Jeff Calder

Albert and Dorothy Marden Professor
School of Mathematics
University of Minnesota
538 Vincent Hall
Phone: 612-626-1324
Email: jwcalder at umn dot edu

Publications


  1. J. Calder and N. Drenska. Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian. arXiv preprint, 2024. [ arXiv ] [ Code ]
  2. L. Bungert, J. Calder, and T. Roith. Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian. To appear in Annals of Applied Probability, 2023. [ arXiv ] [ Code ]
  3. 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. To appear in Journal of Human Evolution, 2023. [ arXiv ] [ Code ]
  4. J. Calder and W. Lee. Monotone discretizations of levelset convex geometric PDEs. arXiv preprint, 2023. [ arXiv ] [ Code ]
  5. K. Miller and J. Calder. Poisson Reweighted Laplacian Uncertainty Sampling for Graph-based Active Learning. SIAM Journal on Mathematics of Data Science, 5, 2023. [ arXiv ] [ Journal ] [ Code ]
  6. J. Enwright, H. Hardiman-Mostow, J. Calder, and A. L. Bertozzi. Deep semi-supervised label propagation for SAR image classification. SPIE Defense and Commercial Sensing: Algorithms for Synthetic Aperture Radar Imagery XXX, 2023. [ Journal ] [ pdf ] [ Code ]
  7. J. Chapman, B. Chen, Z. Tan, J. Calder, K. Miller, and A. L. Bertozzi. Novel Batch Active Learning Approach and Its Application on the Synthetic Aperture Radar Datasets. SPIE Defense and Commercial Sensing: Algorithms for Synthetic Aperture Radar Imagery XXX (Best Student Paper), 2023. [ Journal ] [ pdf ] [ Code ]
  8. J. Brown, R. O'Neill, J. Calder, and A. L. Bertozzi. Utilizing Contrastive Learning for Graph-Based Active Learning of SAR Data. SPIE Defense and Commercial Sensing: Algorithms for Synthetic Aperture Radar Imagery XXX, 2023. [ Journal ] [ pdf ] [ Code ]
  9. J. Calder, D. Slepčev, and M. Thorpe. Rates of convergence for Laplacian semi-supervised learning with low labeling rates. Research in Mathematical Sciences special issue on PDE methods for machine learning, 10(10), 2023. [ arXiv ] [ Journal ]
  10. J. Calder and M. Ettehad. Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth. Journal of Machine Learning Research, 23(318):1--62, 2022. [ arXiv ] [ Journal ] [ Code ]
  11. 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 ]
  12. L. Bungert, J. Calder, and T. Roith. Uniform Convergence Rates for Lipschitz Learning on Graphs. IMA Journal of Numerical Analysis, 2022. [ arXiv ] [ Journal ] [ Code ]
  13. 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 ]
  14. 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 ]
  15. 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 ]
  16. N. Drenska and J. Calder. Online prediction with history-dependent experts: The general case. Communications on Pure and Applied Mathematics, 76, 2022. [ arXiv ] [ Journal ]
  17. 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 ]
  18. 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 ]
  19. 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 ]
  20. 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 ]
  21. 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 ]
  22. 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 ]
  23. 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 ]
  24. 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 ]
  25. J. Calder and C. K. Smart. The limit shape of convex hull peeling. Duke Mathematical Journal, 169(11):2079--2124, 2020. [ arXiv ] [ Journal ]
  26. J. Calder and D. Slepčev. Properly-weighted graph Laplacian for semi-supervised learning. Applied Mathematics and Optimization, 82:1111--1159, 2020. [ arXiv ] [ Journal ]
  27. 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 ]
  28. 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 ]
  29. 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 ]
  30. 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 ]
  31. C. Finlay, B. Abbasi, J. Calder, and A. M. Oberman. Lipschitz regularized Deep Neural Networks generalize and are adversarially robust. arXiv preprint, 2018. [ arXiv ]
  32. J. Calder. The game theoretic p-Laplacian and semi-supervised learning with few labels. Nonlinearity, 32(1):301--330, 2018. [ arXiv ] [ Journal ]
  33. 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 ]
  34. 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 ]
  35. 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 ]
  36. 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 ]
  37. 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 ]
  38. 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 ]
  39. 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 ]
  40. J. Calder. Directed last passage percolation with discontinuous weights. Journal of Statistical Physics, 158(45):903--949, 2015. [ arXiv ] [ Journal ] [ pdf ]
  41. 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 ]
  42. J. Calder, S. Esedoḡlu, and A. O. Hero. A continuum limit for non-dominated sorting. Information Theory and Applications Workshop, 2014. [ Journal ] [ pdf ]
  43. 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 ]
  44. 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 ]
  45. J. Calder and S. Esedoḡlu. On the circular area signature for graphs. SIAM Journal on Imaging Sciences, 5(4):1355--1379, 2012. [ Journal ] [ pdf ]
  46. 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 ]
  47. 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 ]
  48. 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 ]
  49. 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 ]
  50. 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 ]
  51. 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 ]