Table 1 MLE point estimates and confidence intervals computed on the Spiral dataset (\(d=1\)) with the TWO-NN and Gride estimators.

From: The generalized ratios intrinsic dimension estimator

\(d=1\)

TWO-NN

\(\texttt {Gride}(n_1,n_2)\)

 

\(c=1\)

\(c=0.20\)

\(c=0.01\)

\(c=0.001\)

(2, 4)

(100, 200)

(250, 500)

(750, 1500)

Lower Bound

2.910

2.811

2.682

0.692

2.953

2.688

1.557

0.996

Estimate

2.991

2.990

3.541

1.706

3.014

2.699

1.560

0.997

Upper Bound

3.075

3.182

4.681

4.368

3.074

2.710

1.562

0.998

Bias

1.991

1.990

2.541

0.706

2.014

1.699

0.560

-0.003

CI width

0.165

0.371

1.999

3.676

0.121

0.022

0.005

0.002

  1. Different levels of decimation c and different NN orders \((n_1,n_2)\) are presented across the columns. The last two rows report the bias in the estimates, \({\hat{d}}-d\), and the width of the CIs.
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