Jeff Calder

Associate Professor of Mathematics
538 Vincent Hall
School of Mathematics
University of Minnesota
Phone: 612-626-1324
Email: jcalder at umn dot edu

Publications


  1. J. Calder, R. Coil, A. Melton, P. J. Olver, G. Tostevin, and K. Yezzi-Woodley. Use and Misuse of Machine Learning in Anthropology. IEEE BITS special issue on Information Processing in Arts and Humanities, 2022. [ arXiv ] [ Journal ]
  2. L. Bungert, J. Calder, and T. Roith. Uniform Convergence Rates for Lipschitz Learning on Graphs. IMA Journal of Numerical Analysis, 2022. [ arXiv ] [ Journal ] [ Code ]
  3. J. Calder, S. Park, and D. Slepčev. Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications. Journal of Scientific Computing, 92(2):1--59, 2022. [ arXiv ] [ Journal ] [ Code ]
  4. K. Yezzi-Woodley, A. Terwilliger, J. Li, E. Chen, M. Tappen, J. Calder, and P. J. Olver. Using machine learning on new feature sets extracted from 3D models of broken animal bones to classify fragments according to break agent. arXiv preprint, 2022. [ arXiv ] [ Code ]
  5. K. Yezzi-Woodley, J. Calder, M. Sweno, C. Siewert, and P. J. Olver. The Batch Artifact Scanning Protocol: A new method using computed tomography (CT) to rapidly create three-dimensional models of objects from large collections en masse. arXiv preprint, 2022. [ arXiv ] [ Code ]
  6. A. Yuan, J. Calder, and B. Osting. A continuum limit for the PageRank algorithm. European Journal of Applied Mathematics, 33:472-504, 2022. [ arXiv ] [ Journal ] [ Code ]
  7. N. Drenska and J. Calder. Online prediction with history-dependent experts: The general case. Communications on Pure and Applied Mathematics, 2022. [ arXiv ] [ Journal ]
  8. K. Miller, X. Baca, J. Mauro, J. Setiadi, Z. Shi, J. Calder, and A. Bertozzi. Graph-based active learning for semi-supervised classification of SAR data. SPIE Defense and Commercial Sensing: Algorithms for Synthetic Aperture Radar Imagery XXIX, 12095, 2022. [ arXiv ] [ Journal ] [ Code ]
  9. J. Calder and N. García Trillos. Improved spectral convergence rates for graph Laplacians on ε-graphs and k-NN graphs. Applied and Computational Harmonic Analysis, 60:123--175, 2022. [ arXiv ] [ Journal ] [ Code ]
  10. J. Calder and M. Ettehad. Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth. To appear in Journal of Machine Learning Research, 2022. [ arXiv ] [ Code ]
  11. J. Calder, N. García Trillos, and M. Lewicka. Lipschitz regularity of graph Laplacians on random data clouds. SIAM Journal on Mathematical Analysis, 54(1):1169--1222, 2022. [ arXiv ] [ Journal ]
  12. M. Flores, J. Calder, and G. Lerman. Analysis and algorithms for Lp-based semi-supervised learning on graphs. Applied and Computational Harmonic Analysis, 60:77-122, 2022. [ arXiv ] [ Journal ] [ Code ]
  13. B. Cook and J. Calder. Rates of convergence for the continuum limit of nondominated sorting. SIAM Journal on Mathematical Analysis, 54(1):872--911, 2022. [ arXiv ] [ Journal ]
  14. K. Yezzi-Woodley, J. Calder, P. J. Olver, A. Melton, P. Cody, T. Huffstutler, A. Terwilliger, G. Tostevin, M. Tappen, and R. Coil. The Virtual Goniometer: A new method for measuring angles on 3D models of fragmentary bone and lithics. Archaeological and Anthropological Sciences, 13(106), 2021. [ arXiv ] [ Journal ] [ Code ]
