Research

Current Projects

Tensor decomposition, methods, and applications

• Tensor BM-decomposition with application to video compression and background/foreground separation. 

• Tensor completion

Past Projects

Hypermatrix Algebra and Decomposition

Hypermatrices are multidimensional analog of matrices. Classical studies on hypermatrix decompositions (frequently referred to as tensor decompositions) consider a flattening scheme of the higher-order hypermatrix into matrices and proceed with a matrix decomposition. In this study, we follow the Bhattacharya-Mesner (BM) algebra and consider the decomposition of an order-3 hypermatrix as a product of three hypermatrices of the same order. Our singular value decomposition (SVD) theory mirrors the SVD of matrices:

• Singular values and singular matrices are obtained via spectral decompositions of the symmetric hypermatrices constructed from the original input hypermatrix.

• Singular matrices are matrix slices of orthogonal hypermatrices.

• Singular values are entries of diagonal hypermatrices.

Robust Astronomy Catalog Cross-registration

Cross-matching and registering small astronomical images to a large known catalog can be challenging due to the limited number of guide stars observed. This is especially true for the Hubble Space Telescope observations. In this project, we formulated such cross-registration problem as an optimization problem. By borrowing robust statistics tools, we solve for a 3D infinitesimal rotation vector that corrects the image's astrometry and hence improves calibration. 

Statistical Analysis in Clinical Research

I work on data cleaning and analyses in clinical research applications. Among others, I work with objectively measured physical activity data obtained using wearable devices, and study associations between disease severity and activity patterns using functional data analysis tools.