Meta-features

Qmes describes each dataset with complexity measures computed by problexity, an open-source library implementing the data-complexity measures of Lorena et al. Qmes does not define its own measures - it uses problexity's outputs directly as the meta-feature vector passed to the recommender.

Each category below is summarized in one line to convey what it captures; problexity has the exact formula for every individual measure.

Classification

Category	Measures	What it captures
Feature-based	f1, f1v, f2, f3, f4	How informative individual features are for separating classes - via their range, spread, and overlap.
Linearity	l1, l2, l3	Whether the classes are linearly separable — the error and nonlinearity of linear classifiers fit to the data.
Neighborhood	n1, n2, n3, n4, t1, lsc	Presence and density of same- vs. different-class points in local neighborhoods - nearest-neighbor distances, boundary analysis, local set cardinality.
Network	density, cls_coef, hubs	Structure of the data seen as a graph - edge density, clustering tendency, hub connectivity among same-class instances.
Dimensionality	t2, t3, t4	Sparsity and intrinsic dimensionality (e.g. PCA-based).
Class imbalance	c1, c2	Degree of imbalance in the class distribution - entropy and class-proportion ratios.

Regression

Category	Measures	What it captures
Correlation	c1, c2, c3, c4	How strongly features relate to the target, and how much of the data such relationships explain - rank correlation and correlation-guided example elimination.
Linearity	l1, l2	How well a linear function fits - residual error of a multivariate linear regression.
Smoothness	s1, s2, s3	Whether nearby inputs have similar outputs - minimum-spanning-tree distances and nearest-neighbor prediction error.
Geometry	l3, s4, t2	Spatial structure - model sensitivity to interpolated points and the samples-to-features ratio.

See the problexity documentation for the precise definition of each measure.

Which features the default recommenders actually use

The extractors always produce the full 22-/12-dim vector, but the shipped default recommenders subset it internally (feature_indices), keeping only the measures ranked most informative by mutual information with the best-circuit label:

Task	Subset	Features used
Classification	top-5	n4, l3, f1v, l2, density
Regression	top-10	c1, c3, l1, l3, l2, c4, s4, c2, s2, s3

The subsetting is transparent to users - recommend() still expects (and validates) the full extractor output. See Validation for how these subsets were selected.

@article{komorniczak2023problexity,
title={problexity—An open-source Python library for supervised learning problem complexity assessment},
author={Komorniczak, Joanna and Ksieniewicz, Pawe{\l}},
journal={Neurocomputing},
volume={521},
pages={126--136},
year={2023},
publisher={Elsevier}
}

@article{lorena2018complex,
title={How complex is your classification problem},
author={Lorena, A and Garcia, L and Lehmann, Jens and Souto, M and Ho, T},
journal={A survey on measuring classification complexity. arXiv},
year={2018}
}