Kernel PCA and K largest eigenvectors

Question

How can one prove that the optimal kPCA solution $a^*={a_1...a_K}$ are the $k$-largest Eigenvectors of the (centered) kernel matrix $K$?

I referred to a lot of resources and couldn't find a proper explanation.

Parijat Bhatt · Answer

An indirect way would be the ratio of variance in all the dimensions if we know the eigenvalues corresponding to eigenvectors. So if an eigenvector has eigenvalues $e1$ then the ratio contributed by it will be $e1over (e1+e2+e3+e4.... +en)$. The largest eigenvector will have the largest eigenvalue.

Answered by Parijat Bhatt on February 15, 2021

Kernel PCA and K largest eigenvectors

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