Yousef Saad Department Of Computer Science And Engineering
Yousef Saad Department Of Computer Science And Engineering
Yousef Saad Department Of Computer Science And Engineering
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A unified view<br />
* Joint work with Efi Kokiopoulou and J. Chen<br />
➤ Most techniques lead to one of two types of problems<br />
First :<br />
➤ Y results directly<br />
from computing eigenvectors<br />
➤ LLE, Eigenmaps, ...<br />
Second:<br />
➤ Low-Dimens. data:<br />
Y = V ⊤ X<br />
➤ G == identity, or<br />
XDX ⊤ , or XX ⊤<br />
⎧<br />
⎨<br />
⎩<br />
⎧<br />
⎨<br />
⎩<br />
min<br />
Y ∈ R d×n<br />
Y Y ⊤ = I<br />
min<br />
V ∈ R m×d<br />
V ⊤ G V = I<br />
Tr Y MY ⊤<br />
Tr V ⊤ XMX ⊤ V <br />
Observation: 2nd is just a projected version of the 1st.<br />
CSE Colloquium 11/09/09 p. 65
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