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In a lot of articles in my field, this sentence has been repeated: " The 2 matrices has been normalized to have the same average sum-of-squares (computed across all subjects and all voxels for each modality)". Suppose that we have two matrices that the rows define different subjects and the columns are features (voxels). In these articles, no much explanation can be found for normalization method. Does anybody knows how I should normalize data to have "same average sum-of-squares"? I don't understand it at all. Thanks

Mike Sherrill 'Cat Recall'
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F.K1
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  • I don't know your field, maybe it is just something like this: Lets call *M1* and *M2* the two matrices, let *S1* and *S2* be the average sum-of-squares" of *M1* and *M2* respectively. Compute *Q = S1/S2*, divide the elements of the second matrix, *M2*, by *sqrt(Q)*. – Margaret Bloom Jun 07 '16 at 15:33
  • Thank you very much. My field is biomedical engineering, however it doesn't change the concept. From your answer I hasn't know the meaning of "average sum-of-squares" yet! You mean that squares of each element of the matrix should be calculated and then, mean of its summation is calculate? Is this a common normalization method? If this is true, how the negative elements appears in the matrix after this step? It seems that a subtraction is also needed? Please help me. – F.K1 Jun 08 '16 at 17:39
  • I'm afraid I'm not really qualified to answer your question, you teacher/advisor is surely a better choice :) Maybe a different introductionary book on the subject will also help. – Margaret Bloom Jun 09 '16 at 09:57

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For a start normalization in this context is also known as features scaling, which pretty much sums it up. You scale your features, your data to get rid of variances and range of values which would disturb your algorithm and your results in the end.

https://en.wikipedia.org/wiki/Feature_scaling

In data processing, normalization is quite useful (depending on the application). E.g. in distance based machine learning algorithms you should normalize your features in order to get a proportional contribution to the outcome of your algorithm, independent of the range of value the features comprise.

To do so, you can use different statistical measurements, like the Sum of squares: 

SUM_i(Xi-Xbar)²

Other than that you could use the variance or the standard deviation of your data.

https://www.westgard.com/lesson35.htm#4

Those statistical terms can then be used to normalize your data, to improve e.g. the clustering quality of your algorithm. Which term to use and which method highly depends on the algorithms and data you're using and what you're aiming at. Here is a paper which compares some of the approaches you could choose from for clustering:

http://maxwellsci.com/print/rjaset/v6-3299-3303.pdf

I hope this can help you a little.

mrk
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