# Stochastic gradient descent in matrix factorization, sensitive to label's scale?

I'm trying to figure out a strange phenomenon, when I use matrix factorization (the Netflix Prize solution) for a rating matrix:

$R = P^T * Q + B_u + B_i$

with ratings ranging from 1 to 10.

Then I evaluate the model by each label's absolute mean average error in test set, the first column is origin_score, the second(we don't transform the data, then train and its prediction error), the third(we transform the data all by dividing 2, train, and when I use this model to make prediction, firstly reconstruct the matrix and then just multiply 2 and make it back to the same scale)

As you see, in grade 3-4 (most samples are label from 3-4), it's more precise while in high score range(like 9 and 10, just 2% of the whole traiing set), it's worse.

 +----------------------+--------------------+--------------------+ | rounded_origin_score | abs_mean_avg_error | abs_mean_avg_error | +----------------------+--------------------+---------------------+ | 1.0 | 2.185225396100167 | 2.559125413626183 | | 2.0 | 1.4072212825108161 | 1.5290497332538155 | | 3.0 | 0.7606073396581479 | 0.6285151230269825 | | 4.0 | 0.7823491986435621 | 0.6419077576969795 | | 5.0 | 1.2734369551159568 | 1.256590210555053 | | 6.0 | 1.9546560495715863 | 2.0461809588933835 | | 7.0 | 2.707229888048017 | 2.8866856489147494 | | 8.0 | 3.5084244741417137 | 3.7212155956153796 | | 9.0 | 4.357185793060213 | 4.590550124054919 | | 10.0 | 5.180752400467891 | 5.468600926567884 | +----------------------+--------------------+---------------------+ 

I've re-train the model several times, and got same result, so I think it's not effect by randomness.