Hi everybody.

I'm currently working at a problem where it comes very useful to have a linear dimensionality reduction, just as the fuction DimensionReduction[Method-> "Linear"] does.

I would like to use the found reduction matrix in an other context and I was looking for extracting it.

So I used the following code:

dummy = RandomReal[{-1, 1}, {10, 4}];

drf = DimensionReduction[dummy, 2, Method -> "Linear"]

drfM = drf[[1]]["Model"]["Matrix"]

But when then this check tells me that I'm missing something:

In[10]:= dummy.drfM == drf[dummy]

Out[10]= False

In[11]:= dummy.drfM == drf[Standardize@dummy]

Out[11]= False

I also used Standardize because I saw it as a step in:

drf[[1]]["Model"]["Processor"]

So how can I find the linear algebra transformation that the reducerFunction found? And to what method "Linear" correspond to? It is not clear from the documentation...

Thanks in advance :)

PS: I empirically found that there is a systematic -5% error between the two tranformations:

In[106]:= (Standardize[dummy].drfM - drf[dummy])/drf[dummy]

Out[106]= {{-0.0513167, -0.0513167}, {-0.0513167, -0.0513167}, \
{-0.0513167, -0.0513167}, {-0.0513167, -0.0513167}, {-0.0513167, \
-0.0513167}, {-0.0513167, -0.0513167}, {-0.0513167, -0.0513167}, \
{-0.0513167, -0.0513167}, {-0.0513167, -0.0513167}, {-0.0513167, \
-0.0513167}}