### Table 3. Perturbation/Reconstruction Method

"... In PAGE 7: ...ll experiments are performed on an Intel P4 2.0GHz CPU. 6.2 Dynamic Correlation The perturbation and reconstruction methods investi- gated in our experiments are summarized in Table3 , where N stands for noise and R for reconstruction. The of- fline algorithms, for both perturbation and reconstruction, are essentially the existing work on the static, relational data model, using PCA on the entire stream history to iden- tify correlations and add or remove noise accordingly.... ..."

### Table 1: Reconstruction when the perturbation to the linear field is of moderate size. The polynomial coefficients in (32) have variance of 0.1. Note the improvements in the reconstructions when the number of measurements is increased.

"... In PAGE 17: ... The average number of iterations needed to converge is just under 40. Table1 summarizes the results when the coefficients have variance of 0.1.... In PAGE 18: ...2. In comparing with Table1 , note that the reconstructions of the coefficients are markedly better here. Again, we see improvements in the reconstructions when the number of measurements is increased.... ..."

### Table 7: Prediction performance and reconstruction performance in Jester if all entries are used in the perturbation scheme.

"... In PAGE 9: ... As was noted in Figure 5, the k-means based method obtains a smaller reconstruction error when the random noise variance is small while the SVD-based reconstruction method per- forms better when the noise variance is larger. Finally, Table7 lists the results obtained in Jester when all entries are used in the perturbation scheme. We observe that when a Gaussian distribution is used to generate noise, only a small percentage of the rated entries can be recalled (e.... ..."

### Table 7: Prediction performance and reconstruction performance in Jester if all entries are used in the perturbation scheme.

"... In PAGE 9: ... As was noted in Figure 5, the k-means based method obtains a smaller reconstruction error when the random noise variance is small while the SVD-based reconstruction method per- forms better when the noise variance is larger. Finally, Table7 lists the results obtained in Jester when all entries are used in the perturbation scheme. We observe that when a Gaussian distribution is used to generate noise, only a small percentage of the rated entries can be recalled (e.... ..."

### Table 6: Prediction performance and reconstruction performance in Jester if only rated entries are used in the perturbation scheme.

### Table 2: Prediction performance and reconstruction performance in MovieLens if only rated entries are used in the perturbation scheme.

"... In PAGE 7: ... The number of dimensions is set to 10 in the SVD-based algorithm. Table2 lists the results obtained from MovieLens for di erent values of R or R. When R; R = 0, no random noise is actually added to the original z-scores.... ..."

### Table 2: Prediction performance and reconstruction performance in MovieLens if only rated entries are used in the perturbation scheme.

"... In PAGE 7: ... The number of dimensions is set to 10 in the SVD-based algorithm. Table2 lists the results obtained from MovieLens for di erent values of R or R. When R; R = 0, no random noise is actually added to the original z-scores.... ..."

### Table 2: Reconstruction when the perturbation to the linear field is of large size. The polynomial coefficients in (32) have variance of 0.2. In comparing with Table 1, note that the reconstructions of the coefficients are markedly better here. Again, we see improvements in the reconstructions when the number of measurements is increased.

"... In PAGE 17: ...he polynomial coefficients in (32) have variance of 0.1. Note the improvements in the reconstructions when the number of measurements is increased. The second table, Table2 , summarizes the results of the reconstruction for the case where the coefficients have variance 0.2.... ..."

### Table 4: Prediction performance and reconstruction performance in MovieLens if all entries are used in the

"... In PAGE 7: ... larger variance, the SVD-based method has a smaller reconstruction error. Table4 displays prediction and reconstruction er- rors when all entries are used in the perturbation scheme for MovieLens. The baseline prediction performance (when z-scores are not perturbed) of the SVD-based al- gorithm in this case is much worse than the baseline prediction performance in the version where only rated entries are used.... ..."