STree

Oblique Tree classifier based on SVM nodes. The nodes are built and splitted with sklearn SVC models. Stree is a sklearn estimator and can be integrated in pipelines, grid searches, etc.

Installation

bash pip install Stree

Documentation

Can be found in stree.readthedocs.io

Examples

Jupyter notebooks

• Benchmark

• Some features

• Gridsearch

• Ensembles

Hyperparameters

| | Hyperparameter | Type/Values | Default | Meaning | | --- | ------------------- | -------------------------------------------------------------- | ----------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | * | C | <float> | 1.0 | Regularization parameter. The strength of the regularization is inversely proportional to C. Must be strictly positive. | | * | kernel | {"liblinear", "linear", "poly", "rbf", "sigmoid"} | linear | Specifies the kernel type to be used in the algorithm. It must be one of ‘liblinear’, ‘linear’, ‘poly’ or ‘rbf’. liblinear uses liblinear library and the rest uses libsvm library through scikit-learn library | | * | maxiter | <int> | 1e5 | Hard limit on iterations within solver, or -1 for no limit. | | * | randomstate | <int> | None | Controls the pseudo random number generation for shuffling the data for probability estimates. Ignored when probability is False.
Pass an int for reproducible output across multiple function calls | | | maxdepth | <int> | None | Specifies the maximum depth of the tree | | * | tol | <float> | 1e-4 | Tolerance for stopping criterion. | | * | degree | <int> | 3 | Degree of the polynomial kernel function (‘poly’). Ignored by all other kernels. | | * | gamma | {"scale", "auto"} or <float> | scale | Kernel coefficient for ‘rbf’, ‘poly’ and ‘sigmoid’.
if gamma='scale' (default) is passed then it uses 1 / (nfeatures * X.var()) as value of gamma,
if ‘auto’, uses 1 / nfeatures. | | | splitcriteria | {"impurity", "maxsamples"} | impurity | Decides (just in case of a multi class classification) which column (class) use to split the dataset in a node**. maxsamples is incompatible with 'ovo' multiclassstrategy | | | criterion | {“gini”, “entropy”} | entropy | The function to measure the quality of a split (only used if maxfeatures != numfeatures).
Supported criteria are “gini” for the Gini impurity and “entropy” for the information gain. | | | minsamplessplit | <int> | 0 | The minimum number of samples required to split an internal node. 0 (default) for any | | | maxfeatures | <int>, <float>

or {“auto”, “sqrt”, “log2”} | None | The number of features to consider when looking for the split:
If int, then consider maxfeatures features at each split.
If float, then maxfeatures is a fraction and int(maxfeatures * nfeatures) features are considered at each split.
If “auto”, then maxfeatures=sqrt(nfeatures).
If “sqrt”, then maxfeatures=sqrt(nfeatures).
If “log2”, then maxfeatures=log2(nfeatures).
If None, then maxfeatures=nfeatures. | | | splitter | {"best", "random", "trandom", "mutual", "cfs", "fcbf", "iwss"} | "random" | The strategy used to choose the feature set at each node (only used if maxfeatures < numfeatures). Supported strategies are: “best”: sklearn SelectKBest algorithm is used in every node to choose the maxfeatures best features. “random”: The algorithm generates 5 candidates and choose the best (max. info. gain) of them. “trandom”: The algorithm generates only one random combination. "mutual": Chooses the best features w.r.t. their mutual info with the label. "cfs": Apply Correlation-based Feature Selection. "fcbf": Apply Fast Correlation-Based Filter. "iwss": IWSS based algorithm | | | normalize | <bool> | False | If standardization of features should be applied on each node with the samples that reach it | | * | multiclassstrategy | {"ovo", "ovr"} | "ovo" | Strategy to use with multiclass datasets, "ovo": one versus one. "ovr": one versus rest |

* Hyperparameter used by the support vector classifier of every node

** Splitting in a STree node

The decision function is applied to the dataset and distances from samples to hyperplanes are computed in a matrix. This matrix has as many columns as classes the samples belongs to (if more than two, i.e. multiclass classification) or 1 column if it's a binary class dataset. In binary classification only one hyperplane is computed and therefore only one column is needed to store the distances of the samples to it. If three or more classes are present in the dataset we need as many hyperplanes as classes are there, and therefore one column per hyperplane is needed.

In case of multiclass classification we have to decide which column take into account to make the split, that depends on hyperparameter splitcriteria_, if "impurity" is chosen then STree computes information gain of every split candidate using each column and chooses the one that maximize the information gain, otherwise STree choses the column with more samples with a predicted class (the column with more positive numbers in it).

Once we have the column to take into account for the split, the algorithm splits samples with positive distances to hyperplane from the rest.

Tests

bash python -m unittest -v stree.tests

License

STree is MIT licensed

Reference

R. Montañana, J. A. Gámez, J. M. Puerta, "STree: a single multi-class oblique decision tree based on support vector machines.", 2021 LNAI 12882, pg. 54-64