Given $X_{N \times d}$ data, where $N$ is the number of samples and $d$ the size of the features space.

Using Kernel-PCA first it is computed a kernel matrix $K_{N \times N}$, and than, after the eigen vectors $eig_{N \times N}$ have been computed it is possible to preject the data over the first $c \leq d$ components as:

Projected = K*eig(:,1:c);

The new projected data have now size ${N \times c} $.

I would like to know if it is possible to prject an unseen data $x_{1 \times d} $ over the previously computed components vector $eig$. If it's possible what is the correct procedure?

Let $X_{N \times d}$ be the data matrix, where $N$ is the number of samples and $d$ the size of the features space.

Using kernel PCA (kPCA), one first computes a kernel matrix $K_{N \times N}$, and then, after its eigenvectors $E_{N \times N}$ have been computed, it is possible to project the data onto the first $c \leq N$ components as: $$X_\mathrm{projected} = KE_c,$$ where $E_c$ denotes first $c$ columns of $E$. Equivalently, in Matlab notation:

Projected_data = K*E(:,1:c);

The new projected data have now size ${N \times c} $.

I would like to know if it is possible to project an unseen data vector $x_{1 \times d} $ onto the previously computed principal components $E$. If it is possible, what is the correct procedure?

Given $X_{N \times d}$ data, where $N$ is the number of features and $d$ the size of the features space.

Using Kernel-PCA first it is computed a kernel matrix $K_{N \times N}$, and than, after the eigen vectors $eig_{N \times N}$ have been computed it is possible to preject the data over the first $c \leq d$ components as:

Projected = K*eig(:,1:c);

The new projected data have now size ${N \times c} $.

I would like to know if it is possible to prject an unseen data $x_{1 \times d} $ over the previously computed components vector $eig$. If it's possible what is the correct procedure?

Given $X_{N \times d}$ data, where $N$ is the number of samples and $d$ the size of the features space.

Using Kernel-PCA first it is computed a kernel matrix $K_{N \times N}$, and than, after the eigen vectors $eig_{N \times N}$ have been computed it is possible to preject the data over the first $c \leq d$ components as:

Projected = K*eig(:,1:c);

The new projected data have now size ${N \times c} $.

I would like to know if it is possible to prject an unseen data $x_{1 \times d} $ over the previously computed components vector $eig$. If it's possible what is the correct procedure?