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