RM-SMOTE: Robust Mahalanobis SMOTE for Imbalanced Classification (ROBOSRMSMOTE Framework)

Description

Generates synthetic minority class observations using a robust version of SMOTE as part of the ROBOSRMSMOTE (Robust Oversampling with RM-SMOTE) framework. Atypical minority class observations (outliers) are down-weighted based on their robust Mahalanobis distance so that they have a lower probability of being selected as parents in the resampling step. The k-nearest neighbours of each candidate parent are also found using the robust Mahalanobis distance rather than the standard Euclidean distance.

Usage

ROBOS_RM_SMOTE(
  dt,
  target = "positive",
  dup_size = 0,
  eIR = 1,
  k = 5,
  threshold = 0.01,
  weight_func = 1,
  cov_method = "mcd"
)

Arguments

Details

The algorithm proceeds as follows (Algorithm 1 in Taban et al., 2025):

1. Extract minority class observations X_1.

2. Robustly estimate the mean vector \hat{\mu}_1 and covariance matrix \hat{\Sigma}_1 using the selected cov_method.

3. Compute the squared robust Mahalanobis distance for every minority observation.

4. Apply the selected weighting function to obtain a probability distribution \Pi_l over X_1.

5. Build the k-nearest neighbour graph over X_1 using the robust Mahalanobis distance.

6. Repeat until the desired number of synthetic observations is reached:

   1. Sample the first parent x_a according to \Pi_l.

   2. Choose the second parent x_b uniformly from the k neighbours of x_a.

   3. Generate x_{new} = v \cdot x_a + (1-v) \cdot x_b where v \sim \text{Uniform}(0,1).

Value

A data frame with the same columns as dt, containing the original observations plus the newly generated synthetic minority class observations. Row names are reset to NULL.

References

Dunder, E., Cengiz, M.A., Hawrami, Z.S.M. and Alharthi, A. (2025). Robust Covariance-Based Oversampling Strategies for Imbalanced Classification. Manuscript in preparation.

Taban, R., Nunes, C. and Oliveira, M.R. (2025). RM-SMOTE: a new robust balancing technique. Statistical Methods & Applications. doi:10.1007/s10260-025-00819-8

Chawla, N.V., Bowyer, K.W., Hall, L.O. and Kegelmeyer, W.P. (2002). SMOTE: Synthetic Minority Over-sampling Technique. Journal of Artificial Intelligence Research, 16, 321-357.

See Also

get_robust_cov, weighting

Examples

# Load the package example dataset
data(haberman)

# Basic usage: balance with MCD (default) and hard exclusion
balanced <- ROBOS_RM_SMOTE(dt = haberman, target = "positive", eIR = 1)
table(balanced$class)

# Use MVE estimator and soft weighting (omega_B)
balanced_mve <- ROBOS_RM_SMOTE(dt = haberman, target = "positive",
                          eIR = 1, cov_method = "mve", weight_func = 2)
table(balanced_mve$class)

# Control exact number of synthetic samples with dup_size
balanced_dup <- ROBOS_RM_SMOTE(dt = haberman, target = "positive",
                          dup_size = 2, cov_method = "ogk")
table(balanced_dup$class)

Get Robust Center and Covariance Matrix

Description

Computes a robust estimate of the center (location) and covariance matrix for a given dataset using one of seven supported robust estimators.

Usage

get_robust_cov(data, method = "mcd")

Arguments

Details

The following estimators are available via the rrcov package:

mcd

Minimum Covariance Determinant (Rousseeuw & Driessen, 1999). The default and most widely used robust estimator. Suitable for most cases.

mve

Minimum Volume Ellipsoid (Rousseeuw & Van Zomeren, 1990). An alternative to MCD, generally slower.

mest

M-estimator of location and scatter. Iteratively re-weighted least squares approach.

mmest

MM-estimator. Combines high breakdown point with high efficiency.

sde

Stahel-Donoho Estimator. Projection-based robust estimator, useful for high-dimensional data.

sest

S-estimator. High breakdown point estimator based on minimizing a robust scale.

ogk

Orthogonalized Gnanadesikan-Kettenring estimator. Fast and stable for moderate dimensions.

Value

A list with two elements:

center

A numeric vector of length ncol(data) representing the robust location estimate.

cov

A numeric matrix of size ncol(data) x ncol(data) representing the robust covariance matrix estimate.

References

Rousseeuw, P.J. and Driessen, K.V. (1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41(3), 212-223.

Todorov, V. and Filzmoser, P. (2009). An object-oriented framework for robust multivariate analysis. Journal of Statistical Software, 32(3), 1-47.

Examples

# Generate a simple numeric dataset
set.seed(42)
X <- matrix(rnorm(100 * 3), nrow = 100, ncol = 3)

# MCD estimator (default)
result_mcd <- get_robust_cov(X, method = "mcd")
result_mcd$center
result_mcd$cov

# OGK estimator
result_ogk <- get_robust_cov(X, method = "ogk")
result_ogk$center

Haberman Survival Imbalanced Dataset

Description

Binary imbalanced dataset from Haberman survival study (1958-1970). Minority class represents patients who did not survive 5+ years after breast cancer surgery.

Usage

haberman

Format

A data frame with 306 rows and 4 columns:

age

Age of patient at operation (numeric).

year

Year of operation, 1958-1969 (numeric).

nodes

Number of positive axillary nodes detected (numeric).

class

"negative" = survived 5+ years (n=225); "positive" = did not survive (n=81). IR = 2.78.

Source

KEEL Repository https://sci2s.ugr.es/keel/. Used as benchmark dataset in Hawrami et al. (2025).

Examples

data(haberman)
table(haberman$class)
balanced <- ROBOS_RM_SMOTE(dt = haberman, target = "positive", eIR = 1)
table(balanced$class)

Compute Robust Mahalanobis Weights for Minority Class Observations

Description

For each minority class observation, computes the robust Mahalanobis distance (MD) to the class center and assigns a weight based on the chosen weighting function. Observations flagged as outliers (MD exceeds the chi-square threshold) receive reduced or zero weight, lowering their probability of being selected as parents in the SMOTE resampling step.

Usage

weighting(data, threshold = 0.01, weight_func = 1, cov_method = "mcd")

Arguments

Value

The input data frame with three additional columns appended:

MD

Squared robust Mahalanobis distance for each observation.

weights

Raw weight assigned to each observation (1 for non-outliers, reduced for outliers).

prob

Normalised selection probability derived from weights. Sums to 1 across all rows.

References

Taban, R., Nunes, C. and Oliveira, M.R. (2025). RM-SMOTE: a new robust balancing technique. Statistical Methods & Applications. doi:10.1007/s10260-025-00819-8

See Also

get_robust_cov, ROBOS_RM_SMOTE

Examples

# Create a small imbalanced dataset
set.seed(42)
minority <- data.frame(
  x1    = c(rnorm(18), 10, 12),   # last two are outliers
  x2    = c(rnorm(18),  9, 11),
  class = "positive"
)

# Weight with hard exclusion (omega_A)
result <- weighting(minority, threshold = 0.01, weight_func = 1)
table(result$weights)   # outliers get weight 0

# Weight with soft inverse (omega_B)
result2 <- weighting(minority, threshold = 0.01, weight_func = 2)
round(result2$prob, 4)