### Table 1: Statistics of Di erent Data Sets Data Dimensionality Column Id Minimum Maximum

"... In PAGE 7: ... 5.3 Results In Table1 , we have illustrated the statistics of the di er- ent data sets. For each data set, the column which was used to generate the distance function value is denoted by colum- nid.... In PAGE 7: ... This column was also removed from the data set, so that the distance func- tion was modelled using only the remaining features. The resulting dimensionality (after removal of this column) is indicated in Table1 . In the table we have also illustrated the maximum and minimum values of the target objective function once they were synthetically generated.... ..."

### Table 2: Rate of correct dimensionality estimation for high dimensional data

### Table 4 Rate of correct dimensionality estimation for high dimensional data

### Table 1. Data for the one-dimensional Surfpack example.

"... In PAGE 6: ...5.1 Example: One-Dimensional Data Table1 lists the data points used in this example which were obtained from a series of expensive computational fluid dynamics (CFD) simulations. Here, x is the independent parameter which corresponds to an input to the CFD simulation, and f is the dependent parameter which corresponds to a force coefficient value computed in the CFD simulation.... ..."

### Table 5. Data for the four-dimensional Surfpack example.

"... In PAGE 7: ... There are 42 samples in this four-dimensional parameter space, which were generated using a combination of statistical design of experiments methods and random sampling methods. Table5 provides a list of these data points. The objective of this study was to find the point (or region) in the four-dimensional parameter space where the response value was minimized.... ..."