title: Using PCA trained on a large data set for a smaller data set
body: <p>Can I use a pca subspace trained on, say, eight features and one thousand time points to evaluate a single reading? That is, if I keep, say, the top six components, my transformation matrix will be 8x6 and using this to transform test data that is the same size as the training data would give me an 6x1000 vector. </p>
  
  <p>But what if I want to look for anomalies at each time point independently? That is, can rather than use an 8x1000 test set, can I use 1000 separate transformation on 8x1 dimensional test vectors and get the same result? This vector will get transformed into the exact same spot as if it were the first row in a much larger data matrix, but the distance of that one vector from the principal axis doesn't appear to be meaningful. When I perform this same procedure on the truncated reference data, this distance isn't zero either, only the sum of all distances over the entire reference data set is zero. So if I can't show that the reference data is not "anomalous", how can I use this on test data? </p>
  
  <p>Is it the case that the size of the data "object" used to train pca is the size of object that can be evaluated with it? </p>
  
  <p>Thanks for any help you can give. </p>