Skip to main content Link Search Menu Expand Document (external link) Copy Copied
Supplementary materials

List of considered metafeatures

The description is based on the docummentation of pymfe and problexity libraries.

Clustering

Metafeature name/abbreviation Description
CH Calinski-Harabasz Index — The ratio of the sum of between-clusters dispersion and of within-cluster dispersion for all clusters, where dispersion is defined as the sum of distances squared.
INT INT index - Sum of pairwise normalized interclass distances, normalized according to the number of clusters.
NRE Normalized relative entropy — an indicator of uniformity distributed of instances among clusters.
PB Pearson correlation between class matching and instance distances.
SC Number of clusters with size smaller than a given size(default=15).
SIL Mean Silhouette value — The Silhouette Coefficient is calculated using the mean intra-cluster distance and the mean nearest-cluster distance for each sample.
VDB Davies-Bouldin Index — The score is defined as the average similarity measure of each cluster with its most similar cluster, where similarity is the ratio of within-cluster distances to between-cluster distances.
VDU Dunn Index — The lowest intercluster distance divided by the highest intracluster distance.

Complexity

Metafeature name / name abbreviation Description
C1 Entropy of Class Proportions.
C2 Imbalance Ratio
Cls_coef Generates an epsilon-Nearest Neighbours graph. The edges are selected based on the Gower distance between samples, normalized to the range between 0 and 1. Edges between instances of distinct classes are removed. The neighborhood of each vertex is calculated – the instances directly connected to it. Then, the number of edges between the sample’s neighbors is calculated and divided by the maximum possible number of edges between them. The final measure is calculated based on the neighborhood of each point.
Density Generates an epsilon-Nearest Neighbours graph as decribed in Cls_coef. The measure calculates the number of edges in the final graph divided by the total possible number of edges.
F1 Maximum Fisher’s discriminant ratio.
F1v Directional vector maximum Fisher’s discriminant ratio.
F2 Volume of overlapping region.
F3 Maximum individual feature efficiency.
F4 Collective feature efficiency.
Hubs Generates an epsilon-Nearest Neighbours graph as decribed in Cls_coef. The measure scores each sample by the number of connections to neighbors, weighted by the number of connections the neighbors have.
L1 Sum of the error distance by linear programming.
L2 Error rate of linear classifier.
L3 Non linearity of linear classifier.
LSC Local set average cardinality.
N1 Fraction of borderline points.
N2 Ratio of intra/extra class NN distance.
N3 Error rate of NN classifier.
N4 Nonlinearity of NN classifier.
T1 Fraction of hyperspheres covering data.
T2 Number of features per dimension.
T3 Number of PCA dimensions per points.
T4 Ration of the PCA dimension to the original dimension.

Concept

Metafeature name / name abbreviation Description
Cohesiveness Improved version of the weighted distance, that captures how dense or sparse is the distribution.
Conceptvar Concept variation that estimates the variability of class labels among data samples.
Impconceptvar Improved concept variation that estimates the variability of class labels.
wg_dist Weighted distance, that captures how dense or sparse is the distribution.

General

Metafeature name / name abbreviation Description
attr_to_inst The ratio between the number of attributes and instances.
cat_to_num Proportion of categorical and numerical attributes.
freq_class Relative frequency of each distinct class.
inst_to_attr Ratio of number of instances and number of predictive attributes.
nr_attr Total number of attributes in the data without transformations.
nr_bin Number of binary attributes.
nr_cat Number of categorical attributes.
nr_class Number of distinct classes.
nr_inst Number of instances.
nr_num Number of numerical attributes.
num_to_cat Ratio of numerical and categorical features.

Information theory

Metafeature name / name abbreviation Description
attr_conc Concentration coefficient for each pair of distinct predictive attribute.
attr_ent Shannon’s Entropy of each predictive attribute.
class_conc Concentration coefficient between each attribute and class.
class_ent Target attribute Shannon’s entropy.
eq_num_attr Number of attributes equivalent for a predictive task.
joint_ent Estimated joint entropy between each predictive attribute and the target attribute.
mut_inf Mutual information between each attribute and target.
ns_ratio Estimated noisiness of the predictive attributes.

