Research Interests

My current research is devoted to theoretical foundations in Data Clustering, including some matrix factorization methods which solve the Subspace Clustering problem. Related to this, I have worked on the CUR Decomposition for matrices, which is a low-rank matrix approximation method. I have also worked extensively on the interaction between high-dimensional Sampling Theory and Radial Basis Function approximation schemes.

Publications

Journal Articles and Preprints

• [9] K. Hamm and J. Ledford, On the Structure and Interpolation Properties of Quasi Shift-Invariant Spaces, Journal of Functional Analysis, Vol. 274, Issue 7 (2018), 1959-1992 .
• [8] A. Aldroubi, K. Hamm, A. B. Koku, and A. Sekmen, CUR Decompositions, Similarity Matrices, and Subspace Clustering, (Approximately 23 pages, Submitted).
• [7] K. Hamm and J. Ledford, Regular Families of Kernels for Nonlinear Approximation, (Approximately 21 pages, Submitted).
• [6] K. Hamm, On the Gibbs–Wilbraham Phenomenon for Sampling and Interpolatory Series, (Approximately 8 pages, Submitted).
• [5] K. Hamm and J. Ledford, Cardinal Interpolation With General Multiquadrics: Convergence Rates, Advances in Computational Mathematics, Approximately 26 pages, To Appear).
• [4] J.-L. Bouchot and K. Hamm, Stability and Robustness of RBF Interpolation, Sampling Theory in Signal and Image Processing, Vol. 16 (2017), 37-53.
• [3] K. Hamm, Nonuniform Sampling and Recovery of Bandlimited Functions in Higher Dimensions, Journal of Mathematical Analysis and Applications, Vol. 450, Issue 2 (2017), 1459-1478.
• [2] K. Hamm and J. Ledford, Cardinal Interpolation With General Multiquadrics, Advances in Computational Mathematics, Vol. 42, Issue 5 (2016), 1149-1186.
• [1] K. Hamm, Approximation Rates for Interpolation of Sobolev Functions via Gaussians and Allied Functions, Journal of Approximation Theory, 189 (2015), 101-122.

Refereed Conference Proceedings

• [13] A. Sekmen, A. Aldroubi, A. B. Koku, and K. Hamm, Principal Coordinate Clustering, 3rd Special Session on Intelligent Data Mining, 2017 IEEE International Conference on Big Data, Boston, MA, 2095-2102.
• [12] A. Sekmen, A. Aldroubi, K. Hamm, and A. B. Koku, Matrix Reconstruction: Skeleton Decomposition versus Singular Value Decomposition, Proceedings of the 2017 International Symposium on Performance Evaluation of Computer and Telecommunication Systems (SPECTS), Seattle, Washington.
• [11] K. Hamm and J. Ledford, On Bases of Cardinal Functions and Their Role in Approximate Sampling Methods, Proceedings of the 12th International Conference on Sampling Theory and Applications (SampTA 2017), Tallin, Estonia.
• [10] K. Hamm, Sampling and Recovery Using Multiquadrics, Proceedings of the 11th International Conference on Sampling Theory and Applications (SampTA 2015), Washington D.C.

In Preparation

• An Operator Theoretic Approach to the Convergence of Rearranged Fourier Series (with B. Hayes and A. Petrosyan, forthcoming)

Education

• Ph.D., Mathematics, Texas A&M University, 2015
• B.S., Mathematics (Honors), Texas A&M University, 2010
• B.S., Chemical Engineering, Texas A&M University, 2010