Table 2. Dimension estimates on synthetic benchmark datasets.
The table shows true dimension values (d), median-Farahmand-Szepesvári-Audibert (mFSA), corrected median Farahmand-Szepesvári-Audibert (cmFSA), DANCo, Maximum Likelihood (Levina) and 2NN mean estimates from N = 100 realizations. cmFSA and DANCo was applied in integer and in fractal modes. The mean percentage error (MPE) values can be seen in the bottom line, the Matlab version of DANCo estimator (DANCo M) produced the smallest error followed by the cmFSA estimator.
| Dataset | d | mFSA | cmFSA frac | cmFSA | DANCo R | DANCo M frac | DANCo M | Levina | 2NN |
|---|---|---|---|---|---|---|---|---|---|
| M 1 | 10 | 9.09 | 11.19 | 11.08 | 11.34 | 10.42 | 10.30 | 10.15 | 9.40 |
| M 2 | 3 | 2.87 | 3.02 | 3.00 | 3.00 | 2.90 | 3.00 | 3.20 | 2.93 |
| M 3 | 4 | 3.83 | 4.14 | 4.00 | 5.00 | 3.84 | 4.00 | 4.29 | 3.87 |
| M 4 | 4 | 3.95 | 4.29 | 4.00 | 5.00 | 3.92 | 4.00 | 4.38 | 3.91 |
| M 5 | 2 | 1.97 | 2.00 | 2.00 | 2.00 | 1.98 | 2.00 | 2.19 | 1.99 |
| M 6 | 6 | 6.38 | 7.38 | 7.16 | 9.00 | 6.72 | 7.00 | 7.04 | 5.93 |
| M 7 | 2 | 1.95 | 1.98 | 2.00 | 2.00 | 1.96 | 2.00 | 2.18 | 1.98 |
| M 9 | 20 | 14.58 | 20.07 | 20.10 | 19.16 | 19.24 | 19.09 | 16.38 | 15.55 |
| M 10a | 10 | 8.21 | 9.90 | 10.00 | 10.00 | 9.56 | 9.78 | 9.20 | 8.63 |
| M 10b | 17 | 12.76 | 16.95 | 16.96 | 16.04 | 16.39 | 16.24 | 14.33 | 13.58 |
| M 10c | 24 | 16.80 | 24.10 | 24.06 | 23.61 | 23.39 | 23.26 | 18.89 | 18.04 |
| M 10d | 70 | 35.64 | 69.84 | 69.84 | 69.73 | 71.00 | 70.91 | 40.35 | 40.05 |
| M 11 | 2 | 1.97 | 2.00 | 2.00 | 2.00 | 1.97 | 2.00 | 2.19 | 1.98 |
| M 12 | 20 | 15.64 | 21.96 | 21.98 | 21.72 | 20.88 | 20.00 | 17.72 | 17.24 |
| M 13 | 1 | 1.00 | 0.96 | 1.00 | 1.00 | 1.00 | 1.00 | 1.11 | 1.00 |
| MPE | 13.58 | 4.73 | 2.89 | 9.64 | 3.39 | 2.35 | 13.23 | 10.91 |