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I have a list of m x n similarity score matrix, something like

           c1         c2         c3         c4         c5  
      d1  0.2159824  0.3528572  0.2390016  0.3673485  0.2849448
      d2  0.2849448  0.2669695  0.2441495  0.3829949  0.3511353
      d3  0.3281100  0.3251407  0.4328260  0.2895179  0.2814589  

these "similarity scores" lie in between 0-1. What I am trying to do here is to combine these scores into a single score, also in between 0-1.

My issue here is that I am not able to figure out a good approach to combine these scores into this single score. So far I have tried taking the average, max. value, calculating row, column averages and using the max.value out of them. The problem with these scores is that the matrices I have vary a lot in row and column lengths, and I cannot account for this variation using average because at the end of the day I have to sort these matrices based on this similarity score and select n top ranking ones, and from manually checking these observations, I realized that max.value in a matrix is not a suitable single score the similarity between these observations. Do you have any suggestions for an approach to combine these scores ?

Also is there any statistical tests that could be applied on this combined score ? I have tried random sampling approach, but the steps to calculate similarity scores for the observations take a long time to run and iterating these steps ~1,000 times or more is not feasible now.

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  • $\begingroup$ In what way(s) were the scores you computed inadequate for your purposes? Without knowing that, we'd likely suggest things with the same inadequacies. $\endgroup$ – Glen_b -Reinstate Monica Oct 18 '13 at 9:31
  • $\begingroup$ I have edited my post to address your questions $\endgroup$ – deeps Oct 18 '13 at 9:53
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You actually have two problems, not one.

The first problem seems to be to average the scores in a matrix. Here the mean, median, trimmed mean and winsorized mean all seem potentially sensible.

The other is to somehow "account" for the size of the matrix. Here the total size (rxc) seems to be the obvious solution.

If you need more than this, please clarify your question again, but I see no reason why the average (or any of the variations I listed) are poor choices simply because the matrices are different sizes.

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