Gilad Lerman's Home Page

Contact Info

Gilad Lerman
127 Vincent Hall
206 Church St SE
Minneapolis, MN 55455 USA

Office: VinH 534
Phone: (612) 624-5541
Email: lerman@umn.edu

Office Hours

M & W 10:10-11am or by appointment

Research Interests

High-dimensional data analysis and modeling, computational harmonic analysis, geometric measure theory, machine learning, computer vision, bioinformatics

Preprints and Recent Publications

Least squares approximations for probability measures via multi-way curvatures. Gilad Lerman and J. Tyler Whitehouse. Submitted (2010).

Randomized hybrid linear modeling by local best-fit flats. Teng Zhang, Arthur Szlam, Yi Wang and Gilad Lerman.To appear in Proceedings of the 2010 IEEE 23rd International Conference on Computer Vision and
Pattern Recognition (CVPR) , San Fransisco, CA. See also supplemental material

Probabilistic recovery of multiple subspaces in point clouds by geometric lp minimization. Gilad Lerman and Teng Zhang. Submitted (2010).

Spectral clustering based on local linear approximations. Ery Arias-Castro, Guangliang Chen and Gilad Lerman. Submitted (2010). See also supplemental material

Kernel Spectral Curvature Clustering (KSCC). Guangliang Chen, Stefan Atev and Gilad Lerman. 4th international workshop on Dynamical Vision. Computer Vision Workshops (ICCV Workshops), 2009 IEEE 12th International Conference on Computer Vision , p. 765 - 772, Kyoto, Japan. Best paper award. See also supplemental material

Motion Segmentation by SCC on the Hopkins 155 Database. Guangliang Chen and Gilad Lerman. 4th international workshop on Dynamical Vision. Computer Vision Workshops (ICCV Workshops), 2009 IEEE 12th International Conference on Computer Vision , p. 759 - 764, Kyoto, Japan. See also supplemental material

Median K-flats for hybrid linear modeling with many outliers. Teng Zhang, Arthur Szlam and Gilad Lerman. 2nd international workshop on Subspace Methods. Computer Vision Workshops (ICCV Workshops) , 2009 IEEE 12th International Conference on Computer Vision , p. 234 - 241, Kyoto, Japan. See also supplemental material

Spectral Curvature Clustering (SCC), Guangliang Chen and Gilad Lerman, Int J Comput Vis (2009) 81: 317–330. See also supplemental material

Foundations of a Multi-way Spectral Clustering Framework for Hybrid Linear Modeling. Guangliang Chen and Gilad Lerman. Foundations of Computational Mathematics (2009) 9 (5): 517-558 (arxiv version freely available here)

(see also a talk on the above two papers, menitioning also a with Tyler Whitehouse which will be updated soon)

High-Dimensional Menger-Type Curvatures-Part II: d-Separation and a Menagerie of Curvatures. Gilad Lerman and J. Tyler Whitehouse.Constructive Approximation (2009) 30 (3): 325-360 (arxiv version freely available here).

High-dimensional Menger-type curvatures - part I: geometric multipoles and multiscale inequalities. Gilad Lerman and J. Tyler Whitehouse. To appear in Revista Matemática Iberoamericana (2011) 27 (2).

On d-dimensional d-semimetrics and simplex-type inequalities for high-dimensional sine functions. Gilad Lerman and J. Tyler Whitehouse, Journal of Approximation Theory (2009) 56 (1): 52-81 (math arxiv version is freely available here)

Defining functional distance using manifold embeddings of gene ontology annotations. Gilad Lerman and Boris E. Shakhnovich, PNAS 104 (27): 11334-11339 (2007)

Functional Genomics via Multiscale Analysis: Application to Gene Expression and ChIP-on-chip Data. Gilad Lerman, Joseph McQuown, Alexandre Blais, Brian D. Dynlacht, Guangliang Chen and Bud Mishra, Bioinformatics 23 (3): 314-320 (2007)

Teaching

Math 5467, Introduction to the Mathematics of Image and Data Analysis, Spring 2010

Math 2373, IT Linear Algebra and Differential Equations, Fall 2009

Math 8600, Topics in Multi-Manifold Data Modeling, Spring 2009

Other classes with webpages

Supplementary Material and Documented Software

Supplementary material to "Randomized hybrid linear modeling by local best-fit flats" (arXiv:1001.1323)

Supplementary material to "Spectral clustering based on local linear approximations" (arXiv:1001.1323)

Supplementary material to "Median K-Flats (MKF)" (Subspace Methods workshop in ICCV09)

Supplementary material to "Kernel Spectral Curvature Clustering (SCC)" ( ICCV workshop 2009)

Supplementary material to "Spectral Curvature Clustering (SCC)" ( IJCV, 2009 and FOCM, 2009)

Supplementary material to "Defining functional distance using manifold
embeddings of gene ontology annotations" (PNAS, 2007)

Supplementary material to "Functional Genomics via Multiscale Analysis: Application to Gene Expression and ChIP-on-chip Data" (Bioinformatics, 2007)

Recent Past Workshops

High Dimensional Problems and Solutions

Emerging Themes in Geometric Data Modeling with Applications to Imaging

For the Non-expert but Interested Visitor

A talk on Imaging (titled: Mathematics in Everyday Life) for 5th and 6th graders at Highland Park Elementary school in Saint Paul, MN (ppt file written on April 2008)

Highlights of some achievements of current NSF award for the non-specialist (ppt file written on Dec. 2008)

Current Support for Research and Outreach Activities:

National Science Foudation (NSF): DMS-09-15064
National Science Foudation (NSF): DMS-09-56072

Last Modified Thursday August 19, 2010 The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.