title: How to rotate the MNIST pixel vectors by a small angle?
body: <p>I'm working on the MNIST data set, and I want to manipulate the training data in different ways to bulk up the training data set. I had an idea to slightly rotate each image in the training set.</p>
  <p>So, for example, this is an actual 784-item array (28 X 28 pixel), so this represents one image of a number in the data set:</p>
  <pre><code>0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,84,185,159,151,60,36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,222,254,254,254,254,241,198,198,198,198,198,198,198,198,170,52,0,0,0,0,0,0,0,0,0,0,0,0,67,114,72,114,163,227,254,225,254,254,254,250,229,254,254,140,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,17,66,14,67,67,67,59,21,236,254,106,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,83,253,209,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,22,233,255,83,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,129,254,238,44,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,59,249,254,62,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,133,254,187,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,205,248,58,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,126,254,182,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,75,251,240,57,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,19,221,254,166,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,203,254,219,35,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,38,254,254,77,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,31,224,254,115,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,133,254,254,52,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,61,242,254,254,52,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,121,254,254,219,40,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,121,254,207,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
  </code></pre>
  <p>So I just want to rotate this +- say 5 degrees/10 degrees.</p>
  <p>I found something that could sort of be useful <a href="https://docs.scipy.org/doc/numpy-1.9.2/reference/generated/numpy.rot90.html" rel="nofollow noreferrer">here</a> in numpy.rot90, I guess I'm looking for something like this, but 1D, and 5/10 degrees instead of 90.</p>
  <p>I'm not even sure if this makes sense, because I guess the rotation should be relative to something in the background? but with the MNIST data set, this is all I have, an array of pixels?</p>
  <p>Does anyone have any ideas?</p>
  <p>(Sorry as you can see from previous questions, I usually post the sample code I've tried so far, but I can't find any/am not sure if this is possible in python, also I know there are questions out there about rotating 2D vectors, but I don't understand how MNIST can be rotated as a 2D vector).</p>