# Machine Learning Week 5
## PCA(continue)
* Reconstruction
* To find a linear transformation $W\in \mathbb{R}^{M\times m}$ minimize the reconstruction error.
* Projecting to $S_{PCA}$ yields the minimum mean squared error among all possible m-dimensional subspaces.
* Eckart-Young-Mirsky Theorem
* 
* How EYM proves PCA yields minimum reconstruction error
1. WLOG assume zero mean.
2. 
3. 
4. Since
* Proof of EYM Theorem
* See the lecture.