Tensor is a structured data object.

Tensor Decompositions

Tensor is a kind of highly structured data that is a prototype for a wide range of data encountered in daily life, e.g., natural RGB images, videos, medical images, tensorized neural networks etc.

Due to the special structures of tensors, efficient algorithms can be developed based on the such property. Among tensor algorithms, tensor decomposition is a popular and important topic. Common methods include CP decomposition, Tucker decomposition (especailly, HOSVD), Tensor Train etc. Most of decomposition solvers are based on alternating direction minimization (ALS) or Gradient descent minimization (GD).

I am particularly interested in online (stochastic) tensor learning for large-scale dataset and efficient implementation on the Riemannian manifold. I worked from June to September in 2019 with Professor Zheng Zhang @UCSB ECE. I implemented basic tensor decomposition algorithms in MATLAB as exercise, and summarize some of papers in the literature. Slides here.

Relation to Quantum Information

In quantum information, many-body wave function and operators are usually expressed as tensors. How can be express wave functions as efficient as possible by utilizing the tensor structures? To achieve the goal, tensor data analysis, complexity theory and information theory are required. I am interested in this interface topic. From September 2019 I will be holding a weekly seminar on Quantum Computation and Quantum Information and related topics will be discussed.