title: Outliers using RPCA
body: <p>I read about using RPCA to find outliers on time series data. I have an idea about the fundamentals of what RPCA is about and the theory. I got a Python library that does RPCA and pretty much got two matrices as the output (L and S), a low rank approximation of the input data and a sparse matrix.</p>
  
  <p><strong>Input data:(rows being a day and 10 features as columns.)</strong></p>
  
  <pre><code>DAY 1 - 100,300,345,126,289,387,278,433,189,153  
  DAY 2 - 300,647,245,426,889,987,278,133,295,153  
  DAY 3 - 200,747,145,226,489,287,378,1033,295,453
  </code></pre>
  
  <p><strong>Output obtained :</strong></p>
  
  <pre><code>L  
  [[ 125.20560531  292.91525518   92.76132814  141.33797061  282.93586313
     185.71134917  199.48789246   96.04089205  192.11501055  118.68811072]  
   [ 174.72737183  408.77013914  129.45061871  197.24046765  394.84366245
     259.16456278  278.39005349  134.0273274   268.1010231   165.63205458]  
   [ 194.38951303  454.76920678  144.01774873  219.43601655  439.27557808
     288.32845493  309.71739782  149.10947628  298.27053871  184.27069609]]
  
  S  
  [[ -25.20560531    0.          252.23867186   -0.            0.
     201.28865083   78.51210754  336.95910795   -0.           34.31188928]  
   [ 125.27262817  238.22986086  115.54938129  228.75953235  494.15633755
     727.83543722   -0.           -0.           26.8989769    -0.        ]  
   [   0.          292.23079322   -0.            0.           49.72442192
      -0.           68.28260218  883.89052372    0.          268.72930391]]
  </code></pre>
  
  <p><strong>Inference: (My question)</strong></p>
  
  <p>Now how do I infer the points that could be classified as outliers. For ex. by looking at the data, we could say 1033 looks like an outlier. The corresponding entry in S matrix is 883.89052372 which is more compared to other entries in S. Could the notion of having a fixed threshold to find the deviations of S matrix entries from the corresponding original value in the input matrix be used to determine that the point is an outlier ? Or am I completely understanding the concept of RPCA wrong ? TIA for your help.</p>