a wrong description in KPCA #17024
Description
a wrong description in KPCA
# if u is an eigenvector of Phi(X)Phi(X)'
# then Phi(X)'u is an eigenvector of Phi(X)Phi(X)'I now prove it simply.
Phi(X)Phi(X)'u = \lambda u
Phi(X)'Phi(X)Phi(X)'u = \lambda Phi(X)' u
Phi(X)'Phi(X) (Phi(X)'u) = \lambda (Phi(X)' u)
suggest as follows
# if u is an eigenvector of Phi(X)Phi(X)'
# then Phi(X)'u is an eigenvector of Phi(X)Phi(X)'--> should be
# if u is an eigenvector of Phi(X)Phi(X)'
# then Phi(X)'u is an eigenvector of Phi(X)'Phi(X)