Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...
Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...
Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Alternating Least Squares Framework<br />
A Sequence of Three Linear Problems...<br />
UT 3 ⊗ UT 2 ⊗ UT <br />
1 · vec(A) <br />
=<br />
U T 1 · A (1) · (U3 ⊗ U2) F<br />
=<br />
U T 2 · A (2) · (U3 ⊗ U1) F<br />
=<br />
U T 3 · A (3) · (U2 ⊗ U1) F<br />
⇐ 1. Fix U2 and U3 and<br />
maximize with U1.<br />
⇐ 2. Fix U1 and U3 and<br />
maximize with U2.<br />
⇐ 3. Fix U1 and U2 and<br />
maximize with U3.<br />
<strong>The</strong>se max problems are SVD problems...<br />
⊗ Transition to Computational Multilinear Algebra ⊗ <strong>Lecture</strong> <strong>6.</strong> <strong>The</strong> <strong>Tucker</strong> <strong>Representation</strong>
Change language