Results with local SVD

First, we apply the local SVD on the best co-clustering result (smallest RMSE) which is the one obtains with the 20x20 setting using squared Euclidean distance and scheme 3. We vary the number of factor $k$ from $1$ to $10$ with step size $1$, and find that the best performance is at $k$ = 3. Table 6 presents the results of the local SVD with different ways of filling in the missing values based on coclusters. Scheme 5 gives the best performance which reduces the RMSE from 0.90999 to 0.9039. From this table, we also see that the performance of the SVD depends much on the way we initialize the missing values. For example, scheme 3 and 5 give good performance while the others give very bad performance. In particular, the performance of scheme 6 is much worse than the baseline. We also apply this local SVD on other results obtained from the co-clustering algorithm but none of them gives better results.

Table 6: Performance of local SVD on the best co-clustering result with different ways to fill in the missing values

Scheme	RMSE
1	0.9714
2	0.9546
3	0.9048
4	0.9522
5	0.9039
6	1.2179

Finally, we also apply this SVD technique on the coclusters obtained from Graclus. We run the local SVD on the 20x20 coclusters from Graclus and also with different ways of initializing the missing values (Table 7). We also find that the SVD with scheme 5 gives best performance (RMSE = 0.9057) which is not much different from the best one with co-clustering. Since Graclus is faster and more scalable, this result suggests that, for a large dataset, we can use Graclus to get the coclusters then perform the local SVD on those coclusters.

Table 7: Performance of local SVD on Graclus co-clustering result with different ways to fill in the missing values

Scheme	RMSE
1	0.9937
2	0.9860
3	0.9363
4	0.9512
5	0.9057
6	1.0648