recap and Goals

approximate factorization

$W\ L\rightarrow (W+L)/ 2$ rank 下降使得信息缺失了

所以 $M_{100 \times 4} = N_{100 \times P} \times Q_{P \times 4}$ P的值尽量不要小于原来的"秩"

singular value decomposition (SVD)

low rank approximation

no bad! seem good!

SVD theory

验证orthonormal set

• V@V.T = I

当相乘的时候本质上是旋转，不会拉伸

Principal Components

零中心化再来看PCA

Principal Components and Variance

PCA example

Why is useful? 🤔