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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➤ Project set on<br />
a one-dimensional<br />
space spanned by<br />
a vector a.<br />
Then:<br />
a T SBa =<br />
a T SW a =<br />
➤ LDA projects the data so as<br />
to maximize the ratio of these two<br />
numbers:<br />
c<br />
i=1<br />
c<br />
k=1<br />
nk|a T (µ (k) − µ)| 2 ,<br />
<br />
xi ∈ Xk<br />
|a T (xi − µ (k) )| 2<br />
max<br />
a<br />
a T SBa<br />
a T SW a<br />
➤ Optimal a = eigenvector associated with the largest eigenvalue<br />
of:<br />
SBui = λiSW ui .<br />
CSE Colloquium 11/09/09 p. 37