Seminar series
Date
Thu, 08 Feb 2024
14:00
14:00
Location
Lecture Room 3
Speaker
Behnam Hashemi
Organisation
Leicester University
The Tucker decomposition is a family of representations that break up a given d-dimensional tensor into the multilinear product of a core tensor and a factor matrix along each of the d-modes. It is a useful tool in extracting meaningful insights from complex datasets and has found applications in various fields, including scientific computing, signal processing and machine learning.
In this talk we will first focus on the continuous framework and revisit how Tucker decomposition forms the foundation of Chebfun3 for numerical computing with 3D functions and the deterministic algorithm behind Chebfun3. The key insight is that separation of variables achieved via low-rank Tucker decomposition simplifies and speeds up lots of subsequent computations.
We will then switch to the discrete framework and discuss a new algorithm called RTSMS (randomized Tucker with single-mode sketching). The single-mode sketching aspect of RTSMS allows utilizing simple sketch matrices which are substantially smaller than alternative methods leading to considerable performance gains. Within its least-squares strategy, RTSMS incorporates leverage scores for efficiency with Tikhonov regularization and iterative refinement for stability. RTSMS is demonstrated to be competitive with existing methods, sometimes outperforming them by a large margin.
In this talk we will first focus on the continuous framework and revisit how Tucker decomposition forms the foundation of Chebfun3 for numerical computing with 3D functions and the deterministic algorithm behind Chebfun3. The key insight is that separation of variables achieved via low-rank Tucker decomposition simplifies and speeds up lots of subsequent computations.
We will then switch to the discrete framework and discuss a new algorithm called RTSMS (randomized Tucker with single-mode sketching). The single-mode sketching aspect of RTSMS allows utilizing simple sketch matrices which are substantially smaller than alternative methods leading to considerable performance gains. Within its least-squares strategy, RTSMS incorporates leverage scores for efficiency with Tikhonov regularization and iterative refinement for stability. RTSMS is demonstrated to be competitive with existing methods, sometimes outperforming them by a large margin.
We illustrate the benefits of Tucker decomposition via MATLAB demos solving problems from global optimization to video compression. RTSMS is joint work with Yuji Nakatsukasa.