research
My research deals with finding a Symmetry Preserving Singular Value Decomposition (SPSVD) of a matrix. This has applications in face analysis and molecular dynamics.

The Singular Value Decomposition (SVD) is a matrix factorization, such that for any matrix A
A = USV'
where U, V are unitary matrices and S is a diagonal matrix. Recall, U is a unitary matrix if U'U = I. The SVD gives us the best rank k approximation to a matrix, i.e. the SVD gives the solution to
min||A-B||,
where B has rank k less than or equal to r.

For a Symmetry Preserving SVD (SPSVD), we want to find the best rank k approximation to a matrix that preserves symmetry, i.e. find a symmetric B of rank k that solves the following equation:

min||A-B||.
For more information, click our SIMAX article or our Molecular Simulation article.