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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➤ Problem translates to:<br />
⎧<br />
⎨<br />
⎩<br />
min<br />
Y ∈ R d×n<br />
Y D Y ⊤ = I<br />
Tr Y (D − W )Y ⊤ .<br />
➤ Solution (sort eigenvalues increasingly):<br />
(D − W )ui = λiDui ; yi = u ⊤ i<br />
; i = 1, · · · , d<br />
➤ An n × n sparse eigenvalue problem [In ‘sample’ space]<br />
➤ Note: can assume D = I. Amounts to rescaling data.<br />
Problem becomes<br />
(I − W )ui = λiui ; yi = u ⊤ i<br />
; i = 1, · · · , d<br />
CSE Colloquium 11/09/09 p. 64