200 PCA 150 100 z=Wx Large So variance Reduce to 1-D: 1=w1·x 150 200 Small variance Project all the data points x onto w1, and obtain a set of Z1 We want the variance of z1 as large as possible =w1·x are)-∑a-we=1 PCA 𝑤1 𝑥 Project all the data points x onto 𝑤1 , and obtain a set of 𝑧1 We want the variance of 𝑧1 as large as possible Large variance Small variance 𝑉𝑎𝑟 𝑧1 = 1 𝑁 ෍ 𝑧1 𝑧1 − 𝑧ഥ1 2 𝑧 = 𝑊𝑥 𝑧1 = 𝑤1 ∙ 𝑥 𝑧1 = 𝑤1 ∙ 𝑥 Reduce to 1-D: 𝑤1 2 = 1