NEW: Clustered matrix approximation (pdf), ACCEPTED for publication in SIAM Journal on Matrix Analysis and Applications. CMAPP: MATLAB implementation and a number of test examples is available.
My research background is in scientific computing, numerical linear and multilinear algebra. Particular interests:
- Large scale computations for graphs and network problems. Applications: link prediction in dynamic networks; use of multiple sources of information for link prediction and group recommendation.
- Large scale computations with matrices and tensors.
- Analysis, theory and algorithm development for tensors, tensor decompositions, and tensor computations. For example: low multilinear rank approximation of tensors; Krylov-type methods for tensor computations; perturbation analysis of low rank tensor approximations.
- Optimization methods for problems defined on Grassmann and Stiefel manifolds.
For more info see my publications, below.
Developed algorithm codes
CMAPP: Clustered matrix approximations: Clustered matrix approximation is a fast and memory efficient framework for dimensionality reduction of matrices. The method is suited for large and sparse matrices that have some kind of cluster structure. This is the case for many matrices arizing from graphs or networks, bipartite graphs, and large scale information retrieval problems.
MATLAB implementation of CMAPP and a number of examples are available.
Grassmann classes: Object oriented MATLAB code for computations on a Grassmann manifold and product of Grassmann manifolds. You may download the user guide and the class definition files.
Tensor approximation algorithm package: Implementation of Newton and quasi-Newton (BFGS and L-BFGS) algorithms for computing a best low multilinear rank approximation of a tensor. All algorithms are using the above Grassmann classes and the MATLAB Tensor Toolbox.