title: How to verify what's noise what's real data?
body: <p>I am wondering how can I claim that I correctly catch the "noise" in my data ?</p>
  
  <p>To be more specific, take Principle Component Analysis as example, we know that in PCA, after doing SVD, we can zeros out the small singular values and   reconstruct the original matrix using low-rank approximation.</p>
  
  <p>Then can I claim what's been ignored is indeed noise in the data ?
  Is there any evaluation metric for this ? </p>
  
  <p>The only method I can come up with is simply subtract the original data from the reconstructed data.</p>
  
  <p>Then, try to fit a Gaussian over it, seeing if the fitness is good.</p>
  
  <p>Is that conventional method in field like DSP ??</p>
  
  <p>BTW, I think in typical machine learning tasks, the measurement would be the follow up classification performance, but since I am doing purely generative model, there are no labels attached.</p>