SIAM Journal on Optimization· 2013Q1
Optimization-Based Algorithms for Tensor Decompositions: Canonical Polyadic Decomposition, Decomposition in Rank-$(L_r,L_r,1)$ Terms, and a New Generalization
- 279citations
- Q1SCImago
- 2013year
Short summary
New optimization-based algorithms efficiently compute a generalized tensor decomposition that unifies Canonical Polyadic Decomposition (CPD) and rank-(Lr,Lr,1) Block Term Decomposition (BTD).
AI-generated from the title and abstract; the full text is not read.
Key points
- A new tensor decomposition generalizes CPD and rank-(Lr,Lr,1) BTD.
- Algorithms include alternating least squares, general optimization, and matrix-free nonlinear least squares.
- Matrix-free methods exploit Jacobian structure to reduce computational and memory costs.
- Numerical experiments show these methods are efficient and robust for CPD, BTD, and the generalized decomposition.
AI-generated from the title and abstract; the full text is not read.
Abstract
The canonical polyadic and rank-$(L_r,L_r,1)$ block term decomposition (CPD and BTD, respectively) are two closely related tensor decompositions. The CPD and, recently, BTD are important tools in psychometrics, chemometrics, neuroscience, and signal processing. We present a decomposition that generalizes these two and develop algorithms for its computation. Among these algorithms are alternating least squares schemes, several general unconstrained optimization techniques, and matrix-free nonlinear least squares methods. In the latter we exploit the structure of the Jacobian's Gramian to reduce computational and memory cost. Combined with an effective preconditioner, numerical experiments confirm that these methods are among the most efficient and robust currently available for computing the CPD, rank-$(L_r,L_r,1)$ BTD, and their generalized decomposition.
The authors' abstract, as published at the source. SIAM Journal on Optimization, 2013 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Computational Mathematics
Computational MathematicsMathematics