Please help me understand what happens to the matrices bellow

Hi All

I have a matrix t [3 1000]

and then these lines :

     y00   = repmat( mean(t,2), 1, size(t,2))
     MSE00 = mse( t - y00 )
     MSE00 = mean(var(t',1)) 
     nperf = mse(t-y)/MSE00

what does each line do ??

[dpb]

I suggest making up a small sample array (say 3x5) and try each step at the command line and observe, using the documentation to aid your exploration...you'll learn a lot more and retain what you learn much better that way.

[farzad]

I still didn't get the whole meaning of

   repmat( mean(t,2), 1, size(t,2))

[Roger Stafford]

The line "repmat( mean(t,2), 1, size(t,2))" first takes the mean value of each of the three rows of matrix 't', giving a 3-by-1 column vector as a result. Then the 'repmat' operator repeats this vector along the second dimension so that it is again of size 3-by-1000. Each of its thousand columns will then be the same.

[dpb]

NB: that bsxfun will allow writing the following lines w/o the explicit expansion, too...highly recommended as long as the version in use incorporates it (which is getting to be quite some time ago now altho I don't recall just when that was).

Answer 1

[Greg Heath]

The significance of the code is that MSE00 is a very special reference normalization value for mean-square-error.

Consider a net that yields the same output, regardless of input. Given a target matrix, what constant will minimize mean-square error?

When you work it out you will find that the constant should be the row-wise mean value of the target matrix.

Furthermore, the corresponding minimum mean-square-error is just the mean of the biased (i.e., divide by N, not N-1) row-wise variances.

If you consider the mean variance as a measure of how much information is in the target, the normalized MSE of any design

 NMSE = mse(target-output)/MSE00

is a measure of the fraction of that target information that is NOT modelled by the design and correspondingly the coefficient of determination

 Rsquare = 1- NMSE

is a measure of the fraction of that target information that IS modelled by the design.

 http://en.wikipedia.org/wiki/Coefficient_of_determination

I typically try to obtain a Rsquare value that corresponds to modeling at least 99% of the mean target variance.