SMOGN Algorithm

SMOGN generates new examples for imbalanced regression problems. It identifies rare regions of the continuous outcome using a relevance function, over-samples those regions with a combination of SMOTE-style interpolation and the introduction of Gaussian noise, and under-samples the common regions.

Usage

smogn(
  df,
  var,
  threshold = 0.5,
  relevance = NULL,
  neighbors = 5,
  perturbation = 0.02,
  distance = "euclidean"
)

Arguments

df

data.frame or tibble. Must have 1 numeric outcome variable and remaining numeric variables.

var

Character, name of the numeric outcome variable.

threshold

A number between 0 and 1. Outcome values with a relevance at or above this value are treated as rare and over-sampled. Defaults to 0.5.

relevance

A matrix of relevance control points, or NULL (default). When NULL, relevance is derived automatically from the boxplot extremes of the outcome. When supplied, the first column gives outcome values and the second column their relevance in [0, 1].

neighbors

An integer. Number of nearest neighbor that are used to generate the new examples of the rare values.

perturbation

A number. The magnitude of the Gaussian noise added when generating synthetic examples in unsafe regions. Defaults to 0.02.

distance

A character string specifying the distance metric used for nearest neighbor calculations, defaulting to "euclidean". The available metrics fall into three groups.

"euclidean", "cosine", and "mahalanobis" use approximate nearest neighbors via the RANN package and scale well to large datasets.

"squared_chord", "matusita", "hellinger", and "bhattacharyya" are probability-divergence measures that treat each row as a distribution over the predictors, so they require non-negative values. "hellinger" and "bhattacharyya" further require each row to sum to 1. All four also use the RANN package and scale well to large datasets.

"manhattan", "chebyshev", "canberra", "soergel", "lorentzian", "jeffreys", "topsoe", "jensen-shannon", "jensen_difference", "taneja", and "kumar-johnson" compute an exact all-pairs distance matrix. This takes time and memory proportional to the square of the number of observations in a class, so these are best suited to smaller datasets. Everything from "canberra" onwards is a probability divergence requiring non-negative values, is provided by the philentropy package (which must be installed separately), and in the case of "jeffreys", "taneja", and "kumar-johnson" requires strictly positive values, since those divide by individual predictor values.

The probability divergences are meaningful for compositional predictors such as proportions or counts normalized per observation, and are generally not appropriate for standardized predictors.

Value

A data.frame or tibble, depending on type of df.

Details

SMOGN is a pre-processing approach for imbalanced regression. A relevance function assigns each outcome value a relevance score, and values with a relevance at or above threshold are treated as rare. The data is split into contiguous bins of rare and common outcome values. Common bins are under-sampled and rare bins are over-sampled toward a balanced size. New rare examples are generated either by interpolating between an example and a nearby neighbor (when they are close enough to be considered safe) or by perturbing the example with Gaussian noise (when they are not), where the amount of noise is controlled by perturbation.

By default relevance is derived automatically from the boxplot extremes of the outcome, giving the median a relevance of 0 and the extreme values a relevance of 1. A matrix of relevance control points can instead be supplied through relevance, with the first column giving outcome values and the second column their relevance.

All columns used in this function must be numeric with no missing data.

References

Branco, P., Torgo, L., and Ribeiro, R. P. (2017). SMOGN: a pre-processing approach for imbalanced regression. Proceedings of Machine Learning Research, 74:36-50.

See also

step_smogn() for step function of this method

Other Direct Implementations: adasyn(), bsmote(), cluster_centroids(), cnn(), enn(), instance_hardness(), kmeans_smote(), ncl(), nearmiss(), oss(), rose(), smote(), smoten(), smotenc(), svmsmote(), tomek()

Examples

circle_numeric <- circle_example[, c("x", "y")]

res <- smogn(circle_numeric, var = "x")

res <- smogn(circle_numeric, var = "x", neighbors = 10)