Exercise $1\mathrm{.}7***.$ Implementing computation of the principal components

$1)$ Use iris and$/$or MNIST datasets as examples

$2)$ Implement the iterative SVD$-$based first principal component computation using the material from the

lectures

$3)$ Compare the results with the standard implementation of PCA in scikit$-$learn

$4)$ Implement the computation of the second and all higher components

$5)$ Generalize your implementation to the case of weighted data points $($in test example, create weights which

will be much higher for a particular class of data points$)$

$6)$ Think how to generalize your implementation to the case of moderately missing data