant analysis via spectral regression.” In Seventh IEEE International Conference on Data Mining (ICDM 2007), pp. 427-432. IEEE, 2007.
• Yang, Jian, Alejandro F. Frangi, Jing-yu Yang, David Zhang, and Zhong Jin. “KPCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and recognition.” IEEE Transactions on pattern analysis and machine intelligence 27, no. 2 (2005): 230-244.
• Baudat, Gaston, and Fatiha Anouar. “Generalized discriminant analysis using a kernel approach.” Neural computation 12, no. 10 (2000): 2385-2404.
• Roth, Volker, and Volker Steinhage. “Nonlinear discriminant analysis using kernel functions.” Advances in neural information processing systems 12 (1999).
• Xiong, Tao, Jieping Ye, Qi Li, Ravi Janardan, and Vladimir Cherkassky. “Efficient kernel discriminant analysis via QR decomposition.” Advances in neural information processing systems 17 (2004).
• Lu, Juwei, Konstantinos N. Plataniotis, and Anastasios N. Venetsanopoulos. “Face recognition using kernel direct discriminant analysis algorithms.” IEEE transactions on Neural Networks 14, no. 1 (2003): 117-126.
• López, M. M., J. Ramírez, J. M. Górriz, I. Álvarez, D. Salas-Gonzalez, F. Segovia, and R. Chaves. “SVM-based CAD system for early detection of the Alzheimer’s disease using kernel PCA and LDA.” Neuroscience letters 464, no. 3 (2009): 233-238.
• Yang, Yun, Mert Pilanci, and Martin J. Wainwright. “Randomized sketches for kernels: Fast and optimal nonparametric regression.” (2017): 991-1023.
• Pourkamali-Anaraki, Farhad, and Stephen Becker. “A randomized approach to efficient kernel clustering.” In 2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP), pp. 207-211. IEEE, 2016.
• Ding, Xiaojian, and Fan Yang. “Multi-View Randomized Kernel Classification via Nonconvex Optimization.” In Proceedings of the AAAI Conference on Artificial Intelligence, vol. 38, no. 10, pp. 11793-11801. 2024.
• Pérez-Suay, Adrián, Julia Amorós-López, Luis Gómez-Chova, Valero Laparra, Jordi Muñoz-Marí, and Gustau Camps-Valls. “Randomized kernels for large scale Earth observation applications.” Remote Sensing of Environment 202 (2017): 54-63.
• Sinha, Aman, and John C. Duchi. “Learning kernels with random features.” Advances in neural information processing systems 29 (2016).