Ex. 5.17

Ex. 5.17

Show how to convert the discrete eigen-decomposition of \(\bb{K}\) in Section 5.8.2 to estimates of the eigenfunctions of \(K\).

Soln. 5.17

As the text suggests, given a kernel matrix \(\bb{K}\), we first calculate its eigen-decomposition

\[\begin{equation} \bb{K} = \bm{\Phi}\bb{D}_\lambda\bm{\Phi}^T.\non \end{equation}\]

Then \(i-\)th row of \(\bm{\Phi}\) is the estimated vector of basis functions \(\phi(x_i)\), evaluated at point \(x_i\).