# Normalizing data before applying MDS with strain criterion

The features of my dataset are like below:
• BI-RADS assessment: 1 to 5 (ordinal)
• Age: patient's age in years (integer) ranges from 18 to 96
• Shape: mass shape: round=1 oval=2 lobular=3 irregular=4 (nominal)
• Margin: mass margin: circumscribed=1 microlobulated=2 obscured=3 ill-defined=4 spiculated=5 (nominal)
• Density: mass density high=1 iso=2 low=3 fat-containing=4 (ordinal)

When I run MDS with "strain" criterion on such a dataset without normalizing it first, I get a result as follows: However, if I normalize the data the result is as follows:
The second results is pretty similar to results that I have got for other criteria and also for the PCA even I didn't normalize the data for them also.

So, my question is: Why does normalizing data make difference for "strain" criterion?

• Your question seems to be MATLAB-specific. I think you ought to read the procedure's documentation thoroughly and then, if something remains strange, ask. Also, what type of normalization do you do and what is strain criterion - please describe. Nov 12 '12 at 6:52
• Do I understand correctly that you run 2 pieces of code and are unsure why they provide different results? In this case I recommend you to post the relevant code fragments as it is a bit unclear what you are doing exactly with the current information. Nov 16 '12 at 14:55

Suppose you don't normalize your data. You could have a situation like this:

    user1   user2   user3   user4   user5   user6   user7   user8   user9
1   0.00    0.00    0.00    0.00    0.00    0.00    0.00    0.00    0.00
2   18      96      21      45      93      19      21      19      90
3   0.08    0.12    0.19    0.70    0.12    0.01    0.00    0.09    0.04
4   1019    217     53      1082    1010    2       30      0       100


So it is clear that some features influence the results much more than others.

Remember that the MDS is a way to force differences between elements in n dimensions in differences in 2 dimensions, between all the couples of elements! I simply think that in the first case the strain function

is affected by the lack of normalization. When you normalize the data the algorithm is able to catch the real differences among the points considering in a proper way all the different features.