  15. J. Calder and N. Drenska. Asymptotically optimal strategies for online prediction with history-dependent experts. Journal of Fourier Analysis and Applications Special Collection on Harmonic Analysis on Combinatorial Graphs, 27(20), 2021. [ arXiv ] [ Journal ]
  16. J. Calder, B. Cook, M. Thorpe, and D. Slepčev. Poisson Learning: Graph based semi-supervised learning at very low label rates. Proceedings of the 37th International Conference on Machine Learning, PMLR, 119:1306--1316, 2020. [ arXiv ] [ Journal ] [ Code ]
  17. J. Calder, D. Slepčev, and M. Thorpe. Rates of convergence for Laplacian semi-supervised learning with low labeling rates. arXiv preprint, 2020. [ arXiv ]
  18. J. Calder and C. K. Smart. The limit shape of convex hull peeling. Duke Mathematical Journal, 169(11):2079--2124, 2020. [ arXiv ] [ Journal ]
  19. R. O'Neill, P. Angulo-Umana, J. Calder, B. Hessburg, P. J. Olver, C. Shakiban, and K. Yezzi-Woodley. Computation of circular area and spherical volume invariants via boundary integrals. SIAM Journal on Imaging Sciences, 13(1):53--77, 2020. [ arXiv ] [ Journal ] [ Code ]
  20. M. Benyamin, J. Calder, G. Sundaramoorthi, and A. Yezzi. Accelerated variational PDE's for efficient solution of regularized inversion problems. Journal of Mathematical Imaging and Vision, 62(1):10--36, 2020. [ arXiv ] [ Journal ]
  21. J. Calder and A. Yezzi. PDE Acceleration: A convergence rate analysis and applications to obstacle problems. Research in the Mathematical Sciences, 6(35), 2019. [ arXiv ] [ Journal ] [ Code ]
  22. J. Calder and D. Slepčev. Properly-weighted graph Laplacian for semi-supervised learning. Applied Mathematics and Optimization: Special Issue on Optimization in Data Science, 82:1111--1159, 2019. [ arXiv ] [ Journal ]
  23. J. Calder. Consistency of Lipschitz learning with infinite unlabeled data and finite labeled data. SIAM Journal on Mathematics of Data Science, 1(4):780--812, 2019. [ arXiv ] [ Journal ] [ Code ]
  24. C. Finlay, B. Abbasi, J. Calder, and A. M. Oberman. Lipschitz regularized Deep Neural Networks generalize and are adversarially robust. arXiv preprint, 2018. [ arXiv ]
  25. J. Calder. The game theoretic p-Laplacian and semi-supervised learning with few labels. Nonlinearity, 32(1):301--330, 2018. [ arXiv ] [ Journal ]
  26. T. Gangwar, J. Calder, T. Takahashi, J. Bechtold, and D. Schillinger. Robust variational segmentation of 3D bone CT data with thin cartilage interfaces. Medical Image Analysis, 47:95--110, 2018. [ Journal ] [ PDF ]
  27. B. Abbasi, J. Calder, and A. M. Oberman. Anomaly detection and classification for streaming data using partial differential equations. SIAM Journal on Applied Mathematics, 78(2):921-941, 2018. [ arXiv ] [ Journal ]
  28. W. Thawinrak and J. Calder. High-order filtered schemes for the Hamilton-Jacobi continuum limit of nondominated sorting. Journal of Mathematics Research, 10(1):90--109, 2018. [ arXiv ] [ Journal ]
  29. J. Calder. Numerical schemes and rates of convergence for the Hamilton-Jacobi equation continuum limit of nondominated sorting. Numerische Mathematik, 137(4):819--856, 2017. [ arXiv ] [ Journal ]
  30. J. Calder. A direct verification argument for the Hamilton-Jacobi equation continuum limit of nondominated sorting. Nonlinear Analysis Series A: Theory, Methods, & Applications, 141:88--108, 2016. [ arXiv ] [ Journal ] [ PDF ]
