title: How do I use principal component analysis in supervised machine learning classification problems?
body: <p>I have been working through the concepts of principal component analysis in R.</p>
  
  <p>I am comfortable with applying PCA to a (say, labeled) dataset and ultimately extracting out the most interesting first few principal components as numeric variables from my matrix.</p>
  
  <p>The ultimate question is, in a sense, now what?  Most of the reading I've come across on PCA immediately halts after the computations are done, especially with regards to machine learning.  Pardon my hyperbole, but I feel as if everyone agrees that the technique is useful, but nobody wants to actually use it after they do it.</p>
  
  <p>More specifically, here's my real question:</p>
  
  <p>I respect that principle components are linear combinations of the variables you started with.  So, how does this transformed data play a role in supervised machine learning?  How could someone ever use PCA as a way to reduce dimensionality of a dataset, and THEN, use these components with a supervised learner, say, SVM?  </p>
  
  <p>I'm absolutely confused about what happens to our labels.  Once we are in eigenspace, great.  But I don't see any way to continue to move forward with machine learning if this transformation blows apart our concept of classification (unless there's some linear combination of "Yes" or "No" I haven't come across!)</p>
  
  <p>Please step in and set me straight if you have the time and wherewithal.  Thanks in advance.</p>