Question

I have an mxm kernel matrix, K, which is for the sake of simplicity, a linear kernel computed as pdist2(X,X), where X is mxn and the m dimension relates to feature vectors with n dimensions.

since n is large, I save computation time by precalculating K for all X.

Later on, I need to swap two of the features in X, say X_1 and X_5.

Can I somehow rearrange K, without having to recompute the entire matrix?

Answer 1

If pv is your permutation vector and J0=pdist2(X,X), then

Y=X(pv,:); J1=pdist2(Y,Y);

should get you the same answer as

J1=J0(pv,pv);

If you are permuting the columns (I couldn’t quite tell from your question), then it seems like J1 and J0 should be equal…