Title: Tensor Train and Cross Approximations for Large Scale Data Compression

Abstract: In many areas of scientific computing, statistical analysis, and machine learning, the ability to efficiently and accurately handle large scale and high dimensional data is a rapidly growing necessity. Many powerful techniques have been developed to approach this task, one being Tensor-Train (TT) and variants such as Tensor-Train Adaptive Cross Approximation (TTACA). TTACA provides a framework suited for working with extremely large datasets while maintaining low memory and computational complexity. In this talk, I will introduce the foundations at the matrix level and the base TTACA algorithm. I will then present two projects I have worked on: (1) the development of a subtensor parallel implementation of TTACA that utilizes more computing resources to increase efficiency, and (2) a post-processing oversampling algorithm designed to enhance approximation accuracy. Numerical experiments demonstrate improved computational efficiency through subtensor parallelism and systematic error reduction via oversampling.