Dimension Reduction Methods with Application to ... - Rice University
Dimension Reduction Methods with Application to ... - Rice University
Dimension Reduction Methods with Application to ... - Rice University
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PCA<br />
50 / 86<br />
◮ Sample covariance matrix S = (N − 1) −1 X ′ X<br />
◮ Eigenvalue decomposition: S = V∆V ′<br />
◮<br />
◮<br />
∆ = diag(λ 1 ≥ · · · ≥ λ N ) eigenvalues<br />
V = (v 1 , . . . , v N ) unit eigenvec<strong>to</strong>rs<br />
◮ weight vec<strong>to</strong>rs w k = v k<br />
◮ PCs are M k = Xw k , k = 1, . . . , N<br />
◮ Cumulative variation explained by the 1st K PCs<br />
is ∑ K<br />
k=1 λ k
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