  31. K.-J. Hsiao, K. Xu, J. Calder, and A. O. Hero. Multi-criteria similarity-based anomaly detection using Pareto Depth Analysis. IEEE Transactions on Neural Networks and Learning Systems, 27(6):1307--1321, 2016. [ arXiv ] [ Journal ]
  32. K.-J. Hsiao, J. Calder, and A. O. Hero. Pareto-depth for multiple-query image retrieval. IEEE Transactions on Image Processing, 24(2):583--594, 2015. [ arXiv ] [ Journal ] [ PDF ]
  33. J. Calder. Directed last passage percolation with discontinuous weights. Journal of Statistical Physics, 158(45):903--949, 2015. [ arXiv ] [ Journal ] [ PDF ]
  34. J. Calder, S. Esedoḡlu, and A. O. Hero. A PDE-based approach to nondominated sorting. SIAM Journal on Numerical Analysis, 53(1):82--104, 2015. [ arXiv ] [ Journal ] [ PDF ]
  35. J. Calder, S. Esedoḡlu, and A. O. Hero. A continuum limit for non-dominated sorting. Information Theory and Applications Workshop, 2014. [ Journal ] [ PDF ]
  36. J. Calder, S. Esedoḡlu, and A. O. Hero. A Hamilton-Jacobi equation for the continuum limit of non-dominated sorting. SIAM Journal on Mathematical Analysis, 46(1):603--638, 2014. [ arXiv ] [ Journal ] [ PDF ]
  37. K.-J. Hsiao, K. Xu, J. Calder, and A. O. Hero. Multi-criteria anomaly detection using Pareto Depth Analysis. Advances in Neural Information Processing Systems 25:854--862, 2012. [ arXiv ] [ Journal ]
  38. J. Calder and S. Esedoḡlu. On the circular area signature for graphs. SIAM Journal on Imaging Sciences, 5(4):1355--1379, 2012. [ Journal ] [ PDF ]
  39. J. Calder and A.-R. Mansouri. Anisotropic image sharpening via well-posed Sobolev gradient flows. SIAM Journal on Mathematical Analysis, 43(4):1536--1556, 2011. [ Journal ] [ PDF ]
  40. J. Calder, A.-R. Mansouri, and A. Yezzi. New possibilities in image diffusion and sharpening via high-order Sobolev gradient flows. Journal of Mathematical Imaging and Vision, 40(3):248--258, 2011. [ Journal ] [ PDF ]
  41. J. Calder, A. M. Tahmasebi, and A.-R. Mansouri. A variational approach to bone segmentation in CT images. SPIE Medical Imaging, 7962, 2011. [ Journal ] [ PDF ]
  42. J. Calder, A.-R. Mansouri, and A. Yezzi. Image sharpening via Sobolev gradient flows. SIAM Journal on Imaging Sciences, 3(4):981--1014, 2010. [ Journal ] [ PDF ]
  43. R. Deriche, J. Calder, and M. Descoteaux. Optimal real-time Q-ball imaging using regularized Kalman filtering with incremental orientation sets. Medical Image Analysis, 13(4):564--579, 2009. [ Journal ] [ PDF ]
  44. R. Deriche and J. Calder. Real-time magnetic resonance Q-ball imaging using Kalman filtering with Laplace-Beltrami regularization. SPIE Medical Imaging, 7259, 2009. [ Journal ] [ PDF ]

Theses


  1. J. Calder. Hamilton-Jacobi equations for sorting and percolation problems. PhD Thesis, University of Michigan, June 2014. [  PDF ]
  2. J. Calder. Sobolev gradient flows and image processing. Master's thesis, Queen's University, August 2010. [  PDF ]
  3. J. Calder, D. Awamleh, and A. MacAulay. Region tracking over an image sequence. Mathematics and Engineering Undergraduate Thesis, Queen's University, April 2008. [  PDF ]

Patents


  1. D. Schillinger, T. Gangwar, T. Takahashi, and J. Calder Two-stage variational image segmentation of medical images using fracture mechanics. U.S. Patent Application 16/701,562, filed June 4, 2020.
  2. J. Calder and T. Sun. Efficient implementation of branch intensive algorithms in VLIW and superscalar processors. US Patent Number 8019979, Issued on September 13, 2011. [  PDF ]