Scientific Computing Seminar

Date:

Friday, January 7, 2005

Time:

1:00pm-2:00pm

Location:

50A-5132

Seminar Speaker:

Chris Ding
Lawrence Berkeley National Laboratory
http://crd.lbl.gov/~cding

Title:

2-Dimensional Singular Value Decomposition for 2D Maps and Images

Abstract:

Singular value decomposition (SVD) is widely used in broad areas of science and engineering. SVD provides optimal low-rank matrix approximation and can be efficiently computed. Given a set of high dimensional data vectors, SVD is frequently used to project data vectors to the optimal low-dimensional subspace, leading to principal component analysis (PCA) in statistics.

Given a set of 2D objects such as images or weather maps, we project them to low-dimensional 2D objects via an extension of the standard SVD, using principal eigenvectors of row-row and column-column covariance matrices. This 2D-SVD preserves the 2D characteristics of the original data. We study optimality properties of 2D-SVD as low-rank approximations for a set of 2D objects, and show that it provides a framework unifying two recently proposed image approximations. Experiments on images and weather maps illustrate the usefulness of 2D-SVD. (Joint work with Jieping Ye of U. Minnesota)

Sponsor of Seminar:

Esmond Ng

Scientific Computing

Contact Esmond G. Ng EGNg@lbl.gov