Part $2$: Kernel PCA $($KPCA$)$

$2\mathrm{.}1$ KPCA with RBF Kernel:

$($a$)$ Implement Kernel PCA with the Radial Basis Function $($RBF$)$ kernel from scratch.

$($b$)$ Apply your KPCA implementation to the TrainData.

$2\mathrm{.}2$ KPCA with Polynomial Kernel:

$($a$)$ Implement Kernel PCA with a Polynomial kernel from scratch.

$($b$)$ Apply your KPCA implementation to the TrainData.

$2\mathrm{.}3$ KPCA with Linear Kernel:

$($a$)$ Implement Kernel PCA with a Linear kernel from scratch.

$($b$)$ Apply your KPCA implementation to the TrainData.

$2\mathrm{.}4$ Applying SVD for Dimensionality Reduction:

$($a$)$ Implement Singular Value Decomposition $($SVD$)$ for dimensionality reduction.

$($b$)$ Apply SVD to the TrainData and compare the results with PCA and KPCA.