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I posted this question in math.se but given the sheer tumultuous number of questions that keep appearing on math.se and also given that I am trying to accomplish this in Mathematica, I thought I'd post an alternate version of this question here. (I hope that's not totally unacceptable to quasi-reproduce my question from elsewhere). I do realize that I'll receive perhaps different flavors of an answer from math.se and mathematica.se.

Simply put, given two sets of data (Discrete Fourier transform matrices in this case), how do I prove similarity in the data.

Comparing the figure on the Left with that on the Right, I somehow have an inkling that theres similarity in the figures.

What I have is DFT data for these figures too (just the top left corner of the DFT data, with the DC component removed), which looks so:

The DFT corner on the left is for the contour plot on the left and the one on the right is for the contour plot on the right.

I did a bit of research and came up with these: self similarity matrix, Smith Waterman algorithm for gene sequencing, it is implemented in Mathematica (also see ref/SmithWatermanSimilarity), and a somewhat related question posted on Mathematica.SE several months ago.

I understand that this is more math related than Mathematica related but as I'd like to use Mathematica since I pre and post process my data in it, I thought I'd ...ask! :)

I used the MatrixPlot to generate the plots from the data below.

Here is DFT data for the figure on the left:

{{0, 0., 23.1306, 0., 4.63337, 0., 4.87462, 0., 1.13912, 0., 0., 0., 
  0., 0., 0., 0., 0., 0., 0., 0.}, {0., 59.8403, 0., 11.402, 0., 0., 
  0., 1.53024, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 
  0.}, {23.3079, 0., 23.2309, 0., 3.80344, 0., 4.07117, 0., 1.07381, 
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.}, {0., 11.3638, 0., 
  3.51212, 0., 4.17147, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 
  0., 0., 0.}, {4.56479, 0., 3.80023, 0., 4.05799, 0., 0., 0., 0., 0.,
   0., 0., 0., 0., 0., 0., 0., 0., 0., 0.}, {0., 0., 0., 4.1947, 0., 
  1.12046, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 
  0.}, {5.12425, 0., 4.21734, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 
  0., 0., 0., 0., 0., 0., 0.}, {0., 1.54858, 0., 0., 0., 0., 0., 0., 
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.}, {1.07898, 0., 
  1.094, 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., 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.}}

And data for the figure on the right:

{{0, 0., 0.940723, 0., 2.95705, 0., 2.92228, 0., 0., 0., 0., 0., 0., 
  0., 0., 0., 0., 0., 0., 0.}, {0., 18.867, 0., 7.68905, 0., 0., 0., 
  1.61012, 0., 1.07367, 0., 0., 0., 0., 0., 0., 0., 0., 0., 
  0.}, {1.28581, 0., 12.1276, 0., 6.00817, 0., 0., 0., 1.7524, 0., 0.,
   0., 0., 0., 0., 0., 0., 0., 0., 0.}, {0., 8.01748, 0., 14.725, 0., 
  0., 0., 1.05116, 0., 2.1411, 0., 0., 0., 0., 0., 0., 0., 0., 0., 
  0.}, {2.77763, 0., 6.2871, 0., 1.82885, 0., 1.65436, 0., 1.43276, 
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.}, {0., 0., 0., 0., 0., 
  3.54584, 0., 1.45959, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 
  0.}, {3.11339, 0., 0., 0., 1.89853, 0., 3.24873, 0., 0., 0., 0., 0.,
   0., 0., 0., 0., 0., 0., 0., 0.}, {0., 1.83295, 0., 0., 0., 1.57703,
   0., 1.14208, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.}, {0., 
  0., 1.61293, 0., 1.32478, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 
  0., 0., 0., 0., 0.}, {0., 1.02113, 0., 2.18193, 0., 0., 0., 0., 0., 
  0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.}, {0., 0., 0.976133, 0., 
  0.931741, 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.}}
share|improve this question
    
May be you can use fractal dimensions to measure the similarities. Also related post might help 'Measuring fractal dimension of natural objects from digital images' but mainly for images mathematica.stackexchange.com/questions/13125/… –  s.s.o Aug 25 at 12:25
    
@s.s.o That is an interesting point you make. I considered this later in 2012 but dropped the idea entirely as I had to defend and finish my PhD! Perhaps I will do this on an other day to include in my lectures! :) Thank you for your answer/comment! –  drN Aug 25 at 16:48

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