SVM-SMOTE Algorithm

SVM-SMOTE generates new examples of the minority class near the decision boundary, using the support vectors of a fitted SVM to decide where to place synthetic examples.

Usage

svmsmote(
  df,
  var,
  k = 5,
  over_ratio = 1,
  distance = "euclidean",
  m_neighbors = NULL,
  out_step = 0.5
)

Arguments

df

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

var

Character, name of variable containing factor variable.

k

An integer. Number of nearest neighbor that are used to generate the new examples of the minority class.

over_ratio

A numeric value for the ratio of the minority-to-majority frequencies. The default value (1) means that all other levels are sampled up to have the same frequency as the most occurring level. A value of 0.5 would mean that the minority levels will have (at most) (approximately) half as many rows as the majority level.

A named numeric vector can be used instead to give different levels different targets, for example c(a = 1, b = 0.5). The names must be levels of the outcome and the values are ratios of the majority level, exactly as in the single-number case. Levels that are not named are left untouched, as are rows with a missing outcome. Because a vector of targets is not a single value, supplying one means this argument can no longer be tuned. See vignette("ratio", package = "themis") for more details.

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.

m_neighbors

An integer or NULL. Number of nearest neighbors, among all classes, that are used to label each minority support vector as noise, danger, or safe. Defaults to NULL, which means 2 * k.

out_step

A number. Step size used when extrapolating new examples away from safe support vectors. Defaults to 0.5.

Value

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

Details

SVM-SMOTE (Support Vector Machine SMOTE) works the same way as SMOTE, except that instead of generating points around every point of the minority class, it focuses generation near the decision boundary. A support vector machine is fitted to the data and the support vectors that belong to the minority class are used as the base points for generating new examples.

For each minority support vector its nearest neighbors among all classes are calculated. If all of the neighbors come from a different class the support vector is labeled noise and is discarded. If more than half of the neighbors come from a different class the support vector is labeled "danger" and new points are interpolated between it and its minority-class neighbors. The remaining support vectors are considered to be in a safe region and new points are extrapolated away from their minority-class neighbors.

The number of neighbors used for this labeling is controlled by m_neighbors, and how far the extrapolated points are placed is controlled by out_step.

The support vector machine is always fitted with kernlab::ksvm() using a radial basis function kernel (kernel = "rbfdot") and a cost of C = 1, matching the reference implementations of the method. These are not exposed as arguments because the fitted model is only used to identify which minority observations are support vectors, and not for prediction, so the sampling results are relatively insensitive to them.

SMOTE generates new examples of the minority class using nearest neighbors of these cases. For each existing minority class example, new examples are created by interpolating between the example and its nearest neighbors. The number of nearest neighbors used is controlled by the number of neighbors argument (k in smote(), neighbors in step_smote()), and the number of new examples generated is controlled by over_ratio.

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

References

Nguyen, H. M., Cooper, E. W., and Kamei, K. (2011). Borderline over-sampling for imbalanced data classification. International Journal of Knowledge Engineering and Soft Data Paradigms, 3(1), 4-21.

See also

step_svmsmote() for step function of this method

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

Examples

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

res <- svmsmote(circle_numeric, var = "class")

res <- svmsmote(circle_numeric, var = "class", k = 10)

res <- svmsmote(circle_numeric, var = "class", over_ratio = 0.8)

res <- svmsmote(circle_numeric, var = "class", distance = "manhattan")

res <- svmsmote(circle_numeric, var = "class", m_neighbors = 20)