Here is how you can obtain the associated principal components score for a new vector of data:
(* Data from Mathematica documentation on PrincipalComponents *)
data = {{13.2, 200, 58, 21.2}, {10, 263, 48, 44.5}, {8.1, 294, 80,
31}, {8.8, 190, 50, 19.5}, {9, 276, 91, 40.6}, {7.9, 204, 78,
38.7}, {3.3, 110, 77, 11.1}, {5.9, 238, 72, 15.8}, {15.4, 335, 80,
31.9}, {17.4, 211, 60, 25.8}};
(* Get principal component scores from high level function *)
pc = PrincipalComponents[data, Method -> Correlation];
(* Get information needed to transform additional vectors in the same \
way *)
dataMean = Mean[data];
dataSD = StandardDeviation[data];
(* Standardize original data *)
z = (# - dataMean)/dataSD & /@ data;
(* Get principal components and other necessary info the hard way *)
{u, s, v} = SingularValueDecomposition[z];
(* But note that pc and z.v are "essentially the same" except that \
the signs of some columns might be reversed, i.e., principal \
components are not unique with respect to sign *)
MatrixForm[pc]
MatrixForm[z.v]
(* So from here on we use z.v rather than pc because we need the \
other pieces generated by SingularValueDecomposition *)
(* Say we have a new vector of values that we want to transform to \
its corresponding principal component score *)
(* I've used just the first row of the data to show that one gets the \
correct results - one never has enough QA *)
x = {13.2, 200, 58, 21.2};
(* Standardize x with the data mean and standard deviation *)
zx = (x - dataMean)/dataSD;
(* Obtain principal components score for x *)
pcx = zx.v
So that will obtain the principal components for any new data. Like Matthias, I have not seen the term "amplitude" associated with principal component theory. Is that a particular subject matter jargon?