original data decorrelated data PCA-decorrelation X2 z=Wx Cov(z)=D PCA Diagonal matrix co(a)=是∑a-0e-ar=WSWT S=co(0 =WS[w1 ..wk]=W[Sw1 ..Swk] =W[Aiw1 ..Akwk][AWw1 …KWwk] =[Ae1.Akek]=D Diagonal matrix 𝑧 = 𝑊𝑥 𝐶𝑜𝑣 𝑧 = 𝐷 Diagonal matrix 𝐶𝑜𝑣 𝑧 = 1 𝑁 ෍ 𝑧 − 𝑧ҧ 𝑧 − 𝑧ҧ 𝑇 = 𝑊𝑆𝑊 𝑆 = 𝐶𝑜𝑣 𝑥 𝑇 PCA - decorrelation = 𝑊𝑆 𝑤1 ⋯ 𝑤𝐾 = 𝑊 𝑆𝑤1 ⋯ 𝑆𝑤𝐾 = 𝑊 𝜆1𝑤1 ⋯ 𝜆𝐾𝑤𝐾 = 𝜆1𝑊𝑤1 ⋯ 𝜆𝐾𝑊𝑤𝐾 = 𝜆1𝑒1 ⋯ 𝜆𝐾𝑒𝐾 = 𝐷 Diagonal matrix PCA 𝑧1 𝑧2 𝑥1 𝑥2