Dear all,

You are cordially invited to an academic seminar to be delivered by Dr. Young Ju LEE on July 13 (Thursday). Please find the details as follows.

Seminar Information

Topic: An Efficient K-way Constrained Normalized Cut and its Connection to Algebraic Multigrid Method 

Time & Date: 10:00 - 11:00 AM, July 13 (Thursday)

Venue: Room 207, Cheng Dao Building

Speaker: Dr. Young Ju LEE, The Texas State University

Host: Prof. Shihua GONG, The Chinese University of Hong Kong, Shenzhen

Abstract: Normalized Cut (NCut) discourages the isolated segmentation that may result from the standard minimum Cut by adding a volume constraint. Such a volume constraint introduces a significant computational challenge. We propose the K-way constrained Normalized Cut (K-way CNCut). It is formulated as the minimum Cut with a priori chosen constraints or representatives for the cluster. We provide a measure that can assess if the selected constraints can replace the volume constraint as well. For a special case when a single constraint is given as a representative of a single cluster, the K-way CNCut is discovered to have a link with the construction of the prolongation operator in the algebraic multigrid method [J. Xu and L. Zikatanov, “Algebraic multigrid methods,” Acta Numerica, vol. 26, pp. 591–721, 2017] for the normalized Graph Laplacian. We show how successful multiscale image segmentation [E. Sharon, M. Galun, D.Sharon, R. Basri, and A. Brandt, “Hierarchy and adaptivity in segmenting visual scenes,” Nature, vol. 442, no. 7104, p. 810–813, 2006.] can be understood in the framework of the K-way CNCut as well. In particular, we show how the multiscale graph coarsening algorithm can be used to construct a set of constraints for the K-way CNCut. A number of numerical experiments are presented to demonstrate the effectiveness of the proposed framework. 

Biography

Dr. Lee received his Ph.D. in Math from Penn State University in 2004, did a postdoc at UCLA until 2007. He then took a tenure-track faculty job at Math Department at Rutgers, the State University of New Jersey, Piscataway. He worked at Rutgers, until 2013. He joined Texas State University, Mathematics in the fall of 2013. He is a professor at Mathematics. Currently, his main research interest is in investigating the coupled flow and transports as well as the machine learning and data science.