Yousef Saad Department Of Computer Science And Engineering
Yousef Saad Department Of Computer Science And Engineering
Yousef Saad Department Of Computer Science And Engineering
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Trace ratio problem<br />
* Joint work with Thanh Ngo and Mohamed Bellalij<br />
➤ Main point: trace ratio can be maximized inexpensively<br />
Let f(ρ) = max U,U T U=I Trace[U T (A − ρB)U]<br />
<strong>And</strong> let U(ρ) the maximizer of above trace.<br />
➤ Then, under some mild assumptions on A and B :<br />
1) Optimal ρ for trace ratio is a zero of f<br />
2) f ′ (ρ) = −Trace[U(ρ) T BU(ρ)]<br />
3) f is a decreasing function<br />
... + Newton’s method to find zero<br />
amounts to a fixed point iteration:<br />
ρnew = Tr [U(ρ)T AU(ρ)]<br />
Tr [U(ρ) T BU(ρ)]<br />
CSE Colloquium 11/09/09 p. 39
Change language