Itemset

Metafeature name / name abbreviation Description
one_itemset The one itemset is the individual frequency of each attribute in binary format.
two_itemset The two-item set meta-feature can be seen as the correlation information of each one attributes value pairs in binary format.

Landmarking

Metafeature name / name abbreviation Description
best_node Performance of a the best single decision tree node. Construct a single decision tree node model induced by the most informative attribute to establish the linear separability.
elite_nn Performance of Elite Nearest Neighbor. Elite nearest neighbor uses the most informative attribute in the dataset to induce the 1-nearest neighbor. With the subset of informative attributes it is expected that the models should be noise tolerant.
linear_discr Performance of the Linear Discriminant classifier. The Linear Discriminant Classifier is used to construct a linear split (non parallel axis) in the data to establish the linear separability.
naive_bayes Performance of the Naive Bayes classifier. It assumes that the attributes are independent and each example belongs to a certain class based on the Bayes probability.
one_nn Performance of the 1-Nearest Neighbor classifier. It uses the euclidean distance of the nearest neighbor to determine how noisy is the data.
random_node Performance of the single decision tree node model induced by a random attribute.
worst_node Performance of the single decision tree node model induced by the worst informative attribute.

Model-based

Metafeature name / name abbreviation Description
leaves Number of leaf nodes in the DT model.
leaves_branch Size of branches in the DT model. The size of branches consists in the depth of all leaves of the DT model.
leaves_corrob Leaves corroboration of the DT model. The Leaves corroboration is the proportion of examples that belong to each leaf of the DT model.
leaves_homo DT model Homogeneity for every leaf node. The DT model homogeneity is calculated by the number of leaves divided by the structural shape (which is calculated by the ft_tree_shape method) of the DT model.
leaves_per_class Proportion of leaves per class in DT model. This quantity is computed by the proportion of leaves of the DT model associated with each class.
nodes Number of non-leaf nodes in DT model.
nodes_per_attr Ratio of nodes per number of attributes in DT model.
nodes_per_inst Ratio of non-leaf nodes per number of instances in DT model.
nodes_per_level Ratio of number of nodes per tree level in DT model.
nodes_repeated Number of repeated nodes in DT model. The number of repeated nodes is the number of repeated attributes that appear in the DT model.
tree_depth Depth of every node in the DT model.
tree_imbalance Tree imbalance for each leaf node.
tree_shape Tree shape for every leaf node. The tree shape is the probability of arrive in each leaf given a random walk. We call this as the structural shape of the DT model.
var_importance Features importance of the DT model for each attribute. It is calculated using the Gini index to estimate the amount of information used in the DT model.

Statistical

Metafeature name / name abbreviation Description
can_cor Canonical correlations of data.
cor Correlation of distinct dataset column pairs.
cov Absolute value of the covariance of distinct dataset attribute pairs.
eigenvalues Eigenvalues of covariance matrix from dataset.
g_mean Geometric mean of each attribute.
gravity Distance between minority and majority classes center of mass.
h_mean Harmonic mean of each attribute.
iq_range Interquartile range (IQR) of each attribute.
kurtosis Kurtosis of each attribute.
lh_trace Lawley-Hotelling trace.
mad Median Absolute Deviation (MAD) adjusted by a factor.
max Maximum value from each attribute.
mean Mean value from each attribute.
median Median value from each attribute.
min Minimum value from each attribute.
nr_cor_attr Number of distinct highly correlated pair of attributes.
nr_disc Number of canonical correlation between each attribute and class.
nr_norm Number of attributes normally distributed based in a given method.
nr_outliers Number of attributes with at least one outlier value.
p_trace Pillai’s trace.
range Range (max - min) of each attribute.
roy_root Roy’s largest root.
sd Standard deviation of each attribute.
sd_ratio Statistical test for homogeneity of covariances.
skewness Skewness for each attribute.
sparsity Sparsity metric for each attribute.
t_mean Trimmed mean of each attribute.
var Variance of each attribute.
w_lambda Wilks’ Lambda value.

Table of contents