Results by Pipeline
We break down the base results here by pipeline (instead of parcellation type) in two different ways: Intra and Inter pipeline (corresponding to the top and bottom of the figure below). If necessary first see the intro to results page for a guide on how the results in this project are interpreted.

The top part of the figure, IntraPipeline Comparison, shows mean rank for each pipeline as computed only relative to other parcellations evaluated with the same pipeline

The bottom part of the figure, InterPipeline Comparison, shows mean rank as calculated between each parcellationpipeline combination.

The regression line of best fit on the log10log10 data are plotted separately for each pipeline across both figures (shaded regions around the lines of fit represent the bootstrap estimated 95% CI). The OLS fit here was with robust regression.
IntraPipeline Comparison
When comparing in an intrapipeline fashion, we are essentially computing the ranks independently for each choice of ML Pipeline. We also estimate the powerlaw region separately for each.
 ElasticNet: 72000
 SVM: 204000
 LGBM: 73000
We can then model these results as log10(Mean_Rank) ~ log10(Size) * C(Pipeline)
where Pipeline
(the type of ML pipeline) is a fixed effect and can interact with Size (Fullscreen Plot Link).
Dep. Variable:  Mean_Rank  Rsquared:  0.882 

Model:  OLS  Adj. Rsquared:  0.881 
Method:  Least Squares  Fstatistic:  878.8 
Date:  Mon, 03 Jan 2022  Prob (Fstatistic):  2.48e270 
coef  std err  t  P>t  [0.025  0.975]  

Intercept  2.5893  0.019  135.246  0.000  2.552  2.627 
C(Pipeline)[T.LGBM]  0.0208  0.026  0.795  0.427  0.072  0.031 
C(Pipeline)[T.SVM]  0.3020  0.028  10.939  0.000  0.248  0.356 
Size  0.2606  0.009  30.318  0.000  0.278  0.244 
Size:C(Pipeline)[T.LGBM]  0.0162  0.012  1.405  0.160  0.006  0.039 
Size:C(Pipeline)[T.SVM]  0.1291  0.012  10.957  0.000  0.152  0.106 
The resulting statistical table is a little bit difficult to make sense of at first, so letâ€™s also plot the fit to the data to get a better feel.
These results indicate that there are differences between the pipelines (i.e., scaling coefficient, range of scaling and intercept), as well as confirm more generally that scaling, albeit with varying degree, holds regardless of pipeline.
Another interesting way to view how results change when computed separately between pipelines is through an interactive visualization. Click Here for a fullscreen version of the plot.