Algorithm 2.

Generalized Rayleigh

Input: Low column rank data A ∈ $\mathbb{R}$m×k
Output: Rayleigh projection vectors Ξ ∈ $\mathbb{R}$k×r
1:	Compute ΣC and either of ΣA, ΣB
2:	[E, ΛC, ET] = svd(ΣC, k)
3:	AW ∈ $\mathbb{R}$m×n = AE(${\mathrm{\Lambda }}_C^{-1/2}$)	▹ Whiten data
4:	ΣW ∈ $\mathbb{R}$k×k = Cov(AW)
5:	$\left[U_r,{\mathrm{\Lambda }}_r,U_r^T\right]=svd\left({\mathrm{\Sigma }}_W,r\right)$
6:	$\hat{\mathrm{\Xi }}\in {ℝ}^{k\times r}=E*{\mathrm{\Sigma }}_C^{-1/2}*U_r,$	▹ Forward vectors
7:	$\tilde{\mathrm{\Xi }}$ ∈ $\mathbb{R}$k×r = E ∗ ${\mathrm{\Lambda }}_C^{1/2}$ ∗ Ur	▹ Inverse vectors
8:	$\tilde{\mathrm{A}}$ = A$\widehat{\mathrm{\Xi }}$$\tilde{\mathrm{\Xi }}$T	▹ Approximated Data